Jan 2012

UK: Managing Editor International Journal of Innovative Technology and Creative Engineering 1a park lane, Cranford London TW59WA UK E-Mail: [email protected] Phone: +44-773-043-0249

USA: Editor International Journal of Innovative Technology and Creative Engineering Dr. Arumugam Department of Chemistry University of Georgia GA-30602, USA. Phone: 001-706-206-0812 Fax:001-706-542-2626

India: Editor International Journal of Innovative Technology & Creative Engineering Dr. Arthanariee. A. M Finance Tracking Center India 17/14 Ganapathy Nagar 2nd Street Ekkattuthangal Chennai -600032. Mobile: 91-7598208700

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY & CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.1 JANUARY 2012

IJITCE PUBLICATION

INTERNATIONAL JOURNAL OF INNOVATIVE

TECHNOLOGY & CREATIVE ENGINEERING

Vol.2 No.1

January 2012

www.ijitce.co.uk


From Editor's Desk

Dear Researcher, Greetings! The researchers in this issue reflect a range of perspectives on near and Far-field radiation, Peristaltic transport, minimizing the total cost of Lining and review of composite adsorbents. Let us review this month research activities around the world, Microsoft is granted a patent for a GPS that will help pedestrians avoid high-crime areas and high-heat areas. Pedestrians have sometimes felt neglected when it comes to GPS directions. Now Microsoft is designed to make its maps more pedestrian-friendly According to Moore’s Law the computing power of computers doubles approximately every 18 months. Meanwhile, this is how the fastest computers work in the petaflops range. According to this, more than one quadrillion (1015 ) additions or multiplications can be carried out per second. The goal for the next years: The efficient utilization of the then 1000 times faster exaflop computers. The German Research Foundation (DFG) regards the redesign of software development in high performance computing as one of the main future challenges. Thus the DFG is first starting the priority program “Software for Exascale Computing (SPPEXA)” from the strategy fund. TUM informatics professor Hans-Joachim Bungartz from the Chair of Scientific Computing promoted the project and is presently one of the coordinators. SPPEXA is based on a 6 year time frame with a budget amount of 24 million euros. It seems to be open problem that melding multiple e-mail and social network accounts into one interface makes a lot of sense. Why can't anyone make a business out of it? If a new service comes along that tries to succeed where Threadsy failed, Most of the companies that have tried to do it may have given up hope, but still we have one open unsolved problem. A new perspective on the nanoworld: free-electron laser elicits extremely short and brilliant X-ray pulses from neon gas. In future, scientists should be able to observe more closely how plants generate sugar from the energy in sunlight or how electricity is generated from solar cells. Researchers at the Center for Free-Electron Laser Science (CFEL) in Hamburg have built the first-ever atomic X-ray laser at the Californian research centre, SLAC It has been an absolute pleasure to present you articles that you wish to read. We look forward to many more new technology-related research articles from you and your friends. We are anxiously awaiting the rich and thorough research papers that have been prepared by our authors for the next issue. Thanks, Editorial Team IJITCE


Editorial Members Dr. Chee Kyun Ng Ph.D Department of Computer and Communication Systems, Faculty of Engineering, Universiti Putra Malaysia,UPM Serdang, 43400 Selangor,Malaysia. Dr. Simon SEE Ph.D Chief Technologist and Technical Director at Oracle Corporation, Associate Professor (Adjunct) at Nanyang Technological University Professor (Adjunct) at Shangai Jiaotong University, 27 West Coast Rise #08-12,Singapore 127470 Dr. sc.agr. Horst Juergen SCHWARTZ Ph.D, Humboldt-University of Berlin, Faculty of Agriculture and Horticulture, Asternplatz 2a, D-12203 Berlin, Germany Dr. Marco L. Bianchini Ph.D Italian National Research Council; IBAF-CNR, Via Salaria km 29.300, 00015 Monterotondo Scalo (RM), Italy Dr. Nijad Kabbara Ph.D Marine Research Centre / Remote Sensing Centre/ National Council for Scientific Research, P. O. Box: 189 Jounieh, Lebanon Dr. Aaron Solomon Ph.D Department of Computer Science, National Chi Nan University, No. 303, University Road, Puli Town, Nantou County 54561, Taiwan Dr. Arthanariee. A. M M.Sc.,M.Phil.,M.S.,Ph.D Director - Bharathidasan School of Computer Applications, Ellispettai, Erode, Tamil Nadu,India Dr. Takaharu KAMEOKA, Ph.D Professor, Laboratory of Food, Environmental & Cultural Informatics Division of Sustainable Resource Sciences, Graduate School of Bioresources, Mie University, 1577 Kurimamachiya-cho, Tsu, Mie, 514-8507, Japan Mr. M. Sivakumar M.C.A.,ITIL.,PRINCE2.,ISTQB.,OCP.,ICP Project Manager - Software, Applied Materials, 1a park lane, cranford, UK Dr. Bulent Acma Ph.D Anadolu University, Department of Economics, Unit of Southeastern Anatolia Project(GAP), 26470 Eskisehir, TURKEY Dr. Selvanathan Arumugam Ph.D Research Scientist, Department of Chemistry, University of Georgia, GA-30602, USA.

Review Board Members

Dr. T. Christopher, Ph.D., Assistant Professor & Head,Department of Computer Science,Government Arts College(Autonomous),Udumalpet, India. Dr. T. DEVI Ph.D. Engg. (Warwick, UK), Head,Department of Computer Applications,Bharathiar University,Coimbatore-641 046, India. Dr. Giuseppe Baldacchini ENEA - Frascati Research Center, Via Enrico Fermi 45 - P.O. Box 65,00044 Frascati, Roma, ITALY. Dr. Renato J. orsato Professor at FGV-EAESP,Getulio Vargas Foundation,São Paulo Business School,Rua Itapeva, 474 (8° andar) ,01332-000, São Paulo (SP), Brazil Visiting Scholar at INSEAD,INSEAD Social Innovation Centre,Boulevard de Constance,77305 Fontainebleau - France Y. Benal Yurtlu Assist. Prof. Ondokuz Mayis University Dr. Paul Koltun Senior Research ScientistLCA and Industrial Ecology Group,Metallic & Ceramic Materials,CSIRO Process Science & Engineering Private Bag 33, Clayton South MDC 3169,Gate 5 Normanby Rd., Clayton Vic. 3168


Dr.Sumeer Gul Assistant Professor,Department of Library and Information Science,University of Kashmir,India Chutima Boonthum-Denecke, Ph.D Department of Computer Science,Science & Technology Bldg., Rm 120,Hampton University,Hampton, VA 23688 Dr. Renato J. Orsato Professor at FGV-EAESP,Getulio Vargas Foundation,São Paulo Business SchoolRua Itapeva, 474 (8° andar), 01332-000, São Paulo (SP), Brazil Lucy M. Brown, Ph.D. Texas State University,601 University Drive,School of Journalism and Mass Communication,OM330B,San Marcos, TX 78666 Javad Robati Crop Production Departement,University of Maragheh,Golshahr,Maragheh,Iran Vinesh Sukumar (PhD, MBA) Product Engineering Segment Manager, Imaging Products, Aptina Imaging Inc. doc. Ing. Rostislav Choteborský, Ph.D. Katedra materiálu a strojírenské technologie Technická fakulta,Ceská zemedelská univerzita v Praze,Kamýcká 129, Praha 6, 165 21 Dr. Binod Kumar M.sc,M.C.A.,M.Phil.,ph.d, HOD & Associate Professor, Lakshmi Narayan College of Tech.(LNCT), Kolua, Bhopal (MP) , India. Dr. Paul Koltun Senior Research ScientistLCA and Industrial Ecology Group,Metallic & Ceramic Materials,CSIRO Process Science & Engineering Private Bag 33, Clayton South MDC 3169,Gate 5 Normanby Rd., Clayton Vic. 3168 DR.Chutima Boonthum-Denecke, Ph.D Department of Computer Science,Science & Technology Bldg.,Hampton University,Hampton, VA 23688 Mr. Abhishek Taneja B.sc(Electronics),M.B.E,M.C.A., M.Phil., Assistant Professor in the Department of Computer Science & Applications, at Dronacharya Institute of Management and Technology, Kurukshetra. (India). doc. Ing. Rostislav Chot ěborský,ph.d, Katedra materiálu a strojírenské technologie, Technická fakulta,Česká zemědělská univerzita v Praze,Kamýcká 129, Praha 6, 165 21 Dr. Amala VijayaSelvi Rajan, B.sc,Ph.d, Faculty – Information Technology Dubai Women’s College – Higher Colleges of Technology,P.O. Box – 16062, Dubai, UAE Naik Nitin Ashokrao B.sc,M.Sc Lecturer in Yeshwant Mahavidyalaya Nanded University Dr.A.Kathirvell, B.E, M.E, Ph.D,MISTE, MIACSIT, MEN GG Professor - Department of Computer Science and Engineering,Tagore Engineering College, Chennai Dr. H. S. Fadewar B.sc,M.sc,M.Phil.,ph.d,PGDBM,B.Ed . Associate Professor - Sinhgad Institute of Management & Computer Application, Mumbai-Banglore Westernly Express Way Narhe, Pune - 41 Dr. David Batten Leader, Algal Pre-Feasibility Study,Transport Technologies and Sustainable Fuels,CSIRO Energy Transformed Flagship Private Bag 1,Aspendale, Vic. 3195,AUSTRALIA Dr R C Panda (MTech & PhD(IITM);Ex-Faculty (Curtin Univ Tech, Perth, Australia))Scientist CLRI (CSIR), Adyar, Chennai - 600 020,India Miss Jing He PH.D. Candidate of Georgia State University,1450 Willow Lake Dr. NE,Atlanta, GA, 30329 Dr. Wael M. G. Ibrahim Department Head-Electronics Engineering Technology Dept.School of Engineering Technology ECPI College of Technology 5501 Greenwich Road - Suite 100,Virginia Beach, VA 23462 Dr. Messaoud Jake Bahoura Associate Professor-Engineering Department and Center for Materials Research Norfolk State University,700 Park avenue,Norfolk, VA 23504 Dr. V. P. Eswaramurthy M.C.A., M.Phil., Ph.D., Assistant Professor of Computer Science, Government Arts College(Autonomous), Salem-636 007, India.


