İzmir Institute of TechnologyCHEMICAL ENGINEERING DEPARTMENT

2008-2009 Spring Semester

CHE 310CHEMICAL ENGINEERING LABORATORY I

Thermal ConductivityThermal Conductivity

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THERMAL CONDUCTIVITY

1. OBJECTIVES

To understand the use of the Fourier’s law in determining heat rate through solids. To determine the thermal conductivityof a material, k. To determine the Overall Heat Transfer Coefficient for the flow of heat through a combination of different materials in use. To demostrate the effect of cross sectional area on the heat rate. To demostrate the effect of contact resistance on thermal conduction between adjacent materials. To measure the temperature distribution for unsteady state conduction of heat through the uniform plane wall and the wall of the thick cylinder.

2. THEORY AND PRINCIPLES

Conduction (heat transfer by diffusion) is the transport of energy from the more energetic to the less energetic particles of a substance due to a temperature gradient, and the physical mechanism is that of random atomic and molecular activity. For one-dimensional, steady-state heat conduction in a plane wall with no heat generation, temperature is a function of the x coordinate only and heat is transferred exclusively in this direction. Thus, the temperature distribution for the heat conduction through plane wall must be linear as shown in Figure 1.

Ts,1

Ts,2

qx

x x=L

Figure-1: Heat transfer through a plane wall

The heat transfer rate (qx) by conduction through a plane wall is directly proportional to the cross sectional area (A) and the temperature difference (T), whereas it is inversely proportional to the wall thickness (x).

In addition to single plane wall, heat transfer through composite wall is also important. Such walls may involve any number of series and parallel layers made of different materials. In the case of steady state one-dimensional heat conduction with no

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heat generation, temperature profile through each layer becomes linear as shown in Figure 2. Heat transfer through composite systems is usually described by an overall heat transfer coefficient. Simply, the overall heat transfer coefficient is related to the total thermal resistance.

Ts,1

Ts,4

A B C

xA xB xC

Figure-2: Heat transfer through composite systems.

Cylindrical and spherical systems often experience temperature gradients in the radial direction only and may therefore treated as one dimensional. A common example is the hollow cylinder, whose inner and outer surfaces are exposed to fluids at different temperatures, as shown in Figure 3.

Figure-3: Heat transfer through radial systems

The temperature distribution associated with radial conduction through a cylindrical wall is logarithmic, not linear, as it is for the plane wall under the same conditions.

3) EXPERIMENTAL

3.1 THERMAL CONDUCTIVITY CALCULATION IN LINEAR SYSTEMS

Temperature distribution

QFlow

patternRo

Ri

HotFluid Thi

Tco

Thi

ColdFluid Tco

3

T2T3

kA kB kC

Experimental set-up for the linear conductive heat transfer system is shown in Figure 4.

Figure 4: Linear heat conduction unit.

A. Determine the effect of change of heat flow for steady state conduction of energy through a uniform plane

Procedure:

i) Smear the faces of the heated and cooled sections with thermal conducting paste and clamp them together without any intermediate section in place as illustrated in the following scheme.

ii) Ensure that the cooling water is flowing and then set the heater voltage V iii) Monitor temperature T1, T2, T3, T6, T7 and T8 until steady-state is reached.iv) When the temperatures are stabilized, record T1, T2, T3, T6, T7 and T8, V and

I.v) Reset the heater voltage and repeat the above procedure again recording the

parameters T1, T2, T3, T6, T7 and T8, V and I when temperatures have stabilised. vi) Reset the heater voltage and repeat the above procedure again recording the

parameters T1, T2, T3, T6, T7 and T8, V and I when temperatures have stabilised.

