Natural and Forced Convection Experiments-2

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Experiment2Experiment2 INME 4032INME 40321



Table of ContentsTable of Contents

PrinciplePrinciple 33

ObjectiveObjective 33

BackgroundBackground 33

•• Newton’s law of coolingNewton’s law of cooling 33

Experimental SetupExperimental Setup 55

•• Description of the Combined Convection and RadiationDescription of the Combined Convection and Radiation

Heat Transfer Equipment:Heat Transfer Equipment: 55

Useful DataUseful Data 66

ProcedureProcedure 77

1 .1 . Free convection experimentsFree convection experiments 88

ObservationsObservations 88

Analysis of resultsAnalysis of results 88

Comparison to theoretical correlationsComparison to theoretical correlations 99

2 .2 . Forced convection experimentsForced convection experiments 1010

ObservationsObservations 1010

Analysis of resultsAnalysis of results 1010

Comparison to theoretical correlationsComparison to theoretical correlations 1111

DiscussionDiscussion 1212




University of Puerto RicoUniversity of Puerto RicoMayagüez CampusMayagüez Campus

Department of Mechanical EngineeringDepartment of Mechanical Engineering

INME 4032 - LABORATORY IIINME 4032 - LABORATORY II

Spring 2004Spring 2004 Instructor: Guillermo ArayaInstructor: Guillermo Araya

ExperimentExperiment 22:: Natural And Forced Convection ExperimentNatural And Forced Convection Experiment

PrinciplePrinciple

This experiment is designed to illustrate the Newton’s law of cooling by This experiment is designed to illustrate the Newton’s law of cooling by

convection and to understand how the heat transfer coefficient is obtainedconvection and to understand how the heat transfer coefficient is obtained

experimentally. Natural and forced convection over a heated cylinder isexperimentally. Natural and forced convection over a heated cylinder is

analyzed and experimental results are compared with standard correlations.analyzed and experimental results are compared with standard correlations.

ObjectiveObjective

Determine the heat transfer coefficient for a flow around a cylinder underDetermine the heat transfer coefficient for a flow around a cylinder under

free and forced convection. Understand the correlation between Nu,free and forced convection. Understand the correlation between Nu,

Reynolds and Rayleigh numbers. Compare with standard correlation fromReynolds and Rayleigh numbers. Compare with standard correlation from

textbooks on heat transfer. The effect of thermal radiation is also included.textbooks on heat transfer. The effect of thermal radiation is also included.

BackgroundBackground

Newton’s law of coolingNewton’s law of cooling

For convective heat transfer, the rate equation is known as Newton’s law of For convective heat transfer, the rate equation is known as Newton’s law of

cooling and is expressed as:cooling and is expressed as:

)( ∞−=′′ T T hq s

Where Ts is the surface temperature, TWhere Ts is the surface temperature, T∞∞ the fluid temperature, h thethe fluid temperature, h the

convection heat transfer coefficient andconvection heat transfer coefficient and q ′′ the convective heat flux. The heatthe convective heat flux. The heat

transfer coefficient h is a function of the fluid flow, so, it is influenced by thetransfer coefficient h is a function of the fluid flow, so, it is influenced by the

surface geometry, the fluid motion in the boundary layer and the fluidsurface geometry, the fluid motion in the boundary layer and the fluid

properties as well.properties as well.




From the normalized momentum and energy equation in the boundary layer:From the normalized momentum and energy equation in the boundary layer:

2*

*2

*

*

*

**

*

**

Re

1

y

U

x

P

y

U V

x

U U

L ∂

∂+

∂

∂−=

∂

∂+

∂

∂

Momentum equationMomentum equation

2*

*2

*

**

*

**

Pr Re

1

y

T

y

T V

x

T U

L ∂

∂=

∂

∂+

∂

∂

Energy equationEnergy equation

Independently of the solution of these equations for a particular case, theIndependently of the solution of these equations for a particular case, the

functional form for Ufunctional form for U** and Tand T** can be written as:can be written as:

