Natural and Forced Convection Experiment

INME 42361

Table of Contents

Principle 3

Objective 3

Background 3

Newton’s law of cooling 3

Experimental Setup 5

Description of the Equipment: 5

Useful Data 6

Procedure 7

1. Free convection experiments 7

o Observations 7

o Analysis of results 7

o Comparison to theoretical correlations 8

2. Forced convection experiments 9

o Observations 9

o Analysis of results 9

o Comparison to theoretical correlations 9

3. Procedure for transient experiments 10

Tasks Required for Steady State Experiments 11

Tasks Required for Transient Experiments 11

INME 42362

University of Puerto RicoMayagüez Campus

Department of Mechanical Engineering

INME 4236 - Thermal Sciences Laboratory

Natural And Forced Convection Experiment

Principle

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

and to understand how the heat transfer coefficient is obtained experimentally. Natural

and forced convection over a heated cylinder is analyzed and experimental results are

compared with standard correlations.

Objectives

1. Determine the heat transfer coefficient for flow around a cylinder under free and

forced convection.

2. Understand the correlation between Nu, Reynolds and Rayleigh numbers.

3. Compare with standard correlations from textbooks on heat transfer.

4. Determine the effect of thermal radiation for both natural and forced convection.

5. Study the transient temperature response of a solid object as it cools due to

natural or forced convection.

Background

Newton’s Law of Cooling

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

cooling and is expressed as:

)( ∞−=′′ TThq s

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Where Ts is the surface temperature, T∞ the fluid temperature, h is the convection heat

transfer coefficient and q” is the convective heat flux. The heat transfer 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 fluid properties as well.

The normalized momentum and energy equations for a boundary layer can be

expressed as follows,

2*

*2

*

*

*

**

*

**

Re

1

y

U

x

P

y

UV

x

UU

L ∂∂+

∂∂−=

∂∂+

∂∂

2*

*2

*

**

*

**

PrRe

1

y

T

y

TV

x

TU

L ∂∂=

∂∂+

∂∂

.

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

form for U* and T* can be written as,

U* = f(x*,y*,ReL, dp*/dx*),

T* = f(x*,y*,ReL, Pr, dp*/dx*).

Due to the no-slip condition at the wall surface of the boundary layer, heat transfer

occurs by conduction between the solid and the fluid molecules at the wall,

0

"

=∂∂−=

y

fs y

Tkq .

By combining Fourier’s Law evaluated at the wall with Newton’s law of cooling, we can

define the heat transfer coefficient as follows,

∞

=

−∂∂

−=TT

y

Tk

hs

y

f

0 .

In this analysis, T* is defined as s

s

TT

TTT

−−=

∞

* and as a result, h can be written in terms of

this dimensionless temperature profile T* as follows,

0

*

*

0

*

*

**)(

)(

==∞

∞

∂∂=

∂∂

−−

−=y

f

ys

sf

y

T

L

k

y

T

TTL

TTkh

This expression suggests defining a dimensionless parameter,

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0

*

*

* =∂∂==

yf y

T

k

hLNu .

The dimensionless temperature profile implies a functional form for the Nusselt number

that depends on other parameters also,

Nu = f(x*,ReL*,Pr,dp*/dx*).

To calculate an average heat transfer coefficient, we have to integrate over x *, so the

average Nusselt number becomes independent of x*. For a prescribed geometry, *

*

dx

dp is

a result of the flow field and can be determined and specified and so the average

Nusselt number becomes,

Pr),(ReLL fNu =

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

of the Reynolds and Prandtl numbers.

Doing a similar analysis for free convection, it can be shown that, Pr),Gr(fNu = or

Pr),Ra(fNu = .

Gr is the Grashof number and Ra is the Rayleigh number. The Rayleigh number is

simply the product of Grashof and Prandtl numbers (Ra = Gr Pr). For free convection,

the Nusselt number is a universal function of the Grashof and Prandtl numbers or

Rayleigh and Prandtl numbers.

Experimental setup

Description of the Combined Convection and Radiation Heat Transfer Equipment:

The combined convection and radiation heat transfer equipment (Figure 1) allows

investigating the heat transfer of a radiant cylinder located in a crossflow of air and the

effect of increasing the surface temperature. The unit allows investigation of both

natural convection with radiation and forced convection. The experimental setup is

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designed such that heat loss by conduction through the wall of the duct is minimized. A

thermocouple (T10) is attached to the surface of the cylinder. The surface of the cylinder

is coated with a matt black finish, which results in an emissivity close to 1.0. The

experimental setup allows the cylinder and thermocouple (T10) position to be turned

360° and locked in any position using a screw. An index mark on the end of the setup

allows the actual position of the surface to be determined. The cylinder can reach a

temperature in excess of 600°C when operated at maximum voltage and still air. The

recommended maximum for the normal operation is 500°C. Beware of hot

surfaces.

Useful Data:

Cylinder diameter D = 1.0 cm

Cylinder heated length L = 7.0 cm

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

where Ue is the effective fluid velocity and Ua is the fluid incoming velocity.