Specimen position

Heater

T8T7T6T5T4T3T2T1

Thermocouples

Cooling water inlet

Filter

Regulator

Valve

Insulation

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Q

V, I

B. Determine heat rate through solid materials for one dimensional, steady flow of heat

Procedure:

i) Smear the faces of the heated and cooled sections with thermal conducting paste and clamp them together with the Brass Intermediate Specimen in place as illustrated in the following scheme.

ii) Ensure that the cooling water is flowing and then set the heater voltage Viii) Monitor temperature T1, T2, T3, T4, T5, T6, T7 and T8 until steady-state is

reached.iv) When the temperatures are stabilized, record T1, T2, T3, T4, T5, T6, T7 and T8, V

and I.v) Reset voltage and repeat the above procedure again recording the parameters T1,

T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised.

C. Determine overall heat transfer coefficient for the flow of heat through a combination of different materials in use and determine the thermal conductivity k of a metal specimen

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xint

T1T2T3T4T5T6T7T8

QBRASS

V, I

FW

T1T2T3

T6T7T8FW

Procedure:i) Smear the faces of the heated and cooled sections with thermal conducting paste and clamp them together with the Stainless steel and Aluminium Intermediate Specimens in place as illustrated in the following scheme.

ii) Ensure that the cooling water is flowing and then set the heater voltage V for stainless steel specimen and for aluminium specimen.

iii) Monitor temperature T1, T2, T3, T6, T7 and T8 until steady-state is reached.iv) When the temperatures are stabilized, record T1, T2, T3, T6, T7 and T8, V and I.v) Reseet the voltage and repeat the above procedure again recording the parameters

T1, T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised.

D. Determine the effect of cross sectional area on the heat rate

Procedure:

i) Smear the faces of the heated and cooled sections with thermal conducting paste and clamp them together with the reduced diameter brass intermediate specimen in place as illustrated in the following scheme.ii) Ensure that the cooling water is flowing and then set the heater voltage Viii) Monitor temperature T1, T2, T3, T6, T7 and T8 until steady-state is reached.iv) When the temperatures are stabilized, record T1, T2, T3, T6, T7 and T8, V and I.v) Reset the voltage and repeat the above procedure again recording the parameters T1, T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised.

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T1T2T3T4T5T6T7T8

T1T2T3T4T5T6T7T8

FW FW

xint xint

V, I V, I

Stainless steel Aluminium

T1T2T3

T6T7T8

V, I

Q Q

Q

E. Determine the effect of contact resistance on thermal conduction between adjacent materials

Procedure:

i) Ensure that the faces of the heated and the cooled sections are cleaned of thermal conducting paste and that the brass intermediate section is also similarly cleaned.ii) Lightly coat the mating faces between the cooled section and the brass intermediate specimen with thermal paste and assemble them together.iii) Do not coat the mating faces of the heated section and the brass intermediate specimen with thermal paste and assemble.iv) Finally, do not clamp the assembly together as normal but leave the clamps open as illustrated in the following scheme.v) Ensure that the cooling water is flowing and then set the heater voltage V to approximately 12 voltsvi) Monitor temperature T1, T2, T3, T4, T5, T6, T7 and T8 until steady-state is reached.vii)When the temperatures are stabilized, record T1, T2, T3, T4, T5, T6, T7 and T8, V and I.viii)Reset the voltage and repeat the above procedure again recording the parameters

T1, T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised. ix) Clamp the sections together on the unit. Monitor temperatures T1, T2, T3, T4, T5,

T6, T7 and T8 until they become stable and then repeat the above readings.

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dredxred

FW

xint

T1T2T3T4T5T6T7T8

QBRASS

V, I

No thermal paste

Thermal paste

F. Determine the thermal conductivity,k of an insulation material

Procedure:

i) Ensure that the faces of the heated and cooled sections are cleaned of thermal conducting paste. ii) Select the thin cork disc provided, measure and record the thickness xint of the disc as accurately as possible ( A vernier gauge or micrometer is suitable). Place this between the heated and cooled sections then clamp the assembly together as illustrated in the following scheme.

ii) Ensure that the cooling water is flowing and then set the heater voltage Viii) Monitor temperature T1, T2, T3, T6, T7 and T8 until steady-state is reached.iv) When the temperatures are stabilized, record T1, T2, T3, T6, T7 and T8, V and I. v) Reset the voltage and repeat the above procedure again recording the parameters T1, T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised.