Dr. P. Kamakkannan,M.C.A., Ph.D ., Assistant Professor of Computer Science, Government Arts College(Autonomous), Salem-636 007, India. Dr. V. Karthikeyani Ph.D., Assistant Professor of Computer Science, Government Arts College(Autonomous), Salem-636 008, India. Dr. K. Thangadurai Ph.D., Assistant Professor, Department of Computer Science, Government Arts College ( Autonomous ), Karur - 639 005,India. Dr. N. Maheswari Ph.D., Assistant Professor, Department of MCA, Faculty of Engineering and Technology, SRM University, Kattangulathur, Kanchipiram Dt - 603 203, India. Mr. Md. Musfique Anwar B.Sc(Engg.) Lecturer, Computer Science & Engineering Department, Jahangirnagar University, Savar, Dhaka, Bangladesh. Mrs. Smitha Ramachandran M.Sc(CS)., SAP Analyst, Akzonobel, Slough, United Kingdom. Dr. V. Vallimayil Ph.D., Director, Department of MCA, Vivekanandha Business School For Women, Elayampalayam, Tiruchengode - 637 205, India. Mr. M. Rajasenathipathi M.C.A., M.Phil Assistant professor, Department of Computer Science, Nallamuthu Gounder Mahalingam College, India. Mr. M. Moorthi M.C.A., M.Phil., Assistant Professor, Department of computer Applications, Kongu Arts and Science College, India Prema Selvaraj Bsc,M.C.A,M.Phil Assistant Professor,Department of Computer Science,KSR College of Arts and Science, Tiruchengode Mr. V. Prabakaran M.C.A., M.Phil Head of the Department, Department of Computer Science, Adharsh Vidhyalaya Arts And Science College For Women, India. Mrs. S. Niraimathi. M.C.A., M.Phil Lecturer, Department of Computer Science, Nallamuthu Gounder Mahalingam College, Pollachi, India. Mr. G. Rajendran M.C.A., M.Phil., N.E.T., PGDBM., P GDBF., Assistant Professor, Department of Computer Science, Government Arts College, Salem, India. Mr. R. Vijayamadheswaran, M.C.A.,M.Phil Lecturer, K.S.R College of Ars & Science, India. Ms.S.Sasikala,M.Sc.,M.Phil.,M.C.A.,PGDPM & IR., Assistant Professor,Department of Computer Science,KSR College of Arts & Science,Tiruchengode - 637215 Mr. V. Pradeep B.E., M.Tech Asst. Professor, Department of Computer Science and Engineering, Tejaa Shakthi Institute of Technology for Women, Coimbatore, India. Dr. Pradeep H Pendse B.E.,M.M.S.,Ph.d Dean - IT,Welingkar Institute of Management Development and Research, Mumbai, India Mr. K. Saravanakumar M.C.A.,M.Phil., M.B.A, M.Tech, PGDBA, PGDPM & IR Asst. Professor, PG Department of Computer Applications, Alliance Business Academy, Bangalore, India. Muhammad Javed Centre for Next Generation Localisation, School of Computing, Dublin City University, Dublin 9, Ireland Dr. G. GOBI Assistant Professor-Department of Physics,Government Arts College,Salem - 636 007 Dr.S.Senthilkumar Research Fellow,Department of Mathematics,National Institute of Technology (REC),Tiruchirappli-620 015, Tamilnadu, India.


Contents 1. Near and Far-Field Radiation Characterization of Super Hybrid Shaped Microstrip Antenna

……….[1]

2. Minimizing the Total Cost of Lining and Excavation Including Free Board…..[5]

3. Review: Use Of Composite Adsorbents In Adsorption Refrigeration……[11]

4. Peristaltic transport of Bingham fluid in a Channel with permeable walls…….[17]


1

Near and Far-Field Radiation Characterization of Super Hybrid Shaped

Microstrip Antenna 1B.T.P.Madhav, 1T.V.Ramakrishna, 1B.Sadasivarao,

2K. Siva Rama Krishna, 1K.V.L.Bhavani, 2M.Gurunadhan 1Department of ECE, K L University, Guntur DT, AP, India

2Project Student, Department of ECE, K L University, Guntur DT, AP, India

Abstract: The near field and far field radiation patterns wil l give the range of radiation of the antenna in all d irections. The present paper deals with the near and far field radiation characterization of super hybrid shaped s errated microstrip patch antenna. All the four sides of the patch consist of different shapes like square, triangular , pyramidal and conical with different dimensions. Th e performance characteristics of the proposed super h ybrid serrated antenna are simulated with respect to the radiation pattern characterization. The antenna out put parameters like returnloss, gain and field distribu tion are also presented in this paper.

Keywords: Nearfield, farfield, super hybrid microstrip patch antenna.

I. INTRODUCTION

Larger bandwidth of serrated coupling microstrip patch antenna makes it applicable for wideband communications as a simple antenna for both transmission and reception. Edge treatments reduce the discontinuity of the reflector/free space boundary caused by the finite size of the reflector by providing a gradually tapered transition. Common reflector edge treatments include serrations and rolled edges.The serrated edge of a reflector tapers the amplitude of the reflected fields near the edge an alternative interpretation of the effects of serrations is based on edge diffraction. Serrations produce many low impedance diffractions as opposed to four straight edges and corners of the patch edge [1-5].

The antenna serrations with respect to the microstrip patch dimensions will improves the general characteristics of the radiating element but can also act to stabilize the output and reduce uncontrolled oscillations and other undesired behaviors [6-7].The impedance matching will be improved and the return loss can be analyzed interms of the serrations while using measurements of arrange of serrations in microstrip patch antennas improves the performance

through ground plane edge serrations .This will include the low cross-polarization level, increased beam width and impedance tuning [8-9]. Fig. 1. Shows the model of the proposed antenna.

Fig.1. model of the proposed antenna

II.DESIGN EQUATIONS

The serrations described by the boundary functions are expressed as a Fourier series of width and height modulated identical segmented convex function. The Fourier series expansion is given by

h-(x ')=C01+ ∑∞

−∞=n

Cn1 t

C01 =

T

1 {2t1p1+2t2p2(1- 1)

+2t1(p2-p

1)[1-e –a (p2-p

1)]}


2

Cn1 = T

1 {

+ )2sin(12pn

n

tω

ω + )11)(1sin(

22 ap

epnt

n+ω

ω

+[a - (( ))]

+222

222

ωna

apet

+

−[ (a )

2ap

e− ( )] }

Where h-(x ') represents boundary function of the serration ,C01 , Cn1 represents coefficients of the serration and P1, P2 and t1 ,t2 corresponds to width and height modulation factors of the serrations respectively.

III.RESULTS AND ANALYSIS

Fig.2.shows the return loss versus frequency curve for the proposed antenna. The antenna is resonating at dual frequency with return loss of -17,-26.5dB at 4.3 and 6.6 GHz respectively. The return loss curve shows the amount of energy that is lost at the resonating frequencies when load is connected.

2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00Freq [GHz]

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

dB(S

t(1,

1))

Ansoft Corporation Patch_Antenna_ADKv1Return Loss

m1

m2

Curve Info

dB(St(1,1))Setup1 : Sw eep1

Name X Y

m1 4.3010 -17.0006

m2 6.6618 -26.5147

Name Delta(X) Delta(Y) Slope(Y) InvSlope(Y)

d(m1,m2) 2.3608 -9.5141 -4.0300 -0.2481

Fig .2 .Return loss versus frequency

Fig.3.indicates the input impedance smithchart.The rms obtained from the smith chart is about 0.7129 and the bandwidth enhancement is attained up to 0.80 %.

The other parameters like gain margin of 16.98 and phase margin of 258.72 and gain crossover of 2.7 is obtained from the smith chart curve.

5.002.001.000.500.20

5.00

-5.00

2.00

-2.00

1.00

-1.00

0.50

-0.50

0.20

-0.20

0.00-0.000

10

20

30

40

50

6070

8090100110

120

130

140

150

160

170

180

-170

-160

-150

-140

-130

-120-110

-100 -90 -80-70

-60

-50

-40

-30

-20

-10

Ansoft Corporation Patch_Antenna_ADKv1Input Impedance

Curve Info rms bandw idth(1, 0)

St(1,1))Setup1 : Sw eep1

0.7129 3.9493

Fig.3. input impedance smithchart

Fig.4. and Fig.5. indicates the 3 dimensional and 2 dimensional gain plots for the current antenna. Gain of 7.44dB is attained at the desired frequency.

Fig.4. 3 dimensional gain plot

-200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00Theta [deg]

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

Y1

Ansoft Corporation Patch_Antenna_ADKv1ff_2D_GainTotal

m1Curve Info

dB(GainTotal)Setup1 : LastAdaptive

dB(GainTotal)_1Setup1 : LastAdaptive

Name X Y

m1 36.0000 7.4491

Fig.5. 2D gain plot

)1sin()1cos( pnnpn ωωω +

)2sin()2cos( pnnpna ωωω +

1sin()1cos( pnnpna ωωω −

))1sin()2(sin()12(

pnpnppa

e ωω −−−

ωn

t12


3

Fig.6. Near field rE–phi

Fig.7. Near field rE-theta.