UU** = f(x= f(x**,y,y**,Re,ReLL, dp, dp**/dx/dx**))

andand

T T** = f(x= f(x**,y,y**,Re,ReLL, Pr, dp, Pr, dp**/dx/dx**))

Heat transfer, due to the no-slip condition at the wall surface of the boundaryHeat transfer, due to the no-slip condition at the wall surface of the boundary

layer, occurs by conduction;layer, occurs by conduction;

0y

f

"

s

y

Tk q

∂

∂−=

By combining with the Newton’s law of cooling, we obtain:By combining with the Newton’s law of cooling, we obtain:

∞

=

−

∂

∂

−=TT

y

Tk

hs

0y

f

SinceSince T T ** was defined aswas defined as

s

s*

TT

TTT

−

−=

∞

hh can be written in terms of the dimensionless temperature profilecan be written in terms of the dimensionless temperature profile T T **

0

*

*

0

*

*

**)(

)(

==∞

∞

∂

∂=

∂

∂

−

−−=

y

f

y s

s f

y

T

L

k

y

T

T T L

T T k h

This expression suggests defining a dimensionless parameter; This expression suggests defining a dimensionless parameter;




0y

*

*

f *y

T

k

hL Nu

=∂

∂==

From the dimensionless temperature profiles, we can imply a functional formFrom the dimensionless temperature profiles, we can imply a functional form

for the Nusselt number,for the Nusselt number,

Nu = f(xNu = f(x**,Re,ReLL**,Pr,dp,Pr,dp**/dx/dx**))

To calculate an average heat transfer coefficient, we have to integrate over To calculate an average heat transfer coefficient, we have to integrate over

xx**, so the average Nusselt number becomes independent of x, so the average Nusselt number becomes independent of x**. For a. For a

prescribed geometry,prescribed geometry,*

*

dx

dpis specified andis specified and

Pr),(Ref Nu LL =

This means that the Nusselt number, for a prescribed geometry is a universal This means that the Nusselt number, for a prescribed geometry is a universal

function of the Reynolds and Prandtl numbers.function of the Reynolds and Prandtl numbers.

Doing a similar analysis for free convection, it can be shown that,Doing a similar analysis for free convection, it can be shown that,

Pr),Gr (f Nu = oror Pr),Ra(f Nu =

WhereWhere Gr Gr is the Grashof number andis the Grashof number and RaRa is the Rayleigh number. Theis the Rayleigh number. The

Rayleigh number is simply the product of Grashof and Prandtl numbers (Rayleigh number is simply the product of Grashof and Prandtl numbers (RaRa

= Gr Pr = Gr Pr ))

Then, for free convection the Nusselt number is a universal function of the Then, for free convection the Nusselt number is a universal function of the

Grashof and Prandtl numbers or Rayleigh and Prandtl numbers.Grashof and Prandtl numbers or Rayleigh and Prandtl numbers.

Experimental setupExperimental setup

Description of the Combined Convection and Radiation HeatDescription of the Combined Convection and Radiation Heat

Transfer EquipmentTransfer Equipment::

The combined convection and radiation heat transfer equipment allows The combined convection and radiation heat transfer equipment allows

investigate the heat transfer of a radiant cylinder located in flow of air (crossinvestigate the heat transfer of a radiant cylinder located in flow of air (cross




flow) and the effect of increasing the surface temperature. The unit allowsflow) and the effect of increasing the surface temperature. The unit allows

investigation of both natural convection with radiation and forcedinvestigation of both natural convection with radiation and forced

convection. The mounting arrangement is designed such that heat loss byconvection. The mounting arrangement is designed such that heat loss by

conduction through the wall of the duct is minimized. A thermocouple (Tconduction through the wall of the duct is minimized. A thermocouple (T1010) is) is

attached to the surface of the cylinder. The surface of the cylinder is coatedattached to the surface of the cylinder. The surface of the cylinder is coated

with a matt black finished, which gives an emissivity close to 1.0. Thewith a matt black finished, which gives an emissivity close to 1.0. The

cylinder mounting allows the cylinder and thermocouple (T10) position to becylinder mounting allows the cylinder and thermocouple (T10) position to be

turned 360° and locked in any position using a screw. An index mark on theturned 360° and locked in any position using a screw. An index mark on the

end of the mounting allows the actual position of the surface to beend of the mounting allows the actual position of the surface to be

determined. The cylinder can reach in excess 600°C when operated atdetermined. The cylinder can reach in excess 600°C when operated at

maximum voltage and in still air.maximum voltage and in still air. However the recommended maximumHowever the recommended maximum for the normal operation is 500°Cfor the normal operation is 500°C..