G. Observe unsteady state conduction of heat

Procedure:

i) Ensure that the faces of the heated and cooled sections are cleaned of thermal conducting paste.

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T1T2T3

T6T7T8

xint

Insulator

V, I

FW

Q

FW

ii) Select the thin cork disc provided and place this between the heated and cooled sections then clamp the assembly together as illustrated in the following scheme.

ii) Ensure that the cooling water is flowing.iii) Then disconnect the heater dc supply and then set the heater voltage Viv) Start a stopwatch to record regular time intervals and then reconnect the dc supply to the heater with the voltage still set at approximately 9 volts.v) Record V, I and T1 at regular time intervals of say 5 minutes.

USEFUL DATA FOR LINEAR HEAT CONDUCTION UNIT

Heated SectionMaterial: Brass, 25 mm diameter, Thermocouples T1, T2, T3 at 15 mm spacingThermal conductivity: Approximately 121 W/ mK

Cooled SectionMaterial: Brass, 25 mm diameter, Thermocouples T6, T7, T8 at 15 mm spacingThermal conductivity: Approximately 121 W/ mK

Brass Intermediate SpecimenMaterial: Brass, 25 mm diameter 30 mm long. Thermocouples T4, T5 at 15 mm spacing centrally spaced along the length Thermal conductivity: Approximately 121 W/ mK

Stainless Steel Intermediate SpecimenMaterial: Stainless steel, 25 mm diameter 30 mm long. No thermocouples fitted.Thermal conductivity: Approximately 25 W/ mK

Aluminium Alloy Intermediate SpecimenMaterial: Aluminium alloy, 25 mm diameter 30 mm long. No thermocouples fitted.Thermal conductivity: Approximately 180 W/ mK

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T1T2T3

T6T7T8

xint

Insulator

V, I

FW

Q

Reduced Diameter Brass Intermediate SpecimenMaterial: Brass, 13 mm diameter 30 mm long. No thermocouples fitted.Thermal conductivity: Approximately 121 W/ mK

Hot and Cold Face Temperatures

Due to the need to keep the spacing of the thermocouples constant at 15 mm with, or without the intermediate specimens in position, the thermocouples are displaced 7.5 mm back from the end faces of the heated and cooled specimens and similarly located for the brass Intermediate Specimen.

Thot face Tcold face

Thus, the temperatures of the hot and cold faces can be calculated from the following equations:

Thot face = T3 - Tcold face = T6 +

3.2 THERMAL CONDUCTIVITY CALCULATION IN RADIAL SYSTEMS

Experimental set-up for the radial conductive heat transfer system is shown in Figure-5.

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coldhot

T1 T2 T3 T4 T5 T6 T7 T8

Cooling water outletHeater

T1 T2 T3 T4 T5 T6

Thermocouples

Thermal insulation

Metal disc

Figure-5: Radial heat conduction unit.

A. Determine the effect of a change in heat flow for steady-state conduction of heat energy through the wall of a thick cylinder (radial energy flow) and determine the thermal conductivity, k, of the material

Procedure:

i) Ensure that the cooling water is flowing and then set the heater voltage V.ii) Monitor temperature T1, T2, T3, T4, T5 and T6 until steady-state is reached.iii) When the temperatures are stabilized, record T1, T2, T3, T4, T5 and T6, V and I.iv) Reset the voltage and repeat the above procedure again recording the parameters T1, T2, T3, T4, T5, T6, V and I when temperatures have stabilised. v) Reset the heater and repeat the above procedure again recording the parameters T1, T2, T3, T4, T5, T6, V and I when temperatures have stabilised.

B. Determine unsteady-state conduction of heat energy through the wall of a thick cylinder (radial energy flow)

Procedure:

i) Ensure that the cooling water is flowing. ii) Then disconnect the heater dc supply and set the heater voltage V, but do not reconnect the dc supply at this stage. iii) Start a stopwatch to record regular time intervals and then reconnect the dc supply to the heater with the voltage still setiv) Record T1, T2, T3, T4, T5 and T6 at regular time intervals of 1 minute.

