Heat & Mass Transfer Jan 2014

USN 10ME63

Sixth Semester B.E. Degree Examination, Dec.2013 lJan.201^4Heat and Mass Transfer

Time: 3 hrs. Max. Marks:100.::' Note: 1. Answer FIVEfull questions, selecting

.' ' at lesst TWO questions from each part."''':"": "':' ' 2. (Jse of heat transfer data book is permitted. : ::quoq uvvut ao lrcr rraaa

, PART_AI a. Explain briefly the mechanism of conduction, convection and radiation heat transfu:;.

_,'-' (06 Marks)

b. Witli iiketches, write down the mathematical representation of three commonly useddifferent types of boundary conditions for one dimensional heat. e(uation in rectangularcoordinates. (08 Marks)

c. A plate of thickness 'L' whose one side is insulated and the other side is maintained at atemperature Tr i5 dtphanging heat by convection to the surrounding area at a temperature T2,with atmospheric air being the outside medium. Write mathemitical formulation for onedimensional, steady Stste heat transfer, without heat generation. (06 Marks)

2 a- An electric cable of l0mm diameter is to be laid in atmosphere at 20'C. The estimatedsurface temperature of the cable due to heat generation is 65"C. Find the maximumpercentage increase in heat dissipation,,,*hen the wire is insulated with rubber havingK: 0.155 WmK. Take h: 8.5 WrnlK,,. , (06 Marks)Diflerentiate between the effectivenoss;,and efficiency of fins. (04 Marks)In order to reduce the thermal qesistance at the surface of a veftical plane wall (50 x 50cm),

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100 pin fins (1 cm diameter, 10sm long) are attached. If the pin fins are made of copperhaving a thermal conductivity of 300 WmK and the value of the surface heat transfercoefficient is 15 Wm2K,;,Calculate the decreur. in the thermal resistance. Also calculate theconsequent increase in heat transfer rate from the wall if it is ma@@ined.qt a temperature of200"c and the surroundings are ar 30oc. .Zr(j-{)} (r0 Marks)

3a. Show that fhel.'temperature distribution in a body during ]1id cooling is

givenov"ffi=+=*r[#) W-*%7i (06Marks).,..,":','',..,;.T, -T" ei ^ ( pCV / \

ThesGel ball bearings (K: 50 WmK, o : 1.3 x 10-5 m2lsec), er are heated_ _--::::::/,,to'atemperature of 650"C. It is then quenched in a oil bath at 50oC, where the heat transfercoefficient is estimated to be 300 Wm2K. Calculate:' i) The time required for bearings to reach 200"C.

::ii) The total amount of heat removed from a bearing during this time andiii) The instantaneous heat transfer rate from the bearings, when they are flrst immersed in

oil bath and when thev reach 200'C. (14 Marks)

4 a. With reference to fluid flow over a flat plate, discuss the concept of velocity boundary andthermal boundary layer, with necessary sketches. (05 Marks)

b. The exact expression for local Nusselt number for the laminar flow along a surface is givenhxbv Nu' = ,xz\

- 0.332 nll' pJ". Show that the average heat transfer coefficient fromr x k

-'--- --e\ -r

x : 0 to x : L over the length 'L' of the surface is given by 2hr where hl is the local heat

b.

transfer coefficient at x: L.I of2

(05 Marks)

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5a.b.

7a.

ii) , The increase in bulk temperature of air over a 4m length of the tube., ' .

Tale,ths following properties for air pr : 0.6g1, trt:2.57 x 10-5 kg/mi; K : 0.03g6 wmKand Co = 1.025 kJ/kg K. (ro Marks)c. Obtain a ielationship between drag coefficient, c. and heat transf,er'coefficient, hn,, for thellow over a flat plate.r.*." (06 Marks)

a' Derive an expression for LMTD of a counter flow heat exchanger. State the assumptions

b. What is meant by the term fouling factor? How do you determine it? (04 Marks)c' Engine oil is to be coded from 80'C to 50'C by using a single pass counter flow, concentrictube heat exchanger with cooling water available ul20"C. Water flows inside a tube withinner diameter of 2.5cm and at a rate of 0.08 kg/sec and oil flows through the annulus at therate of 0.16 kg/sec. The heat transfer coeficient for the water side and oil side arerespectively h," : 1000 Wm2oC and h.l : 80 Wm2oC. The fouling factors isF,: 0.00018m2oC/W on both the sides ard the tube wall resistance is negligible. Calculatethe tube length required. (08 Marks)

10ME63

A vertical plate 15cm high and 10cm wide is maintained at 140"C. Calculate the maximumheat dissipation rate from both the sides of the plates to air at 20oC. The radiation heattransfercoefficient is 9.0 wm2K. Forairat 80.c, take r:2L09 x 10-6 ni/sec,pr:0.692,kr: o.o3 wmK. (lo Marks)

PART - BExplain the physical signiflcance of i) Nusselt number; ii) Groshoffnumber. (04 Marks)Air at 2 atm and 200oC is heated as it flows at a velocity of 12 m/sec through a tube with adiameter of 3cm. A constant heat flux condition is maintained at the wJl and the wallt-emperature is 20oC above the air temperature all along the length of the tube. Calculate:i) The heat transfer per unit length of tube. .,

,

Sketch a pool boiling curvq for water and explain'briefly the various regimes in boiling heattransfer. ,,, ,-'''. '

?..1". mass transfer coerficient. [8iXff[]A l2cm outside diameter and 2m long tube is used in a big condenser to condense the steamn 0.1 bar,-Estr3{e the unit surface conductance i) in iertical position; iil i, horizontalposition. Also find the amount of condensate formed per hour infin the cases.The satutation temperature of the steam :74.5"C.Aver,age wall temperature : 50.C.

-?The'properties of water film at average temperature of 75'4j50

=62.7oC are given belowl-p:982.2kglm3, hr_ =2480kJ/kg,K:0.65WmK, p:0.47 x 10-3kg/ms. '' \liolvrarks)

(06 Marks)

(06 Marks)function of geometry

(08 Marks)

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b.

c.

8a.b.

State and prove Wiens displacement law of radiation.The temperature of a black surface 0.2rfi in area is 540.c. calculate:i) The total rate of energy emission.ii) The intensity of normal radiation.

Iti) The wavelength of maximum monochromatic emissive power.Derive an expression for a radiation shape factor and show that it is aonly.

c.





Heat & Mass Transfer Jan 2014

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