Fig. 8 and Fig. 9 shows the far filed radiation for E theta and E phi in 3 dimensional plot

Fig.8. far field rEtheta 3 dimensional plot

Fig.9. far field rEphi 3 dimensional plot

The radiation pattern of the antenna can be defined as the spatial distribution of a quantity that characterizes the electromagnetic field generated by an antenna. Figure (6), (7) and (8), (9) shows near and far fields radiation pattern of the antenna in phi and theta directions. The polar plots represent the radiation pattern in elevation and azimuthal angles. The radiation pattern represents the energy radiated from the antenna in each direction, often pictorially.

Figure 10. E-Field Distribution

Figure 11. H-Field Distribution


4

Figure (10), (11) and (12) shows the E-field, H-field and current distribution of the antenna.

Quantity Value Max U 0.00041138W/sr Peak directivity 5.6809 Peak gain 5.5964 Peak realized gain 1.7116 Radiated power 0.00091001W Accepted power 0.00092375W Incident power 0.0030204W Radiation efficiency 0.98513 Front to back ratio 28.496 Decay factor 0

TABLE I Antenna simulated parameters

rEField Value At phi(deg)

At Theta(deg)

Total 0.55694V 180 -34 X 0.34463V 10 -32 Y 0.42389V 170 -26 Z 0.33012V 20 -56 Phi 0.44597V 165 -30 Theta 0.45398V 20 38 LHCP 0.33522V 25 -38 RHCP 0.54185V 175 -34 Ludwig3/x dominant

0.41963V 10 -40

Ludwig3/Y dominant

0.42284V 170 -26

TABLE III simulated Maximum field data

IV.CONCLUSION

A super hybrid microstrip patch antenna is designed and simulated. The main theme behind this paper is to give near and far field radiation characterization of super hybrid shaped serrated microstrip patch antenna. The results are giving moral encouragement to design serrated antennas in our future work. The results got in this paper are excellently suits for wireless communications in all aspects including high gain and high bandwidth.

ACKNOWLEDGEMENT

The authors like to express their thanks to the management and department of ECE, K L University for their support and encouragement during this work.

REFERENCES

[1]I.J.Bahl,P.Bhartia,“Microstrip AntennasHand book”,Artech House microwave library, 2000

[2] C.A. Balanis, “Antenna Theory: Analysis and Design,” 2nd ed., John Wiley & Sons, New York, 1997. [3]Volakis, John L., Antenna Engineering Handbook, 4th ed. New York: McGraw-Hill, 2007. [4]B.T.P.Madhav, V.G.K.M.Pisipati, P.Rakesh kumar,K.V.L.Bhavani“Dual Frequency Microstrip Rectangular Patch Antenna on Liquid Crystal Polymer Substrate” International Journal of Engineering Sciences Research-IJESR-ISSN: 2230-8504; e-ISSN-2230-8512 [5] J S Hollis, T J Lyon and L Clayton, “Microwave Antenna Measurements,” Scientific Atlanta, Inc, Atlanta, Georgia, USA, November 1985. [6] Gary E Evans, “Antenna Measurements Techniques.” Artech House, Inc., 1990. [3] Klaus D Mielenz, “Algorithms for Fresnel Diffraction at Rectangular and Circular Apertures,” Journal of Research of the National Institute of Standards and Technology, Vol 103, Number 5, September- October 1998, pp. 497-509. [7] P.A Beeckman, “Prediction of the Fresnel region field of a Compact Antenna Test Range with serrated edges,” IEE proceeding, Vol 133, pt H, No.2, April 1986, pp.108-114. [8] The-Hong Lee, Walter D. Burnside, “Performance Trade-Off between Serrated Edge and Blended Rolled Edge Compact Range Reflector,” IEEE Transactions on Antennas and Propagation, Vol 44, No 1, Jan 1996, pp. 87-96. [9] Gander, W. and W. Gautschi, "Adaptive Quadrature - Revisited", BIT, Vol. 40, 2000, pp. 84-101.


5

Minimizing the Total Cost of Lining and Excavation Including Free Board

Syed Zafar Syed Muzaffar 1, S. L. Atmapoojya 2, D. K. Agrawal 3, M. Aquil 4

1 Assistant Professor, Anjuman College of Engineering,Nagpur- India [email protected]

2 Principal,S. B. Jain Institute of Technology, Management,Nagpur- India 3 Ex. Dean,Faculty of Engineering & Technology,RSTM & Research, Nagpur University,Nagpur-India.

4 Assistant Professor, M. H. Saboo Siddique College of Engineering, Byculla, Mumbai - 8 - India Abstract - Lined canal with free board reduces the friction slopes, which enables the canal to be laid on a fla tter bed slope. This increases the command area of canal, on other hand, as the lining permits higher average velociti es, the canal can be laid on steeper slope to save the cost of earth work in formation. As the lining provide rigi d boundary, it ensures protection against bed bank er osion. This paper presents design equation for minimizing the total cost of canal lining and excavation with free board. This can be overcome by using manning equation. It involve lining cost, cost of earth work which varie s with the excavation depth, on account of complexities of analysis. The optimal cost equation along with the corresponding section shape coefficient is useful d uring the planning of canal project. A network of canal represent a major cost item in an irrigation projec t and economy of the canal network is vital. The maximum economy is achieved by minimizing the cost of linin g of canal and excavation with free board. This techniqu e is developed by taking illustration numerical example.

Keywords:- Round cornered Trapezoidal section, Lined canal, Depth of flow, Discharge, free board Excavation Optimal canal section.

I. INTRODUCTION

Network of canals is used to convey, distribute and apply water to land for irrigation. A canal in a network may be either lined or unlined. It is found that 45 to 50% water is lost due to seepage from the canal system during journey from head work to field. The seepage also enhances water logging of the adjacent area to the canal which causes reduction of crop production. Hence it is require how to control water due to seepage. A section of unlined canal system does not remain in trapezoidal shape for longer time hence need of lining is to made its surface hard which prevent seepage loss. Therefore the lining of canal is one of the measures which overcome this problem. Lined canals are designed for several purpose for uniform flow considering hydraulic efficiency, practicability and economy. Factor to be considered in the design include.

1. The material forming the channel surface, which determines the roughness coefficient.

2. The minimum permissible velocity to avoid deposition of silt or debris.

3. The limiting velocity to avoid erosion of the channel surface.

4. The topography of the channel route, which fixes the channel bed slope.

5. The efficiency of the channel section which indicates how much the section is hydraulically and/ or economically efficient. A maximum hydraulic gradient results in the section of minimum excavation area and the cost hydraulic design.

When an open channel is constructed the excavation and lining constitute a major cost obviously it is desirable to keep the cost minimum by adopting the most economical canal cross section.

Several types of materials are used for canal lining. The choice of material mainly depends on the degree of water tightness required. Though less water tight soil cement lining and boulder lining preferred on account of their low initial cost. Another low lining is composed of polyethylene plastic. Sheets spread over the boundary surface with adequate earth cover. Brick lining and burnt clay tile lining are popular lining as they were providing reasonable water tightness along with strength.

The total area of construction includes the flow area and free board area. The free board area is considered as

discharge dependent recommended by USBR. But lining of canal is increase the cost; therefore economic

environmental purposes require efficient use of water for irrigation. To get economy purpose in canal construction

the section should be minimum which include cost of excavation and cost of lining.

Minimum cost design of canal involve minimizing the sum of depth dependent excavation cost


6

and cost of lining subject to uniform flow condition in the canal, which result in the non linear objective function and non linear equality making the problem hard to solve analytically.

In this paper, an attempt has been made to derive most economical (optimal) canal, section by minimizing the total cost of construction which include lining cost and excavation cost with free board. We can reduce the cost of lining, related to free board and excavation i.e. earthwork cost finally a step by step design procedure with equation, example of cost minimizing is presented. The optimal cost equation of lining and excavation with free board is useful during the planning of a canal project.

Fig. 1. Trapezoidal Round Cornered section of Lined Canal with excavation and free board

The flow area A for a round cornered section as shown in Fig 1 is given by

A = by + r2Z2 + Zy2 + 2ryZ1 – 2r2Z1 …………….(1)

Where

b = bed width of the section

Z = side slope i.e. 1V: ZH

Y = depth of flow

Z1= √ (1+Z2) - Z

Z2 = (π/180) tan-1(1/z)

r = radius of arc

The wetted perimeter P of the section is given by

P = b+2y√ (1+Z2) -2rZ1+2rZ2 ……………….. (2) 2. Discharge Dependent Free Board The total area of Canal section At is given by At = b(y+f) +r2Z2+Z(y+f) 2+2r(y+f) Z1-2r2Z1 …………… (3)

At/ b = y+f

At/ y= b+2Z(y+f) +2rZ1

( At/ b)/ ( At/ y) = (y+f)/b+2Z(y+f) +2rZ1

= (1+f/y)/ (b/y+2Z (1+f/y) +2r/yZ1)

( At/ b)/ (dAt/ y) = (1+m)/ (b/y+2Z (1+m) +2r/yZ1) …

(4) Where m = f/y

( At/ b)/ ( At/ y) = ( AR2/3/ b)/ ( AR2/3/dy)

1+m/(b/y+2Z(1+m)+2r/yZ1)=[3b/y+10√(1+Z2)-14r/yZ1+

10(r/y)Z2-2Z+4r2/y2Z1-

2r2/y2Z2]/[5(b/y)2+10b/yZ+16z√(1+Z2)

-20r/yZZ1+8r2/y2ZZ1+10r/yb/yZ2+20r2/y2Z1Z2+20r/yZZ2-

4r2/y2ZZ2+6b/y√(1+Z2)+12r/yZ1√(1+Z2)-12(r2/y2) Z12]

