1) The document describes an experiment on radial heat conduction. Thermocouples were used to measure the temperature at different points in a brass cylinder as heat was applied to determine the thermal conductivity. 2) Thermal conductivity values were calculated at different measurement points using Fourier's law. The values ranged from 0 to 187.948 W/m°C. 3) Radial heat conduction is important in applications like heat exchangers and engines. It allows understanding how temperature varies from the center to outer surfaces of materials.

1. Duhok Polytechnic University.
Technical College Engineering.
Energy Engineering Department.
Heat Transfer.
(Experiment:2)
Radial Heat Conduction.
Student name:
Diyar Zeki

2. Table Of Contains:
Abstract ………………………………………………….. (3)
Objective ………………………………………………… (3)
Introduction ……………………………………………. (3-4)
Equipment ……………………………………………… (4)
Discerption ………………………………………………. (4-5-6)
Theory …………………………………………………….. (6-7-8-9)
Procedure ………………………………………………… (9)
Data And Result ……………………………………….. (9-11)
Discussion ………………………………………………… (11-12)

3.  Abstract:
Radial heat conduction is a fundamental process that occurs in many
engineering and scientific applications, including heat exchangers, nuclear
reactors, and geological processes. In steady-state conditions, the
temperature distribution in a radial geometry is governed by the heat
equation, which describes the balance between heat flux and thermal
conductivity. The solution to this equation provides insights into the
thermal behavior of the system and can be used to optimize design and
operation parameters. In this abstract, we will review the theoretical
framework for radial heat conduction in steady state, including boundary
conditions, analytical and numerical solutions, and thermal resistance
concepts. We will also discuss practical applications of radial heat
conduction in various fields and highlight current research trends and
challenges..
 Objective:
The objective of Our experiment Was About Calculating the value of
Thermal conductivity by using the Fourier's Law and to study the factor
which could affect the Radial conduction heat transfer.
 INTRODUCTION:
Radial conduction heat transfer refers to the transfer of heat energy
through a solid material in a radial direction, from the center of the
material towards its outer surface. This type of heat transfer occurs due
to a temperature difference between the center and outer surface of the
material.
Steady state refers to a condition where the temperature at any given
point within the material remains constant over time. In other words, the
rate of heat transfer into and out of the material is equal, resulting in a
constant temperature distribution within the material.
Studying radial conduction heat transfer in steady state is important for a
wide range of applications, such as designing and optimizing heat
exchangers, calculating the temperature distribution in engine
components, and determining the thermal behavior of electronic devices.

4. In order to understand radial conduction heat transfer in steady state, it
is important to be familiar with the fundamental principles of heat
transfer, including the Fourier law of heat conduction, which relates the
rate of heat transfer to the temperature gradient in the material, as well
as the concept of thermal conductivity, which characterizes the ability of
the material to conduct heat.
By studying radial conduction heat transfer in steady state, students can
gain a deeper understanding of the physics of heat transfer and how it can
be applied to practical engineering problems.
 Equipment:
1-The WL 372 experimental
unit. (figure 1)
2-Brass sample isolated in
cylinder disk shape with
4mm length
 Discerption:
The WL 372 experimental unit can be used to determine basic laws and
characteristic variables of heat conduction in solid bodies by way of
experiment. The experimental unit comprises a linear and a radial
experimental setup, each equipped with a heating and cooling element.
Different measuring objects with different heat transfer properties can be
installed in the experimental setup for linear heat conduction. The
experimental unit includes with a display and control unit.
record the temperatures at all relevant points. The measured values are
read from digital displays and can be transmitted simultaneously
via USB directly to a PC, where they can be analyzed using the software
included.
Figure 1

5. 1-experimental setup for linear heat conduction.
2-experimental setup for radial heat conduction.
3-measuring object.
4-display and control unit.
5-Temperatur selector (or Measuring Point).
6-Temperatur Display.
7-Power Valve (To Increase And Decrease The Power).
8-Power Display.
9-Heater (Off and On).
10-Operating Mode (Manual Or PC).
Figure 3