Physical properties of air at atmospheric pressure: Appendix of Heat Transfer textbook.

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Figure 1. Combined Convection and Radiation Heat Transfer Equipment.

Procedure for convection experiments

a) Connect instruments to the heat transfer unit

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

and velocity of the air flow and the power supplied by the heater.

c) Repeat step 2 for different velocities the air flow and various levels of power

input.

1. Free convection experiments

Observations

SetV I T9 T10

Volts Amp °C °C1 32 63 94 125 156 18

Analysis of results

SetQinput hr hC hC1th hC2th

W W/m2K W/m2K W/m2K W/m2K123456

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The total heat input is,

Qinput = V×I

The heat transfer rate by radiation is,

Qrad = ε σ A (Ts4 – Ta4) = hr A (Ts – Ta).

So,

as

4a

4s

r TT

)T(T σ εh

−−=

The heat transfer rate by convection is then,

Qconv = Qinput - Qrad

From Newton’s law of cooling,

)TA(ThQ ascconv −=

And finally we can determine the heat transfer coefficient as follows,

)TA(T

Qh

as

convc −

= .

You must report these results for all the data points collected.

Comparison to theoretical correlations

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

nDD Ra C

k

D hNu ==

C and n are a coefficient and exponent respectively that depend on the Rayleigh

number as shown in the following table.

Rayleigh number C n10-10 – 10-2 0.675 0.058

10-2 – 102 1.02 0.148

102 – 104 0.850 0.188

104 – 107 0.480 0.250

107 – 1012 0.125 0.333

The Rayleigh number defined as,

Prυ

D )T(T β gRa

2

3as −= ,

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where β is the compressibility and for an ideal gas is calculated as β = 1/T film (Tfilm in

absolute scale) and Tfilm = ½(Ts+Ta).

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

numbers,

NuD={0.600.387 Ra1 /6

[10.559/Pr 9/16 ]8 /27 }

2

, Ra <1012

From both correlations, we can determine hC1th and hC2th and compare with hc obtained

from the experiment.

2. Forced convection

Observations

SetV I Ua T9 T10

Volts Amp m/s °C °C1 0.52 13 24 35 46 57 6

Analysis of results

SetQinput hr hC Re Nu1 Nu2 hC1th hC2th

W W/m2K W/m2K - - - - -1234567

Comparison with theoretical correlations

For an isothermal long horizontal cylinder, Hilper suggests the following correlation,

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3/1PrRemDD Ck

DhNu == ,

where C and m are coefficients that depend on the Reynolds number.

ReD C m0.4-4 0.989 0.3304-40 0.911 0.385

40-4000 0.683 0.4664000-400000 0.193 0.618

40000-400000 0.027 0.805

All properties are evaluated at the film temperature,

2

TTT as

film

+= .

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

NuD=0.30.62 Re1 /2 Pr1 /3

[1 0.4Pr

2/3

]1/4 [1ReD

282000 5 /8

]4/5

,

where all properties are evaluated at the film temperature.

Using both Hilper’s and Churchill and Bernstein’s correlations we can determine the

theoretical heat transfer coefficient values hC1th and hC2th and compare with the value

obtained from the experiment hc.

3. Procedure for transient experiments

1. Start the heat transfer unit and set a voltage between 15 - 18 volts.

2. Start the heater until a steady state temperature is obtained on the heater

surface without operating the fan. Record the current, voltage, ambient

temperature (T9) , and initial surface temperature (T10).

3. Using a chronometer record the time and measure the surface temperature (T10)

to generate a time series table of at least 20 data points when the heater power

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is turned off and the fan is operating at a predetermined speed between 2 - 6

m/s.

4. Repeat steps 2 and 3 for the same power input but without operating the fan

during the transient.

Tasks Required for Steady State Experiments

You will collect all the experimental data required during the experiments for both

natural and forced convection and will include this data in your report. In addition to the

required analysis and comparison with correlations, you will generate the following plots

for both natural and forced convection experiments:

(a) Surface temperature vs heat input to cylinder for the natural convection experiment.

(b) Surface temperature vs incoming fluid velocity for the forced convection experiment.

(c) On the same graph, plot the Nusselt numbers determined from the experimental

data and correlations vs Rayleigh or Reynolds number depending on the case.

(d) Show tables comparing the experimental values to the predicted values using the

respective correlations and calculate the percentage difference between these values.

(e) What is the contribution of radiative heat transfer to the process?

Tasks Required for Transient Experiments

(a) Generate graphs that show the surface temperature versus time in order to compare

to the expected theoretical temperature values on the same graph.

(b) Calculate the experimental and theoretical heat transfer rate from the system to the

surroundings as a function of time and present the results in graphical form.

(c) Report the experimental and theoretical thermal time constant of the system.

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(d) What is the contribution of radiative heat transfer to the process? Discuss the

effectiveness of the lumped thermal capacitance model to describe the transient

temperature response of the cylinder.

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