(1+m)[5(b/y)2+10b/yZ+16Z√(1+Z2)-20r/yZZ1+8r2/y2ZZ1+

+10r/yb/yZ2+20r2/y2Z1Z2+20(r/y)ZZ2-

4r2/y2ZZ2+6b/y√(1+Z2) +12r/yZ1√(1+Z2) -12r2/y2Z12] =

(3b/y+10√ (1+Z2)-14r/yZ1

+10r/yZ2-2z+4r2/y2z1-2r2/y2Z2) (b/y+2Z (1+m) +2r/yZ

5[(1+m)(b/y)2+(1+m)[10Z+10r/yZ2+6√(1+Z2)]b/y+(1+m)[1

6Z√(1+Z2)-20r/yZZ1+8r2/y2ZZ1+20r2/y2Z1Z2+20r/yZZ2-

4r2/y2ZZ2 +12r/yZ1√(1+Z2)-

12r2/y2Z12]=3(b/y)2+[10√(1+Z2)-14r/yZ1 +10r/yZ2-

2Z+4r2/y2Z1-2r2/y2Z2+6Z+6Zm+6r/yZ1]b/y

+[2Z(1+m)+2r/yZ1][10√(1+Z2)-14r/yZ1+10r/yZ2-

2Z+4r2/y2Z1-2r2/y2Z2]

(2+5m)(b/y)2+[10Z+10r/yZ2+6√(1+Z2)+10Zm+10r/yZ2m+

6m√(1+Z2)-10√(1+Z2)+14r/yZ1-10r/yZ2-4Z-

4r2/y2Z1+2r2/y2Z2-6Zm-6r/yZ1]b/y+(1+m)[16Z√(1+Z2)-

20r/yZZ1 +8r2/y2ZZ1 +20r2/y2Z1Z2+20r/yZZ2-

4r2/y2ZZ2+ 12r/yZ1√(1+Z2)-12r2/y2Z-

20Z√(1+Z2)+28r/yZZ1-20r/yZZ2+4Z2- 8r2/y2ZZ1

+4r2/y2ZZ2]-2r/yZ1[10√(1+Z2)-14r/yZ1+10r/yZ2-

2Z+4r2/y2Z1-2r2/y

2Z2]=0

(2+5m)(b/y)2+[6Z-4√(1+Z2)+8r/yZ1- 4r2/y2Z1+

2(r2/y2)Z2+(4Z+6√(1+Z2)+10(r/y)Z2)m+[-4Z√(1+Z2)

+4Z2+8r/yZZ1+20r2/y2Z1Z2+12r/yZ1√(1+Z2)-


7

12r2/y2Z12](1+m)-2r/yZ1[10√(1+Z2)-14r/yZ1+10r/yZ2-

2Z+4r2/y2Z1-2r2/y2Z2]=0

K1(b/y)2+K2b/y-{[4Z√(1+Z2)-4Z2-8r/yZZ1-20r2/y2Z1Z2 –

12(r/y)Z1√(1+Z2)+12r2/y2Z12](1+m)+2r/yZ2[10√(1+Z2)-

14r/yZ1+10r/yZ2-2Z+4r2/y2Z1-2(r2/y2)Z2]}=0

K1(b/y)2+K2b/y-K3=0

This is quadratic equn in b/y form

………………. (5) Where, K1 = 2+5m

K2 = 6Z-4√ (1+Z2) +8r/yZ1- 4r2/y2Z1+2r2/y2Z2+ (4Z+ 6√

(1+Z2) +10r/yZ2) m

K3 = [4Z√ (1+Z2)-4Z2-8r/yZZ1-20r2/y2Z1Z2- 12r/yZ1 √

(1+Z2) +12r2/y2Z12] (1+m) +2r/yZ2 [10√(1+Z2)-14r/yZ1

+10r/yZ2-2Z+4r2/y2Z1 - 2(r2/y2) Z2]

3. Depth Dependent Free Board Put f = K√y At = b(y+ K√y) +r2Z2+Z(y+ K√y) 2+2r(y+ K√y) Z1-2r2Z1

At/db = y+ K√y

At/ y=b (1+k/2√y) +2Z(y+k√y) (1+k/2√y) +

2r(1+k/2√y)Z1

=b(1+K/2√y)+2Zy(1+K/√y)(1+K/2√y)+2r(1+K/2√y)Z1

=b(1+K/2√y)+2Zy(1+K/2√y+K/√y+K2/2y)+

2r (1+K/2√y) Z

t/ y = b(1+K/2√y)+2Zy(1+K2/2y+3K/2√y)+

2r(1+K/2√y)Z1

( At/ b)/ ( At/ y) =(y+K√y)/b (1+K/2√y) +2Zy

(1+K2/2y+3K/2√y) +2r (1+K/2√y) Z1

( At/ b)/ ( At/ y) = (1+K/√y)/ [b/y (1+K/2√y) +2Z

(1+K2/2y+3K/2√y) +2r/y (1+k/2 √y) Z1]

( At/ b)/ ( At/ y) = (1+m1)/ [b/y (1+m1/2) +2Z

(1+m12/2+3m1/2) +2r/y (1+m1/2) Z1] ….. (6)

Equating the above equations

( At/ b)/ ( At/ y) = ( AR2/3/ b)/ ( AR2/3/ y)

(1+m1)/ [b/y (1+m1/2) +2Z (1+m12/2+3m1/2) +2r/y

(1+m/2) Z1] = [3b/y+10√ (1+Z2)-14r/yZ1+10r/yZ2-

2Z+4r2Z1- 2r2Z2]/5(b/y)2 +10b/yZ+16Z√(1+Z2)- 20r/yZZ1

+8(r2/y2)ZZ1 +10r/y b/yZ2 +20r2/y2Z1Z2 -

4r2/y2ZZ2+6b/y√(1+Z2) +12r/yZ1√(1+Z2)-

12(r2/y2)Z12 +20(r/y)ZZ2]

[(1+m1)[5(b/y)2+10b/yZ+16Z√(1+Z2)- 20r/yZZ1+8r2/y2ZZ1

+10r/y b/yZ2+20r2/y2Z1Z2+20(r/y)ZZ2 - 4r2/y2ZZ2+6b/y

√(1+Z2)+12r/yZ1√(1+Z2)-12(r2/y2)Z12] = [3b/y+10√(1+Z2)

-14r/yZ1+10r/yZ2-2Z+4r2/y2Z1-2r2/y2Z2] [b/y (1+m1/2) +2Z

(1+m12/2+3m1/2) +2r/y (1+m1/2) Z1]

5(1+m)(b/y)2+[10Z+6√(1+Z2)+10r/yZ2](1+m1)b/y+(1+m1)[

16Z√(1+Z2)-20r/yZZ1+8r2/y2ZZ1+20r2/y2Z1Z2+20r/yZZ2-

4r2/y2ZZ2+12r/yZ1√(1+Z2)-12r2/y2Z12] = 3(1+m1/2)(b/y)2

+[10√(1+Z2) +10(r/y)Z2-14r/yZ1-2Z+4r2/y2Z1- 2r2/y2Z2)

(1+(m1/2))+6Z(1+m12/2+3m1/2)+6r/y(1+m1/2)Z1]b/y

+[2Z(1+m12/2+3m1/2)+2r/y(1+m1/2)Z1][10√(1+Z2)14r/yZ1

+10r/yZ2-2Z-4r2/y2Z1-2r2/y12Z2]

[(2+7m1/2)(b/y)2+[10Z+6√(1+Z2)+10r/yZ2+10Zm1+6m1√(

1+Z2)+ 10m1r/yZ2-10√(1+Z2)+14r/yZ1-10r/yZ2+2Z-

4r2/y2Z1 +2r2/y2Z2-5m1√(1+Z2)+7r/yZ1m1-

5r/yZ2m1+zm1- 2r2/y2z1m1 +r2/y2Z2m1-6Z-3Zm12-9Zm1-

6r/yZ1- 3r/ym1Z1]b/y+(1+m1) [16Z√(1+Z2)-

20r/yZZ1+8r2/y2ZZ1+20r2/y2Z1Z2+20r/yZZ2-

4r2/y2ZZ2+12r/yZ1√(1+Z2)-12r2/y2Z12]-

[2Z(1+m12/2+3m1/2) +2r/y(1+m1/2)Z1][10√(1+Z2)-

14r/yZ1 + 10(r/y) Z2-2Z-4(r2/y2) Z1-2(r2/y2)Z2] = 0

K1 (b/y) 2+ [6z-4√ (1+Z2)-8r/yZ1- 4r2/y2Z1+2r2/y2Z2 + (2Z

+√ (1+Z2) +5r/yZ2+4r/yZ1-2r2/y2Z1+r2/y2Z2-3zm1) m1] b/y-

K3=0

K1 (b/y)2+k2b/y-k3=0

Where K1=2+7/2m1


8

K2= [6Z-4√ (1+Z2) +8r/yZ1-4r2/y2Z1+2r2/y2Z2+ (2Z+√

(1+Z2) +5r/yZ2+4r/yZ1-2r2/y2Z1+r2/y2Z2-3zm1) m1]

K3=[2Z(1+m12/2+3m1/2)+2r/y(1+m1/2)Z1][10√(1+Z2)-

14r/yZ1+10r/yZ2-2Z-4r2/y2Z1-2r2/y2Z2] - (1+m1)

[16Z√(1+Z2)- 20r/yZZ1+8r2/y2ZZ1 + 20r2/y2ZZ1

+20r2/y2ZZ1-4r2/y2ZZ2+12r/yZ1√(1+Z2)-12r2/y2Z12

+20(r/y)ZZ2]

The total Cost per meter Length of Canal can be determined by the following equation. C= [bK1(y+f) +2rK1(y+f) Z1+K1