USEFUL DATA FOR RADIAL HEAT CONDUCTION UNITHeated DiscMaterial: Brass outside diameter: 0.110 mDiameter of heated copper core: 0.014 mThickness of disc: 0.032 m Radial position of thermocouples:

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Valve

Pressure regulator

Filter

Cooling water inlet

T1 = 0.007 mT2 = 0.010 mT3 = 0.020 mT4 = 0.030 mT5 = 0.040 mT6 = 0.050 mThermal conductivity of brass disc:121 W/m.K

4) DATA ANALYSIS

a. Sketch temperature distribution for each experiment.b. Determine the thermal conductivity of aluminium and compare this value with that

given in the manual. If the values are not similar, discuss possible reasons. c. Determine the thermal conductivity of stainless steel and compare this value with that

given in the manual. If the values are not similar, discuss possible reasons. d. Determine the thermal conductivity of brass using all temperature measurements. Is

thermal conductivity similar in every case? If not, discuss possible reasons. e. Determine the overall heat transfer coefficient using temperature measurements and

compare this value with that resulting from the thermal resistance of the composite material.

f. Calculate the temperature gradients in the heated and reduced diameter bar. Is the ratio of these gradients similar to the ratio of areas? If not, discuss possible reasons.

g. Determine the thermal conductivity of the insulation material.

5) QUESTIONS FOR CONSIDERATION

i) How would a change in the heating rate affect the temperature distribution for both linear and radial systems? ii) How would a change in the flowrate of the cooling water affect the results? iii) Discuss the effect of varying cross-sectional area of the specimen on the temperature gradient. iv) Discuss the effect of contact resistance between two adjacent surfaces. What can be done to reduce the contact resistance? v) Under the same conditions (cross sectional area, thickness, heating/cooling rate), hypothetically sketch the temperature distributions if the intermediate specimen is brass, stainless steel and paper? Explain the differences.

vi) How does a change in insulation thickness affect the total resistance to flow? vii) For unsteady-state conductive heat transfer, what modifications should be introduced to both linear and radial systems in order to shorten the time to reach the steady-state conditions? viii) Why do you think it takes longer time for the unsteady-state linear conductive heat transfer system to reach steady-state when compared to the radial system?

6) REFERENCES

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i) Incropera, F. P., De Witt, D.P., Fundamentals of Heat and Mass Transfer, John Wiley & Sons, Singapore, 1990.ii) McCabe, W. L., Smith, J.C., Harriot, P., Unit Operations of Chemical Engineering, McGraw-Hill, Singapore, 1985,

Acknowledgment: Author thanks Dr. S. Alsoy Altunkaya for her help in preparing this manual.

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CONFIGURATION OF CONTROL PANEL

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A on/off switchB Manual/Remote controlC Voltage control potentiometerD Display Volts (V), Current (I), Thermal radiation (R), Light illumination (L),

air velocity (Ua), Cooling water flow rate (Fw)E Rotary selector switch for V, I, R, L, Ua, and FwF IO portG Measurement selector switch fro thermocouplesHIJ Display temperatureKLM Allow connection of specific transducers to record parameterNOPRQ Power supply sockets for current loads up to 4 Amps maximumS DC voltage socketsT Circuit breakerU Circuit breakerV Circuit breakerX Power supply sockets for current loads up to 1 Amps maximumW Power supply sockets for DC voltage

LINEAR HEAT CONDUCTION UNIT

1 heating section2 intermediate section3 cooling section4 manual control valve6 hose coupling7 pressure regulator11 outlet hose12 toggle clamps13 PVC base plate14 thermocouple plugs (extreme right)15 plug and lead

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RADIAL HEAT CONDUCTION UNIT

1 brass disc2 solid disc of brass (110mm diameter)3 heating section4 central heater5 solid copper core (14mm diameter)6 insulation material7 six fixed thermocouples8 miniature plug9 manual control valve11 pressure regulator13 hose coupling15 plug and lead

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