This document describes an experiment conducted to measure the thermal conductivity (K) of a cylindrical iron specimen. The specimen was heated using an electrical heater while thermocouples measured the temperature at three points. Heat transferred from the specimen to surrounding water until steady-state. Calculations were done to determine K values at each point, which were then averaged. The measured K of 7.878 W/m-C was compared to the theoretical value for iron of 80.2 W/m-C, with a high error rate of 91.77% observed. Applications of this experiment include heating processes and heat transfer analysis.

1. Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
[HEAT TRANSFER Laboratory II]
University of Baghdad

2. Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
TABLE OF CONTENTS
MIN..................................................................................I
THEORY............................................................................II
Calculations and results...................................................V
DISCUSSION ...................................................................VI

3. Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
Conduction Heat Transfer
Saif Al-din Ali -A-
1. MIN
Measuring the thermal conductivity K for a cylindrical specimen made from
iron and has certain dimensions and specifications
*Types of Heat Transfer are:
1. Conduction
2. Convection
3. Radiation
2. THEORY
1. The Apparatus used:
Draw a schematic shape for the apparatus demonstrating its parts clearly
2. The Experiment Procedure:
The specimen is heated by using an electrical heater located specimen. As a result.
the temperature of the specimen rises and three different locations on the
specimen surface is indicated to measure their temperature values by using
thermocouple wires attached to a selector and then to a digital thermometer The
heat is transferred from the specimen to the water contained in a reservoir ted and
in order to achieve a heat transfer by construction only the specimen is insula
completely so that neither convection nor nor radiation heat transfer take place.
The reservoir is supplied with water from a continuous source until reaching steady
state at which temperature values for the three points and the inlet and outlet
water temperature is recorded and this happens after approximately two hours.

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3. Calculations and results
After the heat is transferred from the specimen to the water. The
following heat balance is written:
Heat transfer from specimen = heat added to water
−𝑘𝐴
𝑑𝑇
𝑑𝑥
= 𝑚`
𝑐 𝑝𝑤∆𝑇
Where:
K Thermal conductivity for specimen (w/m.c`)
A Cross - sectional area (m^2)
𝑑𝑇
𝑑𝑥
Temperature gradient (c`/m)
m`(w) Water mass flow rate (kg/sec)
p(w) Water density 1000 kg / m^3 (k / sec)
𝑐 𝑝𝑤 = 4.136 Specific heat at constant pressure (Kj/KG.C`)
** The average temperature of the specimen surface temperatures is
calculated which result in calculating three values for the thermal
conductivity k1. K2. K3 and then take the average for these three values,
** When the steady state condition is reached you must make the
following table for the data obtained during this experiment as shown
below:
TIME (min) 𝑇 𝑤𝐼𝑁 𝑇 𝑤𝑂𝑈𝑇 𝑇1 𝑇2 𝑇3
0 24 29 109.8 92 69.3
5 24 29 109.1 91.4 69.2
10 24 29 109.1 91.4 69.2
15 24 29 109.1 91.4 69.2
AV
7.5 24 29 109.25 91.5 69.25

5. Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
Calculations
𝑨 =
𝝅
𝟒
𝒅 𝟐
𝐴 =
𝜋
4
(0.024)2
𝐴 = 4.52 × 10−4
𝑚2
𝒎^
= 𝝆
𝑽
𝒕
𝑚^
= 1000
29 × 10−6
300
= 9.66 × 10−5
𝑘𝑔/𝑠𝑒𝑐
𝑸 𝒘 = 𝒎` 𝒄 𝒑𝒘∆𝑻
𝑄 𝑤 = 9.66 × 10−5
∗ 4.136 ∗ 103
∗ (29 − 24) = 1.997688 𝑤
∆𝑇
∆𝑥
= 𝑇1 − 𝑇2 ∆𝑿𝟏⁄
1- (1 − 2)
∆𝑇
∆𝑥
= 109.25 − 91.5 32⁄ × 10−3
= 547.65625 𝑐 𝑚⁄
2- (1 − 3)
∆𝑇
∆𝑥
= 109.25 − 69.25 71⁄ × 10−3
= 560.21 𝑐 𝑚⁄
2- (2 − 3)
∆𝑇
∆𝑥
= 91.5 − 69.25 39⁄ × 10−3
= 570.512 𝑐 𝑚⁄
𝐐 𝐰 = 𝐤𝐀
𝐝𝐓
𝐝𝐱
𝐤 =
𝐐 𝐰
𝐀
𝐝𝐓
𝐝𝐱
1-k =
1.997688
4.52×10−4∗234.15
= 8 𝑤 𝑚. 𝑐`⁄
2-k =
1.997688
4.52×10−4∗560.21
= 7.88929 𝑤 𝑚. 𝑐`⁄
3-k =
1.997688
4.52×10−4∗570.512
= 7.746837 𝑤 𝑚. 𝑐`⁄

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𝑘 = 𝑘1 + 𝑘2 + 𝑘3 3⁄
𝑘 = 8 + 7.88929 + 7.746837 3⁄
𝑘 = 7.878709 𝑤 𝑚. 𝑐`⁄
4. DISCUSSION
1. After calculating the experimental value of (K) for iron compare the
calculated results with the theoretical value of (K) from tables for iron,
then determine the percentage error between the two values and
discuss the reason of the difference between the two values and find the
type of iron used.
Error=|
kthe−kex
kthe
|*100
1. |
80.2−7.878
80.2
| ∗ 100 =91.77%
kthe = 80.2
kex = 7.878
We observe a high line rate and this depends on the process of taking
the readings from the device and the process of continuous calibration
of the device and the time period to take readings and the accuracy of
conversion of the signal type in the thermocouple device

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2. Find the top surface temperature and bottom surface temperature for
the Specimen algorithmically and find them also from the plot. Then
compare between the two results obtained from the two methods.
𝐐 𝐰 = 𝐤𝐀
𝐝𝐓
𝐝𝐱
1 − 1.997688 = 7.89 ∗ (4.52 × 10−4
)
𝑇𝑆 − 109.025
15 × 10−3
TS=117.427 C`
2 − 1.997688 = 7.89 ∗ (4.52 × 10−4
)
117.427 − 𝑇𝐵
100 × 10−3
Tb=61.4057 C`
Note that the inverse relationship between heat and distance from the
heat generating site as we move away from the heat source is less
valuable
0
20
40
60
80
100
120
140
0 0.02 0.04 0.06 0.08 0.1 0.12
Y-TC`

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3. Can you calculate (K) for two different materials at the same time?
Why?
It can not be calculated because the different materials have different k
and different stability condition can not reach the fixed state of the
metal Mean at the same time and heat.
The device used is specially designed to measure as a unit material,
depending on its shape
4. Define the steady state condition. Was the experiment at this condition
or not
Steady-state
Designating or of a system, operation, mixture, rate, etc. that does not
change with time or that contains a state of relative equilibrium even
after undergoing fluctuations or transformations, Yes it has been
adopted

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5. State number of applications for this experiment
1. Burning of wood on coal
2. Melting of iron in blast furnace
3. Fission reactions in nuclear fuel rods of nuclear reactors
4. Cooking of food in metal utensils
6. What are the main results that you have given from this experiment?
1. Calculate the value of K and practically compare it with the
theoretical and knowledge of the metal class through it
2. Calculation of error ratio between theoretical and practical