2(y+f)2 Z- 2r2Z1

+r2Z2]Ce+bCb+2rZ2Cc+(2(y+f) √(1+Z2)-2rZ1)Cs

Illustrative Example Q= 100m3/sec, Cost of Excavation Ce = Rs. 80/m3 r/y = 0.7, Cost of Lining for base Cb = Rs. 180/sqm S0= 1 in 5000, Cost of Lining for Curve Cc = Rs. 210/ sqm Z= 1.5, Cost of Lining for sides Cs = Rs. 200/ sqm n= 0.014 f= 0.75 Z 1= 0.30277 Z 2= 0.5888 4. Discharge Dependent Free Board. Assume b/y = 0.5

[Qn/√ So]3/8 = [100×0.014/√(1/5000)]3/8 = 5.6021

Φ2 = (b/y+2√ (1+Z2) -2 r/y Z 1 +2 r/y Z 2) 1/4 / (b/y+ r2/y2

Z 2 +Z+2r/y Z1-2 r2 /y2Z1)5/8

Φ2=(0.5+2×1.8027-2×0.7×0.30277+2×0.7×0.588)1/4/

(0.5+0.72×0.588+1.5+2×0.7×0.30277-2×0.72

×0.30277)5/8

Φ2 = 1.4569/1.73522

Φ2 = 0.8396

Y = Φ2 (Qn/√So)3/8

= 0.3896×5.6021

Y = 4.7035

m = f/y

= 0.75/4.7035

m = 0.159

K1= 2+ 5m

= 2+ 5×0.159

K1= 2.797

K2= 6 z - 4 √ (1+Z2) +8 r/yZ1-4 r2 / y2Z1 + 2 r2/y2Z2 + (4Z

+ 6√ (1+Z2) +10 r/y Z2) m

= 6×1.5 - 4 +8×0.7×0.30277 - 4×0.72

×0.30277 +2×0.72 × 0.5888

+(4×1.5+6×1.80277+10×0.7×0.588) ×0.159

K2= 6.796

K3= [4Z√ (1+Z2) – 4Z2 - 8r/yZZ1- 20 r2/y2Z1Z2 – 12 r/yZ1√

(1+Z2) + 12 r2/y2 Z12] (1+m) + 2 r/y Z2 [10 √ (1+Z2) -14 r/y

Z1

+ 10 r/y Z2 – 2Z+4 r2/y2 Z1 – 2 r2/y2 Z2]

K3= [ 4× 1.5 × 1.80277 – 4×1.52 - 8×0.7 × 1.5 × 0.30277

– 20 ×0.72 × 0.30277 × 0.588 -12 ×0.7 ×0.30277

×1.80277 + 12× 0.72 × 0.302772] (1+0.159)+

(2×0.7×0.588) [10×1.80277 -

14×0.7×0.30277+10×0.7×0.588 - 2×1.5 + 4×0.72 ×

0.30277- 2×0.72 × 0.588]

K3= [10.8166-9-2.5432-1.7446- 4.5849+0.539] (1.159)

+0.8243[18.0277-2.9671+4.116-3+0.593-0.577]

= -7.553+13.3475

K3= 5.7945

= (-6.796+ )/

2×2.797 = (-6.796+10.5363)/ 5.594 b/y= 0.668

b = b/y ×y

= 0.668×4.7035

b = 3.144

r = r/y ×y

= 0.7×4.7035

r = 3.292

At = b(y+f) + r2 Z2+ Z(y+f) 2 +2r(y+f) Z1-2r2 Z1


9

=3.144(4.7035+0.75) +3.2922 ×0.588 +1.5(4.7035 +

0.75)2+2×3.292(4.7035+0.75) ×0.30277-2×3.2922

×0.30277

= 17.145+6.3809+44.61+10.8712-6.562

At = 72.445 M2

C= [bK1(y+f) +2rK1(y+f) Z1+K12(y+f)2Z-2r2 Z1+r2 Z2]Ce

+b Cb+2r Z2 C + (2(y+f) √ (1+Z2) - 2rZ1) Cs

C = Rs. 8473.938 per met. Length

5. Depth Dependent Free Board m1 = k/√y

= 0.7/

= 0.7/ 2.16875

m1= 0.32276

K1= 2+7/2 m1

= 2+7/2×0.32276

K1= 3.12968

K2= 6Z- 4√(1+Z2)+8 r/y Z1 – 4 r2/y2 Z1 + 2r2/y2Z2+(2Z+

√(1+Z2)+5 r/yZ2 +4 r/yZ1- 2 r2/y2 Z1+ r2/y2 Z2 -3Zm1) m1

= 6×1.5 – 4×1.8027+8×0.7×0.30277-4×0.72 ×0.30277

+2×0.72×0.588+(2×1.5+1.8027+5×0.7×0.588+4×0.7×0.3

0277-2×0.72×0.30277+0.72×0.588-3×1.5

×0.32276)0.32776

= 3.467552+2.01642889

K2= 5.48398

K3= [2Z(1+m12/2+(3m1/2))+2 r/y(1+m1/2)Z1] [10 √(1+Z2)-

14r/y Z1+10 r/y Z2-2Z -4r2/y2 Z1 -2r2/y2Z2] – (1+m1))[16Z

√(1+Z2) –20r/yZZ1+8r2/y2ZZ1+20r2/y2Z1Z2 +20r/yZZ2-

4r2/y2ZZ2+12r/yZ1 √(1+Z2)-12r2/y2Z12]

=[2×1.5(1+0.322762/2+3/2×0.32276)+2×0.7(1+0.32276/

2)×0.30277] [10×1.8027- 14×0.7×0.30277 +10×0.7

×0.588-2×1.5-4×0.72×0.30277-2×0.72×0.588] –

(1+0.32276) [16×1.5×1.802720×0.7×1.5 ×0.30277+

8×0.72×1.5×0.30277+20×0.72×0.30277×0.588+20×0.7×

1.5×0.588- 4×0.72 ×1.5×0.588+12×0.7 ×0.30277

×1.8027-12×0.72×0.3027]2

=76.5461-72.8795

K3 = 3.666551

= - 5.48398+√

(5.48398x5.48398+4x3.12968x3.66551)/2 ×3.12968

= - 5.48398+8.716336/6.25936

b/y= 0.5164

b =b/y×y

= 0.5164×4.7035

b =2.4288874

r =r/y×y

= 0.7×4.7035

r= 3.29245

r= 3.29245

At=b(y+K√y) +r2Z2+Z(y+K√y)2+2r(y+K√y)Z1-2r2Z1

=2.42889(4.7035+0.7×2.1687)+3.2922×0.588+1.5(4.703

5+0.7×2.1687)+2×3.29245(4.7035+0.7×2.1687)0.30277

-2×3.2922×0.30277

At=85.3877 M2

C = [2.4289 x 0.7x (4.7035+0.75) +2 x 3.29 x 0.7 x

(4.7035+0.75) xo.30277+0.72 (4.7035+0.75)2x0.5-

2x3.292 x0.30277+3.292 x0.5888] x 80

+2.4288x180+2x3.292 x0.5888x210+

(2(4.7035+0.75) √ (1+1.52) - 2x3.929 x0.30277) x 200

= [9.272+7.605+7.286 - .554+6.373]80+437.184+

813.098+3533.887

C = Rs. 6703.729 per met Length

CONCLUSION

The condition for the optimal trapezoidal rounded cornered canal section for minimizing the total cost of lining and excavation considering free board has been developed and method based on trial and error numerical technique are suggested. Following conclusions are drawn in the analysis.

1. The discharge dependent free board gives a wider optimal section as compare to the best section for the


10

same discharge i.e. obtained section with high b/y ratio as well as cost.

2. The depth dependent free board gives a narrow optimal section as compare to the best section i.e. obtained section is with low b/y ratio as well as cost proposed method can be adopted to design the optimal section with consideration of free board.

REFERENCES

[1]. A Das “Optimal Channel Cross Section with Composite roughness” Journal of Irrigation and drainage Division ASCE Vol. 126 No.1. 2000 pp68-71.

[2] Arif A Anwar & Derick Clark “Design of Hydraulically Efficient Power law Channels with free Board “Journal of Irrigation and Drainage engineering @ ASCE/November/December/2005.

[3] Amlan Das “Optimal Design of Channel Having Horizontal Bottom and Parabolic sides” 192 / Journal of Irrigation and Drainage Engineering © ASCE /March/April-2007.

[4] Guo_”Optimal Canal Cross section with free board “Journal of Irrigation and drainage engineering ASCE. Vol.110 No. 8 September 1984.

[5] G.V. Loganathan “Optimal design of parabolic canal” Journal of Irrigation and drainage division ASCE Vol.117 No.5 1995.pp716-735.

[6] Howard H Chang and Zbig Osmolski “Computer Aided Design for Channelization” Journal of Hydraulic Engineering Vol.114 No.11 November 1988 @ ASCE ISSN 0733.

[7] K. Babaeyan-Koopaei’ “Dimensionless Curve for Normal- depthCalculations in Canal Section s” 386/ Journal of Irrigation and Drainage Engineering/ November/December 2001.

[8] Lawrence E. Flynn S.M “Canal Design Optimal cross Section” Drainage Engineering Vol.113 No.3 Aug 87, @ ASCE ISSN 0733.

[9] M.Riyaz and Z. Sen European “Aspect of Design and benefits of Alternative lining systems water 11/12, 17-27, 2005@EW Publications.

[10] P Monadjemi “General formulation of Best Hydraulics Channel Section” Journal of Irrigation and drainage division ASCE Vol. 120 No. 1994.pp27-35.

[11] Prabhata K Swamee Govinda C. Mishra and Bhagur R Chahar, “Minimum Cost Design of Lined Canal Sections”

[12] P N Modi and SM Seth “Design of most Economical Trapezoidal Section of Open Channel” Journal of Irrigation and Power. New Delhi, 1968. PP 271-280.

