Experiment # 03
Objectives:
To measure the temperature distribution for steady-state conduction of energy through the wall of
a cylinder (radial energy flow) and demonstrate the effect of a change in heat flow.
Apparatus:
• Heat Transfer Base Unit (TD1002)
• Computer Compatible Radial Heat Conduction Accessory TD1002b.
Theory:
When the temperature of the inner and outer surfaces of a thick-walled cylinder change uniformly,
heat flows radially through the cylinder wall due to temperature difference. The disk can be
considered to be constructed as a series of successive layers.
From continuity, if the flow is steady, the radial heat flow through each of successive layers in the
wall must be constant. But since the area of the successive layers increases with radius, the
temperature gradient must decrease with radius.
As from Fourier’s Law
𝛥𝑇 𝛥𝑇 𝑄
𝑄 = 𝑘𝐴 𝑂𝑟, =
𝛥𝑋 𝛥𝑋 𝑘𝐴
i.e. 𝛥𝑇 is inversely proportional to A.
𝛥𝑋
Conduction:
Conduction is a mode of heat transfer that occurs when there is direct contact between two objects
at different temperatures, resulting in the transfer of thermal energy from the hotter object to the
cooler object. This transfer of energy happens due to the collision of atoms or molecules in the
hotter object with those in the cooler object, leading to the movement of heat from the hotter object
to the cooler object. The rate of conduction depends on various factors, such as the temperature
difference between the two objects, the distance between them, and the thermal conductivity of the
materials involved. Conduction is a common method of heat transfer in solids, where heat energy
is transferred through the vibration of particles within the substance. Metals are good conductors
of heat due to their free-moving electrons, which transfer energy quickly.
Types of Conduction:
1. Steady state conduction:
Steady state conduction is a type of heat transfer in which the temperature within a material or
system remains constant over time, with no changes in temperature or other properties. In steady
state conduction, the rate of heat transfer into a material is equal to the rate of heat transfer out of
the material, resulting in a stable thermal equilibrium. This type of conduction is often modeled
using Fourier's law of heat conduction, which describes the relationship between temperature,
thermal conductivity, and the rate of heat transfer. Steady state conduction is commonly used in
engineering applications to design and optimize heat transfer systems, such as in heat exchangers,
thermal insulation, and cooling systems.
2. Transient heat conduction
Transient heat conduction is a type of heat transfer in which the temperature within a material or
system changes over time, with varying temperature and other properties. In transient heat
conduction, the rate of heat transfer into a material or system is not constant, leading to changes
in temperature and other properties. This type of conduction is often modeled using the heat
diffusion equation, which describes the relationship between temperature, thermal conductivity,
specific heat, and the rate of heat transfer over time. Transient heat conduction is commonly
observed in many practical scenarios, such as during the heating or cooling of materials, or during
the operation of heat-generating systems, such as engines or electronic devices. Understanding
transient heat conduction is important for designing and optimizing heat transfer systems that
operate under changing temperature conditions.
Apparatus Setup:
The Apparatus is setup as shown in the following figure. Attach the TD1002b Radial Heat
Conduction Experiment module with the TD1002 Heat transfer experiment Base unit.
Fig:01 Types of Flows through a Cylinder
Fig:02 Radial Conduction Heat Transfer Procedure:
Readings and Calculations:
Thickness of brass disk = 3.2 mm
Inner radius of disk = 7 mm
Outside radius of disk = 55 mm
Heater
Sr No. Power T1 (K) T2 (K) T3 (K) T4 (K) T5 (K) T6 (K) T7 (K)
(Watt)
1.
2.
3.
4.
5.
Graph:
Plot a graph of temperature against distance along the bar and draw the best straight line
through the points.
Results analysis and Discussion:
We can readily see from the graph that radial heat conduction is faster than linear heat conduction
for the same geometry and temperature difference of the material.
This is because in radial heat conduction heat is transmitted over shorter distances perpendicular
to the direction of heat flow while in linear heat conduction heat is transmitted over longer
distances parallel to the direction of heat flow. Hence, radial heat conduction allows heat to flow
at higher velocities over shorter distances than linear heat conduction.
However, the heat transfer rate of radial heat and linear heat conduction also depends on the
thermal conductivity of the material, the temperature difference between the two ends, and the
cross-sectional area of the material. Therefore, the effective heat transfer rate will then depend on
the specific conditions of the given system