6. 11-The Six Thermocouples.
12-Water inlet.
13-Water outlet.
14- experimental setup for radial heat conduction.
 Theory:
If the inner surface of a thick walled cylinder is at a temperature higher
than its surroundings then heat will flow radially outward.
If the cylinder is imagined as a series of concentric rings, each of the same
material and each in close contact, then it can be seen that each cylinder
presents a progressively larger surface area for heat transfer.
If the heat input at the center remains constant then the heat transfer per
unit area must reduce as the heat moves towards the outside diameter.
Therefore, the temperature gradient will decrease as the radius increases.
When the inner and outer surfaces of a thick walled cylinder are a uniform
temperature difference, heat flows radially through the cylinder wall.
Due to symmetry, any cylindrical surface concentric with the central axis
of the tube has a constant temperature (is isothermal) and the direction
of heat flow is normal (at right angles) to the surface
. For continuity, the radial heat flow per unit length of tube through these
isothermal surfaces must remain steady. As each successive layer
presents an increasing surface area with radius the temperature gradient
must decrease with radius. The temperature distribution will be of the
form shown below

7. Considering a plane section of flat surface, according to Fourier’s law of
heat conduction:
If a plane section of thermal conductivity k, thickness Δx and constant area
A maintains a temperature difference ΔT then the heat transfer rate per
unit time 𝑸̇by conduction through the wall is found to be:
𝑸.
= −𝒌𝑨
∆𝑻
∆𝒙
The negative sign follows thermodynamic convention in that heat transfer
is normally considered positive in the direction of temperature fall.
Returning to the thick walled cylinder, if an elemental thickness of dr is
considered then the area of this length of cylinder x can be considered as
2πr x. The temperature gradient normal to the elemental thickness is
(dT/dr).

8. Applying Fourier’s law to this elemental cylinder:
𝑄.
= −𝑘2𝜋 𝑟𝑥 (
𝑑𝑇
𝑑𝑟
)
Since Q is independent of r, by integration between Ri and Ro it can be
shown that
𝑄.
ln (
𝑅°
𝑅𝑖
) = −2𝜋𝑘𝑥(𝑇° − 𝑇𝑖)
Where ln = 𝑙𝑜𝑔𝑒
By rearranging the equation
𝑘 = −
𝑄.
ln (
𝑅°
𝑅𝑖
)
2𝜋𝑥(𝑇° − 𝑇𝑖)
For the purposes of the experiment, the negative sign in the above
equation may be ignored.
Overleaf are sample test results and illustrative calculations showing the
application of the above theory.
Heat transfer through a solid material is not instantaneous. If heat is
introduced at the center of a disc at a constant rate Q the temperature
closest to the heat source will begin to rise as soon as the heat input
starts. Due to conduction, the heat will transfer through the material
away from the heat source towards any area of lower temperature.
The rate of heat transfer through the disc and the subsequent
temperature rise will not only depend upon the thermal conductivity
(W/mK) of the bar but also the material specific heat (J/kg K), the material
density (kg/m3) and the bar dimensions.

9. The heat will transfer through the disc and the temperatures at various
points along the radius will rise until a steady state condition exists where
all intermediate temperatures are constant. As long as the heat input and
the sink temperature are constant, the system will remain in equilibrium.
It is under these conditions that all previous experiments (1 to 2) have
been undertaken.
The subject of unsteady state heat transfer is beyond the capabilities of
this unit but the procedure allows the concept unsteady state heat
transfer to be introduced.
Overleaf are sample test results showing the temperature rise of T1 to T6
with time.
 Procedure:
1-set up the unit adjust the cooling water flow rate.
2-connect up the power and data cables appropriately.
3-switch on the unit and adjust the desired temperature drop via
the power setting on the control and display unit .
4-when the thermal conduction process has reached a steady
state condition , i.e the temperature at the individual measuring
points are stable and no longer changing, note the measurement
result at the individual measuring points and the electrical
power supplied to the heater. (This In General).
*We Gave 92 Watts To an isolated cylinder disc With Length of
(4mm) and the distance Between each of (six Thermocouples) to
another was (10mm) by those thermocouples we got (6)
differences temperature and we had the needed data to
calculate every thermal conductivity.
 Data And Result:
Specimen :Brass
𝑸 = 𝟗𝟐 𝑾 𝒍 = 𝟒𝒎𝒎
Measuring Points: 6
𝒒 =
𝟐𝝅𝒌𝒍∆𝑻
𝐥𝐧(
𝒓𝒐𝒖𝒕
𝒓𝒊𝒏
)
𝒌 =
𝒒∗𝐥𝐧(
𝒓𝒐𝒖𝒕
𝒓𝒊𝒏
)
𝟐𝝅𝒍∆𝑻

