EXP2

Mechanical Engineering Dep. Dr. Eng.
Kamel Guedri Heat Transfer: Lab Manual
EXPERIMENT #2
MEASUREMENT OF THERMAL CONDUCTIVITY OF A METAL
OBJECTIVE
The objective of this experiment is to measure of thermal conductivity of a material and
verify Fourier’s Law for linear heat conduction along a simple bar.
INTRODUCTION
In order to make accurate predictions of heat transfer rates through materials, it is
necessary to first know the value of the thermal conductivity of the material itself.
Thermal conductivity can be measured using standard methods, devices and techniques.
In this experiment, we will measure thermal conductivity of a metal, and in addition,
calculate an overall heat transfer coefficient for three metals in series.
THEORY
In this experiment we will investigate conduction in an insulated long slender brass bar
like the one in Figure 1. We will assume that the bar is of length L, a uniform hot
temperature Th is imposed on one end, and a cold temperature Tc is imposed on the
other. We will also assume, because the bar is insulated in the peripheral direction, that
all the heat flows in the axial direction due to an imposed temperature differential along
the bar.
Figure 1: Schematic of a Long Cylindrical Insulated Bar
Experiment#2 Page 1/5

Mechanical Engineering Dep. Dr. Eng. Kamel Guedri Heat Transfer: Lab Manual
The equation that governs the heat flow is known as Fourier's Law, and in the axial
direction it is written as
(1)
where qx is the rate of heat conduction in the x-direction, k is the thermal conductivity of
the material, Ax is the cross-sectional area normal to the x-direction, and dT/dx is the
temperature gradient in the x-direction. The negative sign indicates that heat is
transferred in the direction of decreasing temperature. Temperature is measured at
discrete points along the rod in this experiment.
In this experiment we will investigate Fourier's Law by finding the thermal conductivity
k for stainless steel and comparing this value to the actual value from one or more
references.
For one dimensional heat flow, we can write the following:
(2)
where T1 is the temperature at the warmest point on the rod at the left end, TIL is the
interface temperature between the left end rod and the center rod, TIR is the interface
temperature between the center rod and the right end rod, T6 is the temperature at the
coolest point of the rod on the right, and the x's correspond to the appropriate distances.
The interface temperatures are sketched in Figure 2. Thermal conductivity k values
correspond to the appropriate materials. The first and third materials are brass. The center
section is stainless steel.
By manipulation of Equations 1 and 2, it is possible to express the heat transferred along

the rods in terms of a heat transfer coefficient, U, as
(3)
where
(4)

Figure 2: Determination of interface temperatures from the measured

temperature values.
The preceding equations do not include the effect of contact resistance.
APPARATUS
The apparatus we will be using in this experiment is the P.A. Hilton H940 Heat
Conduction Unit, which consists of three items. The description of this unit is presented
in Experiment #1.
Figure 3 is a sketch of the apparatus used in this experiment. It consists of three separable
sections. The center section is removable. The left end section contains a brass rod, and
an electrical heater. The heat input to the heater can be controlled and measured. The
right end section is also made of brass, and contains a hollowed out cavity with water
tubes attached. Thus heat flows through from the heater through the left end section, then
through the center section, and finally through the right end section to the water.

Figure 3: A schematic of the apparatus used to verify Fourier’s Law of Conduction.
The entire apparatus is insulated so that one dimensional heat conduction is well
approximated. The end sections contain instrumentation for measuring temperature. The
rods in the end sections have a diameter of 25 mm while the distance between adjacent
temperature measurements is 10 mm. The center section is 30 mm long. Temperature
versus length readings can be obtained with this apparatus. Several experiments can be
performed depending on what is used in the center section.
PROCEDURE
1. Connect the equipment (as shown in Figures 3 and 4 of Experiment#1), making sure
that the calibration unit is switched off before connecting the transformer to the AC
outlet.
2. Apply a very small amount (a drop) of thermal conducting paste to make a thin layer
on each side of the test unit surface and spread it uniformly.
3. Insert the stainless steel sample (30 mm length and 25 mm diameter) into the unit and
allow cooling water to flow through the test unit.
4. Connect all the seven thermocouples in the appropriate order.
5. Switch the calibration unit on and adjust the power control knob to deliver 10 W of
power to the test unit; allow the system to reach steady state (approximately 20
minutes).

6. Record the temperatures at each thermocouple and the power input.
RESULTS
1. Plot temperature versus distance along the rods.
2. Determine from your plot the interface temperatures (see figure 2).
3. Using published thermal conductivity values for the brass, and Equation 2.3, find the
thermal conductivity of stainless steel and compare your results to published
values. Discuss the validity of the assumptions made and sources of error within
the equipment or through measurements.
4. Calculate the overall heat transfer coefficient.
RAW DATA TABLES

Table 1: Raw Data for Experiment #2
q T1 T2 T3 T4 T5 T6
(W) (°C) (°C) (°C) (°C) (°C) (°C)
ASSIGNED READING:
Fundamentals of Heat and Mass Transfer; Incropera and DeWitt; pp. 3-6, pp. 58-67, App. A.
SAFETY GUIDELINES:
1. To avoid burns, do not touch any metal or plastic surfaces on the hot end of the
sample or test unit.
2. Avoid using a high cooling water flow to prevent disconnection of the hose from
the test unit.
3. Do not exceed 20 W power delivery under any circumstances, and do not allow
the temperature to go above 100 °C at any of the thermocouple locations.
4. Avoid using too much conducting paste as this may ‘fry’ the unit.

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Mechanical Engineering Dep. Dr. Eng.

Kamel Guedri Heat Transfer: Lab Manual

Figure 1: Schematic of a Long Cylindrical Insulated Bar

Experiment#2 Page 1/5

For one dimensional heat flow, we can write the following:

By manipulation of Equations 1 and 2, it is possible to express the heat transferred along

Experiment#2 Page 2/5

Figure 2: Determination of interface temperatures from the measured

The preceding equations do not include the effect of contact resistance.

Experiment#2 Page 3/5

Figure 3: A schematic of the apparatus used to verify Fourier’s Law of Conduction.

Experiment#2 Page 4/5

6. Record the temperatures at each thermocouple and the power input.

RAW DATA TABLES

Experiment#2 Page 5/5

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