Useful Data:Useful Data:

Cylinder diameter D = 0.01 mCylinder diameter D = 0.01 m

Cylinder heated length L = 0.07 mCylinder heated length L = 0.07 m

Effective air velocity local to cylinder due to blockage effect Ue = (1.22)Effective air velocity local to cylinder due to blockage effect Ue = (1.22)××

(Ua )(Ua )

Physical Properties of Air at Atmospheric PressurePhysical Properties of Air at Atmospheric Pressure

T T V V kk PrPr

K K mm22/s/s W/mK W/mK --

300300 1.568E-51.568E-5 0.026240.02624 0.7080.708

350350 2.076E-52.076E-5 0.030030.03003 0.6970.697

400400 2.590E-52.590E-5 0.033650.03365 0.6890.689450450 2.886E-52.886E-5 0.037070.03707 0.6830.683

500500 3.790E-53.790E-5 0.040380.04038 0.680.68

550550 4.434E-54.434E-5 0.043600.04360 0.680.68

600600 5.134E-55.134E-5 0.046590.04659 0.680.68

Where:Where:




T is the absolute temperature, T is the absolute temperature, V V is the Dynamic viscosity of air, k is theis the Dynamic viscosity of air, k is the

thermal conductivity and Pr is the Prandtl number.thermal conductivity and Pr is the Prandtl number.

ProcedureProcedure

a )a ) Connect instruments to the heat transfer unitConnect instruments to the heat transfer unit

b )b ) Measure the reading for the surface temperature of the cylinder, theMeasure the reading for the surface temperature of the cylinder, the


Combined Convection and RadiationCombined Convection and Radiation Heat Transfer EquipmentHeat Transfer Equipment Schematic Diagram showing theSchematic Diagram showing the

Combined Convection and RadiationCombined Convection and Radiation Heat Transfer E ui mentHeat Transfer E ui ment



temperature and velocity of the air flow and the power supplied by thetemperature and velocity of the air flow and the power supplied by the

heater.heater.

c )c ) Repeat steps 1 and 2 for different velocities the air flow and powerRepeat steps 1 and 2 for different velocities the air flow and power

input.input.

Free convection experimentsFree convection experiments

ObservationsObservations

SetSetVV II T T99 T T1010

VoltsVolts AmpAmp °°CC °°CC

11 44

22 88

33 1212

44 1616

Analysis of resultsAnalysis of results

SetSetQQinputinput hhrr hhC1thC1th hhC2thC2th

WW W/mW/m22K K W/mW/m22K K W/mW/m22K K

11 44

22 88

33 1212

44 1616

The total heat input is: The total heat input is:

QQinputinput = V= V×× II

The heat transfer rate by radiation is: The heat transfer rate by radiation is:

QQradrad == εε σσ A (TA (Tss44 – Ta– Ta44) = h) = hrr A (TA (Tss – T– Taa))

So,So,




a s

a s

r T T

T T h

−−

=)(

44ε σ

The heat transfer rate by convection is: The heat transfer rate by convection is:

QQconvconv = Q= Qinputinput - Q- Qradrad

From Newton’s law of coolingFrom Newton’s law of cooling

)( a scconvT T AhQ −=

AndAnd

)( a s

conv

cT T A

Qh

−=

Comparison to theoretical correlationsComparison to theoretical correlations

For an isothermal long horizontal cylinder, Morgan suggests a correlation of For an isothermal long horizontal cylinder, Morgan suggests a correlation of

the form,the form,

n

DD cRak

Dh Nu == (1)(1)

c and n are coefficients that depend on the Rayleigh numberc and n are coefficients that depend on the Rayleigh number