[13] Prabhata K. Swamee, Govinda C Mishra and Bhagur R Chahar. “Minimum Cost Design of Lined Canal Sections water resources management 14. 1-2-2000. © 2000 Kluwer Academic Publishers. Netherland.

[14] Prabhata K. Swamee “Optimal Irrigation Canal Section” Journal of Irrigation and Drainage engineering Nov/ Dec /1995/467.

[15] Subramanyan K “Open Channel Flow” Tata McGraw Hill Publishing Company Ltd. New Delhi-1986.

[16] S.L. Atmapoojya and R.N Ingle” The Optimal Canal Section with consideration of free board” I E (I) Journal_CV Vol. 83 Feb 2003.

[17] Stone Pitched Lining for Canal of Practice, 1S, 4515-1993. [18] Subhasish dey’ “choke- free Flow in Circular channel with

increase in Bed Elevation” Journal of Irrigation and Drainage Engineering/November/December 1998/317.

[19] Syed Zafar Syed Muzaffar, S.L. Atmapoojya, D.K. Agarwal, M.Aquil “The Optimal Rounded Cornered Canal Section with Consideration of free Board”, International Journal of Engineering Research and Applications(IJERA) 2011, vol. 1 issue 4, pp1317-1322, ISSN:2248-9622.

[20] Syed Zafar Syed Muzaffar, S.L. Atmapoojya, D.K. Agarwal, S.S.Rathore ”Optimal cross section of a Trapezoidal Round

Cornered Canal” International J. of Math,Sci & Engineering Applications (IJMSEA) 2011, vol.5 issue 4pp 433-441 ISSN 0973-9424

[21] Syed Zafar Syed Muzaffar, S.L. Atmapoojya, D.K. Agarwal, 2012, vol.2 issue 1, “Minimum Lining Cost of Trapezoidal Round Cornered Section Canal” International Journal of Advances in Engineering & Technology” (IJAET) pp 433-436.

[22] V.L Streeter and E.B Wylie “Fluid Mechanics” McGraw Hills Inc, New York, 1979.

[23] V.T Chow-“Open Channel Hydraulics” The McGraw Hill book Company New York Nu.1959.

[24] V T Chow “Open Channel Hydraulics” The McGraw Hill Book Co, New York, NY 1959.

[25] Yen. B.C (2002)”Open Channel Flow Resistance” J. Hydraul. Eng. 128(1) 20-39.


11

REVIEW: USE of COMPOSITE ADSORBENTS in ADSORPTION REFRIGERATION

Vaibhav N. Deshmukh#1 Satishchandra V. Joshi*2

# Department of Mechanical Engineering Maharashtra Institute of Technology Pune – 411038 (India) [email protected]

* Department of Mechanical Engineering Vishwakarma Institute of Technology Pune – 411037 (India) [email protected]

Abstract

The urbanization across the world has resulted in increased demand for refrigeration and air conditio ning. The main disadvantage with the conventional method i.e. vapor compression system is environment pollution. Another problem faced during urbanization is energy crisis. The adsorption refrigeration system is one of the solutions to this problem. The advantages of this s ystem are environment friendly, less noise, use of waste heat or solar energy. But the disadvantage with adsorption system is low coefficient of performance (COP) and bulkiness. Researchers across the world are working on this issue to make adsorption system a viable alter native to the compression systems. Since the last two deca des considerable work is being done on the use of compo site adsorbents to improve the heat and mass transfer performance. This kind of adsorbent is usually obta ined by the combination of a chemical adsorbents and physical adsorbents.

Keywords: Refrigeration, Compression System, Adsorption System, Composite Adsorbents, Coefficient of performance (COP).

I. INTRODUCTION

There are two refrigeration systems that are benign to the environment. They are absorption systems and adsorption systems. Both of them use refrigerants having zero ozone depletion potential and zero global warming potential. Out of these two systems absorption systems are used on a large scale. Researchers have started working on adsorption systems in the last two decades because they have following advantages over absorption refrigeration systems:

1) They can be powered by a large range of heat source temperatures from 500C to 5000C.

2) They do not need a liquid pump or the rectifier for refrigerant.

3) They do not present corrosion problems due to the working pairs normally used.

4) They are less sensitive to shocks and to the installation position.

Although adsorption systems present all the benefits listed above they have drawbacks such as very less coefficient of performance, low specific cooling power and they are bulky. Many researchers are working to reduce the size of the adsorption system and to improve its performance by using composite or consolidated adsorbent for better heat and mass transfer. There is still potential scope in the enhancement of heat and mass transfer properties in the adsorber by increasing the adsorption properties of working pairs and by better heat management during the adsorption cycle. The study may involve the evaluation of the adsorption phenomenon and the physical chemical properties of the working pairs.

II. REVIEW OF RECENT STUDY

Adsorption refrigeration is one of the most attractive technologies for refrigeration applications, because it is quite benign to the environment: zero ozone depletion potential, zero global warming potential, simple control, low operating cost, less noise, high performance to avoid extra primary energy consumption [1–4]. Ammonia is widely used as a refrigerant in adsorption refrigeration systems [5]. The advantages include high enthalpy of evaporation, stability, wide temperature range and low freezing temperature. One of the most commonly used adsorbents for ammonia sorption reported is alkaline-earth metal chlorides, such as MgCl2 [6], CaCl2 [7,8], SrCl2 [9] and


12

BaCl2 [10], which have large adsorption capacity as well as low evaporating temperature. However, the poor heat and mass transfer performance caused by the phenomena of agglomeration and swelling during the reaction with ammonia make the choice of proper compound adsorbents become vital important. Hybrid materials, which are composed of chemical adsorbents and porous medium, can improve the heat and mass transfer performances of chemical or physical adsorbents effectively [11, 12]. So far, composites for ammonia sorption have been synthesized with CaCl2 impregnated into various porous mediums, such as activated carbon [13], the synthetic carbon, etc. [14–16]. However, the researches on the basic adsorption equilibrium data are still insufficient to provide comprehensive understanding about the chemical adsorption refrigeration process. The conventional adsorption cycle mainly includes two phases:

1) Adsorbent cooling with adsorption process which results in refrigerant evaporation inside evaporator and thus in the desired refrigeration effect. In this phase the sensible heat and adsorption heat are consumed by a cooling medium.

Fig.1: Adsorption (Refrigeration) process

2) Adsorbent heating with desorption process also called generation which results in refrigerant condensation at the condenser and heat release to the environment. The heat necessary for the generation process can be supplied by a low grade heat source such as waste heat or solar energy,etc.

Fig.2: Desorption (Regeneration) process

In comparison with mechanical vapor compression systems, adsorption systems have the benefits of energy saving if powered by waste heat or solar energy, simpler control, no vibration and lower operation costs.

Adsorption systems can be much simpler than absorption systems. For example, in the NH3–H2O absorption system, dephlegmate equipments must be coupled to the system because the boiling point of water is similar to that of ammonia.

III. ADSORBENTS

The adsorption process is divided into physical adsorption [17–19] and chemical adsorption [20–22]. The adsorbents can be broadly classified in to three types: a) physical adsorbents b) Chemical adsorbents and c) Composite adsorbents.

A. Physical Adsorbents

Physical adsorption is caused by Vander Waals force between the molecules [23] of the adsorbent and the adsorbate. Physical adsorbents with mesopores can adsorb consecutives layers of adsorbate, while those with micropores have the volume of the pores filled with the adsorbate. Physical adsorbents develop the selectivity to the adsorbate after the former undergo specific treatments, like react under a gas stream or with certain agents. The kind of treatment will depend on the type of sorbents [24].

The common physical adsorbents for adsorption refrigeration are activated carbon, activated carbon fibre, silica gel and zeolite.

B. Chemical adsorbents Chemical adsorption is caused by the reaction between adsorbates and the surface molecules of adsorbents. Electron transfer, atom rearrangement and fracture or formation of chemical bond always occurs in the process of chemical adsorption [25]. Only one layer of adsorbate reacts with the surface molecules of chemical adsorbent. The adsorbate and adsorbent molecules after adsorption never keep their original state, e.g., complexation occurs between chlorides and ammonia. Moreover, there are the phenomena of salt swelling and agglomeration, which are critical to heat and mass transfer performance. Chemical adsorbents mainly include metal chlorides, metal hydrides and metal oxides.


13

C. Composite adsorbents Composite adsorbents [26–28] started to be studied about twenty years ago [29], and they aimed to improve the heat and mass transfer performance of the original chemical adsorbents [27, 30, 31]. This kind of adsorbent is usually obtained by the combination of a chemical adsorbent and a porous medium, that can be or not a physical adsorbent, such as activated carbon, graphite, carbon fibre, etc. [27, 32, 33]. Composite adsorbents are developed and studied with mainly two goals: (1) Improve heat and mass transfer performance of chemical adsorbents [34], specially due to the swelling and agglomeration phenomena. Salt swelling reduces the heat transfer, and salt agglomeration reduces the mass transfer. Therefore, the additive for chemical adsorbents must have a porous structure and high thermal conductivity, such as expanded graphite, to help avoiding the above-mentioned problems [35, 36]. (2) Increase the adsorption quantity of physical adsorbents [37]. The addition of chemical sorbents in the physical sorbents increases the adsorption capacity of the latter, without resulting in the problems found in the former. The composite adsorbents made from porous media and chemical sorbents are commonly a combination of metal chlorides and activated carbon, or activated carbon fibre, or expanded graphite, or silica gel or zeolite. Increasing popularity of consolidated sorbents can be explained by simplicity of its production and application. The type of consolidated sorbent is determined by application, which influences the type of chosen material [39]: 1) Consolidated sorbents using porous metal hydrides or metal matrix alloys containing Ni, Fe, La, Al, H, with or without subsequent sintering; 2) Consolidated sorbents using metal foams as porous matrices; 3) Consolidated materials using carbon-based materials as inert binder. There are several kinds of composites proposed in the literature. One of the most popular is IMPEX (IMPregnated blocks of recompressed EXpanded graphite) e an expanded graphite (EXG) composite developed by Mauran and his coworkers [38, 40, 41], patented and manufactured