10. 𝒌𝟏 =
𝟗𝟐 ∗ 𝐥𝐧(
𝟏𝟎
𝟎
)
𝟐𝝅 ∗ (𝟒 ∗ 𝟏𝟎−𝟑) ∗ (𝟏𝟓)
= 𝟎(
𝒘
𝒎 ∗ ℃
)
𝒌𝟐 =
𝟗𝟐 ∗ 𝐥𝐧(
𝟐𝟎 ∗ 𝟏𝟎−𝟑
𝟏𝟎 ∗ 𝟏𝟎−𝟑)
𝟐𝝅 ∗ (𝟒 ∗ 𝟏𝟎−𝟑) ∗ (𝟏𝟑. 𝟓)
= 𝟏𝟖𝟕. 𝟗𝟒𝟖(
𝒘
𝒎 ∗ ℃
)
𝒌𝟑 =
𝟗𝟐 ∗ 𝐥𝐧(
𝟑𝟎 ∗ 𝟏𝟎−𝟑
𝟐𝟎 ∗ 𝟏𝟎−𝟑)
𝟐𝝅 ∗ (𝟒 ∗ 𝟏𝟎−𝟑) ∗ (𝟏𝟎. 𝟑)
= 𝟏𝟒𝟒. 𝟏𝟎 (
𝒘
𝒎 ∗ ℃
)
𝒌𝟒 =
𝟗𝟐 ∗ 𝐥𝐧(
𝟒𝟎 ∗ 𝟏𝟎−𝟑
𝟑𝟎 ∗ 𝟏𝟎−𝟑)
𝟐𝝅 ∗ (𝟒 ∗ 𝟏𝟎−𝟑) ∗ (𝟗. 𝟓)
= 𝟏𝟏𝟎. 𝟖𝟓(
𝒘
𝒎 ∗ ℃
)
𝒌𝟓 =
𝟗𝟐 ∗ 𝐥𝐧(
𝟓𝟎 ∗ 𝟏𝟎−𝟑
𝟒𝟎 ∗ 𝟏𝟎−𝟑)
𝟐𝝅 ∗ (𝟒 ∗ 𝟏𝟎−𝟑) ∗ (𝟔. 𝟐)
= 𝟏𝟑𝟏. 𝟕𝟒𝟔(
𝒘
𝒎 ∗ ℃
)
Measuring
Point
Distance
(mm)
Temperature
(℃)
∆𝑻(℃) K (
𝒘
𝒎∗℃
)
1 - 85 15 0
2 10 70 13.5 187.948
3 20 56.5 10.3 144.10
4 30 46.2 9.5 110.85
5 40 36.7 6.2 131.746
6 50 30.5 -

11.  Discussion:
Which is better to conduction heat transfer (linear or
radial heat conduction transfer)?
Radial conduction heat transfer refers to the transfer of heat
energy through a solid material in a radial direction, from the center
of the material towards its outer surface. This type of heat transfer
occurs due to a temperature difference between the center and
outer surface of the material.
Steady state refers to a condition where the temperature at any
given point within the material remains constant over time. In other
words, the rate of heat transfer into and out of the material is
equal, resulting in a constant temperature distribution within the
material.
Studying radial conduction heat transfer in steady state is
important for a wide range of applications, such as designing and
optimizing heat exchangers, calculating the temperature
distribution in engine components, and determining the thermal
behavior of electronic devices.
In order to understand radial conduction heat transfer in steady
state, it is important to be familiar with the fundamental principles
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60
Distance(mm)
Temperature ℃

12. of heat transfer, including the Fourier law of heat conduction,
which relates the rate of heat transfer to the temperature gradient
in the material, as well as the concept of thermal conductivity,
which characterizes the ability of the material to conduct heat.
By studying radial conduction heat transfer in steady state,
students can gain a deeper understanding of the physics of heat
transfer and how it can be applied to practical engineering
problems.
Is it possible to change thermocouples places in radial
heat conduction ?
In radial heat conduction in steady state, the temperature
distribution within the material remains constant over time. This
means that the temperature at any given point within the material
is not changing with time. Therefore, if a thermocouple is placed at
a specific radial distance from the center of the material and
allowed to reach thermal equilibrium, the temperature reading
obtained will reflect the temperature at that specific radial
distance.
If the thermocouple is then moved to a different radial distance
from the center of the material, the temperature reading obtained
will reflect the temperature at that new radial distance. However,
the temperature at the original radial distance will remain the
same, as the temperature distribution is steady state and does not
change with time.
Therefore, it is possible to change the position of a thermocouple
in radial heat conduction in steady state to measure the
temperature at different radial distances from the center of the
material. However, it is important to note that the temperature
distribution within the material will not change as a result of
moving the thermocouple, as the steady-state condition has
already been reached.