RayleighRayleigh numbernumber

cc nn

1010-10-10 – 10– 10-2-2 0.6750.675 0.0580.058

1010-2-2 – 10– 1022 1.021.02 0.1480.148

101022 – 10– 1044 0.8500.850 0.1880.188

101044

– 10– 1077

0.4800.480 0.2500.250101077 – 10– 101212 0.1250.125 0.3330.333

The Rayleigh number is calculated from, The Rayleigh number is calculated from,




Pr D)TT(g

Ra2

3

as

υ−β

=

wherewhere

filmT

1=β

andand

2

TTT asfilm

+=

Churchill and Chu recommend a single correlation for a wide range ofChurchill and Chu recommend a single correlation for a wide range of

Rayleigh number,Rayleigh number,

[ ]

2

27/816/9

6/1

D

Pr)/559.0(1

Ra387.060.0 Nu

++= 12

10Ra ≤ (2)(2)

From correlation (1) and (2) we can determine hFrom correlation (1) and (2) we can determine hC1thC1th and hand hC2thC2th and compareand compare

with hwith hcc obtained from the experiment.obtained from the experiment.

Forced convectionForced convection

ObservationsObservations

SetSetVV II VVaa T T99 T T1010

VoltsVolts AmpAmp m/sm/s °°CC °°CC

11 2020 0.50.5

22 2020 1133 2020 22

44 2020 33

55 2020 44

66 2020 55

77 2020 66

Analysis of resultsAnalysis of results




SetSetQQinputinput hhrr hhCC ReRe NuNu11 NuNu22 hhC1thC1th hhC2thC2th

WW W/mW/m22K K W/mW/m22K K -- -- -- -- --

11

22

3344

55

66

77

The total heat input is: The total heat input is:

QQinputinput = V= V×× II

The heat transfer rate by radiation is: The heat transfer rate by radiation is:

QQradrad == εε σσ A (TA (Tss44 – Ta– Ta44) = h) = hrr A (TA (Tss – T– Taa))

So,So,a s

a s

r T T

T T h

−−

=)(

44ε σ

The heat transfer rate by convection is: The heat transfer rate by convection is:

QQconvconv = Q= Qinputinput - Q- Qradrad

From Newton’s law of coolingFrom Newton’s law of cooling

)( a scconv T T AhQ −=

andand

)TT(A

Qh

as

conv

c−

=

Comparison with theoretical correlationsComparison with theoretical correlations

For an isothermal long horizontal cylinder, Hilper suggests,For an isothermal long horizontal cylinder, Hilper suggests,

3/1m

DD Pr ReCk

Dh Nu == (3)(3)




where C and m are coefficient that depend on the Reynolds number:where C and m are coefficient that depend on the Reynolds number:

ReReDD CC mm

0.4-40.4-4 0.9890.989 0.3300.330

4-404-40 0.9110.911 0.3850.385

40-400040-4000 0.6830.683 0.4660.466

4000-4000004000-400000 0.1930.193 0.6180.618

40000-40000040000-400000 0.0270.027 0.8050.805

All properties are evaluated at the film temperatureAll properties are evaluated at the film temperature

2

TTT asfilm

+=

Churchill and Bernstein proposed the following correlation for Re Pr>0.2Churchill and Bernstein proposed the following correlation for Re Pr>0.2

5/48/5

D

4/13/2

3/12/1

D282000

Re1

Pr

4.01

Pr Re62.03.0 Nu

+

+

+=(4)(4)

where all properties are evaluated at the film temperature.where all properties are evaluated at the film temperature.

From correlation (3) and (4) we can determine hFrom correlation (3) and (4) we can determine hC1thC1th and hand hC2thC2th and compareand compare

with hwith hcc obtained from the experiment.obtained from the experiment.

DiscussionDiscussion


Natural and Forced Convection Experiments-2

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