by La Carbone Lorraine. It is characterized by strong anisotropic (radial) heat and mass transfer capabilities. The layered structure of compressed EXG improves gas diffusion in direction perpendicular to that of compression [40, 42]. Experimentally obtained values of heat transfer coefficients are λ = 0.2-40 W/mK [43]. Mazet et al. [44] analyzed heat transfer coefficient of IMPEX blocks with apparent density 200 kg/m3 and obtained λ = 16 W/mK. Han and Lee measured effective heat transfer of a composite based on calcium chloride, barium chloride and manganese chloride. The results were λ = 10-49 W/mK and showed that effective thermal conductivity strongly depends on the bulk density, weight fraction of graphite and the ammoniated state of salt [45]. Han et al. [46] has analyzed the influence of acid treatment (intercalation with sulfuric acid at different temperatures) on the porosity and chemical composition of expanded graphite, obtaining higher values (range 10-12-10-15 m2) at lower treatment temperatures. Radial thermal conductivity was in range 4.6-42.3 W/mK. Bou et al. [47] introduced layered, foliated graphite blocks, where each sheet is characterized by different apparent density, and the active agent is dispersed in it. This solution leads to noticeably increased reaction rates (for t ≤ 40 min). Lee et al. [48] introduced non-uniform reaction blocks, where apparent density changes with radius direction 165, 222, 279, 337, 394 kg/m3 gradually), which lead to increased transfer capabilities and reaction rates.

IV. COMPOSITE ADSORBENTS OF SILICA GEL

AND CHLORIDES

They are mainly developed by impregnation process [50-53], where the silica gel is immersed in a salt solution, and then dried. According to Aristov et al. [54], the adsorption characteristics of silica gel composite adsorbents can be modified by: (1) changing the silica gel pore structure; (2) changing the type of salt and (3) changing the proportion between salt and silica gel. The adsorption isotherms of silica gel/CaCl2/water pair with different mass ratio of CaCl2 is shown in Fig. 3 [49]. The letter S in the legend, followed by a number, represents the concentration of the salt solution used to make the composite adsorbent. For example, S0 represents silica gel with no salt, and S40 represents the composite adsorbent made with a 40% CaCl2 solution. Fig. 3 shows that the increment in the equilibrium adsorption quantity with the solution


14

concentration decreases when the solution concentration is higher than 40%. As the salt can easily liquefy during the adsorption process when the compound is prepared with a high concentration solution, the best concentration to avoid such a problem and ensure high adsorption capacity would be around 40%.

Fig. 3. Isotherms at 400C [49].

V. POROUS MEDIA FOR COMPOSITE ADSORBENTS

Four types of porous media are used to produce composite adsorbents with chlorides: expanded graphite, activated carbon, activated carbon fibre and vermiculite. Expanded graphite is utilized to make composite adsorbents with chlorides, which present enhanced heat transfer and mass transfer properties, and almost no expansion during the adsorption process [55]. The structure of the expandable graphite greatly changes after expansion, and this change can be seen in the scanning electron microscope (SEM) picture shown in Fig. 4 [55]. A composite adsorbent of CaCl2 and expanded graphite called IMPEX, for which the solution of 20 wt% CaCl2 was utilized to impregnate with the graphite block, was developed by the research group of Mauran [58, 55–57]. The dimension stability of IMPEX was studied, and results showed that the volume expansion rate wall null if the density of graphite block used to produce composite adsorbent was 156 kg/m3.

Fig. 4. SEM photo of granular graphite [55]. (a) Before expansion; (b) after expansion. Shanghai Jiao Tong University [59,60] also researched the adsorption performance of composite adsorbents with CaCl2 and expanded graphite, and results showed that SCP as high as 1000W/kgCaCl2 can be obtained when the mass ratio between expanded graphite and CaCl2 is 1:1, evaporation temperature is -20 to -10 0C, and the heat sink temperature is 20–30 0C. The overall heat transfer coefficient for this compound was 787 W/(m2 0C). The advantage of composite adsorbent made with activated carbon, when compared with the composite adsorbent made with activated carbon fibre, is the fact that the salt does not separate from the former and accumulates at the bottom of the adsorber when the compound is prepared as a simple mixture. Activated carbon fibre is used in combination with chlorides to enhance the heat transfer in the adsorbent bed. Most of the researches are related to impregnated carbon fibres (ICFs) with MnCl2 and graphite fibres intercalation compounds (GFICs) [61, 62]. The optimal adsorption performance of ICF–ammonia is similar to the performance of GFIC–ammonia and this value is 1 kg/kg for the latter and 0.95 kg/kg for the former. Vasiliev [63,64], also developed a composite adsorbent, which is called Busofit, of activated carbon fibres impregnated with salt, but the solvent was water instead of alcohol. The salt was evenly distributed over the carbon fibre surface as a 2–3 mm film. Such a type of adsorbent is mainly utilized for resorption system using ammonia as refrigerant.


15

VI. CONCLUSION

The adsorption refrigeration is an alternative refrigeration system that uses refrigerants having zero ozone depletion potential and zero global warming potential. There is a growing need for refrigeration and air-conditioning across the world. At the same time we need to protect our environment. Hence the focus is on greener technologies. Adsorption refrigeration is one of the solutions. But it has very low coefficient of performance. Researchers are working on the techniques to improve the performance of adsorption systems. Various combinations of composite adsorbents are being explored. The use of composite adsorbents in the adsorption refrigeration has resulted in the performance improvement. But, there is still a lot of scope in this field.

REFERENCES

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17

Peristaltic transport of Bingham fluid in a Channel with permeable walls

K.Chakradhar, T.V.A.P.Sastry**, S.Sreenadh*** * Department of Mathematics, Dr.Y.S.R. Engg. College of Technology, Kadapa, A.P., INDIA ** Department of Mathematics, Keshav Memorial Institute of Technology,Hyderabad, AP,

*** Department of Mathematics, Sri Venkateswara University, Tirupathi, A.P., INDIA E-Mail: [email protected]

Abstract: Peristaltic transport of a Bingham fluid in a channel with permeable walls is studied under long wavelength and low Reynolds number assumptions. This model can be applied to the blood flow in the sense that erythrocytes region and the plasma regions may be described as plug flow and non-plug flow regions. The effect of yields stress, Darcy number and slip parameter on the pumping characteristics are discussed through graphs.

Keywords : Peristaltic transport, Bingham fluid, permeable walls.

I. INTRODUCTION

Peristaltic transport is a form of fluid transport that occurs when a progressive wave of area contraction or expansion propagates along the length of a distensible channel/tube containing the fluid. Peristalsis is used by a living body to propel or mix the contents of the tube such as, transport of urine from the kidney through the ureter to the bladder, food through the digestive tract, bile from the gall bladder into the duodenum, movement of ovum in the fallopian tube etc. It is accepted that most of the physiological fluids behave like non-Newtonian fluids. This approach provides a satisfactory understanding of the peristaltic mechanism involved in small blood vessels, lymphatic vessels, intestine, ductus efferentus of the male reproductive tract and in transport of spermatozoa in the cervical canal.

Nicoll and Webb (1946) and Nicoll reported that peristalsis plays an important role in blood circulation. Some theoretical and experimental investigations have been made on the peristaltic motion of blood considering blood as a non-Newtonian fluid. Latham (1966) first made an experiment to study the fluid mechanics of peristaltic transport. Base on this experiment work.

Shapiro et al. (1971) made a study on peristaltic pumping a tube and a channel under the assumptions of low Reynolds number and long wave lengths.

Peristaltic transport of chyme modeled by a nonNewtonian fluid or power-law fluid in small intestine and oesophagus has been studied by Srivastava and Srivastava (1985)

El Shehawey et al. (1999) investigated the peristaltic flow of a Newtonian fluid through a porous medium. Mekheimer and Al-Arabi (2003) have discussed the peristaltic flow of a Newtonian fluid through a porous medium in a channel under the effect of magnetic field. Elshahed and Haroun (2005) discussed peristaltic flow of a Johnson Segalman fluid under the effect of a magnetic field. Ravi Kumar et al. (2010) studied the peristaltic pumping in a finite lengths tube with permeable wall. Most of the researchers considered various non-Newtonian fluid models under peristaltic transport. Ravi Kumar et al. (2011) considered power-law fluid in an asymmetric channel with permeable walls under peristalsis in their studies. Krishna Kumari et al. (2011) studied the peristaltic pumping of a Casson fluid in an inclined channel under the effect of a magnetic field.

In view of this, peristaltic pumping of a Bingham fluid in a channel with permeable walls is studied under long wavelength and low Reynolds number assumptions. The effect of various parameters on the pumping characteristics is discussed through graphs.

II. MATHEMATICAL FORMULATION

Consider the peristaltic pumping of a Bingham fluid in a channel with permeable walls, under long wave length and low Reynolds number assumptions (Figure.1). The flow in a channel is governed by Navier - Stokes equations whereas


18

the flow in the permeable wall is described by Darcy’s law. The channel is of half width ‘a ’.

The region between 0y = and 0y y= is called

plug flow. In this region 0yxτ τ≤ . In the region

between 0y y= and hy = , we have 0yxτ τ> .

The wall deformation is given by

2

( , ) s in ( )H X t a b X c tπ

λ= + −

(1)

where b is the amplitude, λ is the wave length ‘c’

is the wave speed.

Under the assumptions that the channel length is

an integral multiple of the wave length λ and the

pressure difference across the ends of the tube is

a constant, the flow becomes steady in the wave

frame(x,y)moving with velocity ‘c’ away from the

fixed frame (X,Y) The transformation between

these two frames is given by

x=X-ct, y=Y, u(x,y)=U(X-ct,Y)-c, v(x,y)=V(X-ct,Y)

where (U, V) are velocity components in the

laboratory frame and (u, v) are velocity

components in the wave frame.

We introduce the following non-dimensional

quantities:

After non-dimensionalisation (after dropping bars),

the governing equations and boundary conditions

become

0( )yy

p

y xτ ψ

∂ −∂− =

∂ ∂ (2)

0p

y

∂=

∂ (3)

00; yyψ ψ τ= = at 0y = (4)

1yDa u

yu ψ

α∂= − −∂

= at y h= (5)

where ψ is the stream function, Da=2

K

a,

α =Slip parameter, and 0τ is the yield stress.

SOLUTION OF THE PROBLEM

Solving equation (2) and (3) subject to the boundary conditions (4) and (5) we obtain the velocity as

2 20

02

2[1 (1 )] 1 ( )

2

Ph y y DaPh

h Ph hu

τ τα

− − − − + −=

(6)

We find the upper limit of plug flow region using the boundary condition that

yyψ =0 at 0y y= so we have 00 P

yτ=

Also by using the condition yx hττ = at y h=

we obtain h

hP

τ=

Hence, 0 0 ,0 1h

y

h

ττ

τ τ= = < < (7)

Taking 0y y= in equation (6) and using the

relation (7) we get the velocity in plug flow region as

220

0 0 [(1 ) ( )] 1,02P

yPh DaPh y y

hu τ

α= − + − − ≤ ≤ (8)


19

Integrating the equations (6) and (8) and using the

conditions Pψ = 0 at 0y = , and pψ ψ= at

0y y=

we get stream function as

2

3 3 002

2

0 021

[ ( ) ( )] ( ) ,02 3 2

Ph y Day y y y y Ph y y y

h h h

τ τα

ψ=− + − − − − + − ≤ ≤

(9)

The volume flux q through each cross – section on the wave frame is give by

0

00

y y

y

Pu udyq dy= +∫ ∫

3

3 20 03 1[1 ( ) ( ) ] (1

3 2 2)

y yPh Dah h

h h ατ− + − + −= (10)

The instantaneous volume flow rate Q(x, t) in the laboratory frame between the centre line and the permeable wall is

0

( , , )( , )h

U X Y t dyQ X t = ∫3

3 20 0 03 1[1 ( ) ( ) ] (1 )

3 2 2

y y yPh Dah

h h hα− + + −=

(11)

From equation (10) we have

3 3 20 0 03 1[1 ( ) ( ) 3 (1 )

2 2

3( )dP

dx y y yDah

h h h

q h

hα

=− + + −

− +

3 233 1[1 ] 3 (1 )

2 2

3( )Da

h

q h

hα

ττ τ=

− + + −

− + (12)

Averaging equation (2.11) over one period

yields the time mean flow Q as

0

11

T

Q Qdt qT

= = +∫ (13)

Integrating the equation (12) with respect to x over one wave length, we get the pressure rise over one cycle of the wave as

1

3 3 20

3( )

3 1[1 ] 3 (1 )

2 2

q hdx

Dah h

Pτ τ τ

α

+

− + + −∆ = −∫ (14)

where ( ) 1 sin 2h x xφ π= +

The time average flux at zero pressure

rise is denoted by 0Q and the pressure rise

required to produce zero average flow rate is

denoted by 0P∆ so we have

1

3 3 20

0(3 3)

3 1[1 ] 3 (1 )

2 2

hdx

Dah h

Pτ τ τ

α

−= −− + + −

∆ ∫

(15)

It is observed that when 0τ → and Da 0→ equation (6), (10) and (14) reduce to the corresponding results of Jaffrin and Shapario (1971) for the peristaltic transport of a Newtonian fluid in a channel.

The dimensionless friction force F at the wall across one wave length is given by

1

0

( )dP

hdx

F dx−= ∫

1

30 2

3( )

3 1[1 ] 3 (1 )

2 2

q h

Dah h

dxτ τ τ

α

+=− + + −

∫

(16)


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III. DISCUSSION OF THE RESULT

From equation (14), we have calculated the

pressure difference as a function of Q for different

values of τ, the ratio of yield stress to the wall

shearing stress for a fixed amplitude ratio (φ ),

Darcy number (Da), and slip parameter (α ) is shown in figure (2). It is observed that for a Bingham fluid, the peristaltic wave passing over the channel wall pumps against more pressure rise

( P∆ ) compared to Newtonian fluid. This type of behaviour may be due to the presence of plug flow in Bingham fluid. Further, we observe that there is no difference in flux for Bingham fluid and

Newtonian fluids for free pumping case ( P∆ =0).

For a given P∆ the flux Q for a Bingham fluid

depends on yield stress and it increases with increasing yield stress.

The variation of pressure rise with time averaged flow rate is calculated from equation (14)

for different amplitude ratios (φ ) and is shown in

figure (3) for fixed τ =0.2, Da=0.001, α =0.1. We observe that the higher the amplitude ratio, the greater the pressure rise against which the pump

works. For a given P∆ , the flux Q for Bingham

fluid depends on yield stress and it increases with

increasingφ .

From equation (14), we have calculated

the pressure difference as a function of Q for

different values of Darcy number Da, for fixed

φ =0.6, τ =0.2, α =0.1 and is shown in figure (4).

We observe that for a given ∆Ρ , the flux Q

depends on Darcy number and it decreases with increasing Darcy number Da. For free pumping the

flux Q is constant and it is independent of Da.

The variation of pressure rise with time averaged flow rate is calculated from (14) for different values of α and is shown in figure (5) for fixed Da=0.001,

τ =0.2 and φ =0.6. We observe that the longer

the slip parameter, the greater the pressure rise

against which the pump works. For a given ∆Ρ ,

the flux Q increases with increasing ‘α ’. For a

given flux Q , the pressure difference ∆Ρ

increases with increasing α .

From equation (16), we have calculated

the frictional force as a function of Q for fixed

φ =0.6, Da=0.001, α =0.1 and for different values

of τ and depicted of figure (6). As τ increases

the flux Q decreases for a given frictional force.

Further the frictional force for different amplitude ratios, different Darcy numbers , and different slip parameters is shown in the figures(7)-(9) and it is observed that the frictional force F has the opposite behavior compared to pressure rise

( P∆ ).

We have calculated the pressure rise from equation (15) required to produce zero average

flow rate 0P∆ as a function of the amplitude

ratioφ , Darcy number Da for different values of

τ and is shown in the figure (10). The value of

0P∆ is larger for Bingham fluid when compared to

Newtonian fluid ( 0τ = ). As φ →1, 0P∆

becomes indefinitely large for a given value of τ .

Fig 1: Physical Model


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Fig.2: The variation of P∆ with Q for

different τ with φ =0.6, Da=0.001, α=0.1


different φ with τ=0.2, Da=0.001, α=0.1


different Da with φ =0.6, τ=0.2, α=0.1


different α with φ =0.6, τ=0.2, Da=0.001,

Fig.6: The variation of F with Q for

different τ with φ =0.6, Da=0.001, α=0.1

Fig.7: The variation of F with Q for different φ with τ=0.2, Da=0.001, α=0.1


22

Fig.8: The variation of F with Q for

different Da with φ =0.6, τ=0.2, α=0.1

Fig.9: The variation of F with Q for different

Da with φ =0.6, τ=0.2, Da=0.001

Fig.10: The variation of ∆∆∆∆P0 with φφφφ for different ττττ with Da = 0.001, αααα = 0.1


23

REFERENCES: (1) Nicoll,P.A.,R.L.L., WEBB., A.nn.N.Y.A. Acd.Sci.46, 697 (1946) (2) Latham,T.W., Fluid motion in a Peristaltic pump, M.Sc, Thesis Cambridge, Mass: MIT-Press (1966). (3)Shapiro,A.H. and Jaffrin,M.Y Reflux in peristaltic pumping: Is it determined by the Eulerian or Lagrangian mean velocity? Trans ASME J.Appl.Mech, 38 (1971), 1060-1062. (4) Srivastava, L.M., and Srivastava, V.P. Peristaltic transport of a non– Newtonian fluid: application to the vas deferens and small intestine, Annals Biomed. Engng. 13(1985), 137-153. (5)El Shehawey,E.F., Mekheimer, Kh. S., Kaldas, S. F. and Afifi, N. A. S. Peristaltic transport through a porous medium, J. Biomath. 14 (1999). (6) Mekheimer Kh.S.,T.H. Al-Arabi, Non-linear peristaltic transport of MHD flow through a porous medium, Int. J. Math. Math. Sci. 26 (2003) 1663. (7) Elshahed, M. and Haroun, M. H. Peristaltic transport of Johnson-Segalman fluid under effect of a magnetic field, Math. Probl. Engng, 6 (2005), 663–677. (8)Y.V.K.RaviKumar, S.V.H.N.KrishnaKumari, M. V. Raman Murthy, S.Sreenadh, Unsteady peristaltic pumping in a finite length tube with permeable wall, Trans. ASME, Journal of Fluids Engineering, 32 (2010), 1012011 – 1012014. (9)Y.V.K.RaviKumar, S.V.H.N.Krishna Kumari P., M.V.RamanaMurthy, S.Sreenadh Peristaltic transport of a power-law fluid in an asymmetric channel bounded by permeable beds Advances in Applied Science Research 2(3) (2011), 396-406. (10)S.V.H.N.Krishna Kumari P., M.V.Ramana Murthy, M.Chenna KrishnaReddy,Y.V.K.Ravi Kumar, Peristaltic pumping of a magnetohydrodynamic Casson fluid in an inclined channel, Advances in Applied Science Research, 2(2) (2011), 428-436.


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