Introduction to Thermodynamic Engineering

TME20403
JULY 2022
EXPERIMENT 1
HEAT TRANSFER BY CONDUCTION
LECTURER: DR. SAFAA NAJAH SAUD AL-
HUMAIRI

NAME ID MARKS
GOKUELA GESHNU 012022020071
VEENODRAN A/L MC012022020060
PERUMKOTHAISELVAM
MICHAEL AGAH ANAK 012022021563
KURONG
Theory

Aim:

1. To find the thermal conductivity of a material by the two slabs guarded hot plate method.

2. To find the thermal resistance of the sample.

Apparatus:

A circular main heater plate (MH) is surrounded by an annular guard heater plate (GH) with a narrow
air gap in between. Each heater is made up of electrical resistance wire sandwiched between two
copper plates. Thermocouples are fixed to the plates to measure their surface temperatures.

Two identical circular slabs of the material to be tested are placed on either side of and in good
thermal contact with the heater plates. On the outer sides of the two slabs, in good thermal contact,
are two circular water-cooled slabs whose surface temperatures can also be monitored with
thermocouples (Fig 1).

The purpose of the guard heater is to prevent heat loss from the edge of the main heater by
maintaining the temperature outside the main heater at the same temperature as the main heater.
This ensures that all heat lost from the main heater flows through the test slabs.

Theory:

The theory of heat transfer seeks to predict the energy transfer that may take place between
material bodies as a result of temperature difference. This energy transfer is defined as heat. The
three modes by which heat can be transferred from one place to another are conduction, convection
and radiation.

In conduction, heat is carried by means of collisions between rapidly moving molecules closer to the
hot end of a body of matter and the slower molecules closer to the cold end. Some of the kinetic
energy of the fast molecules passes to the slow molecules, and as a result of successive collisions,
heat flows through the body of matter from the hot end to the cold end. Solids, liquids, and gases all
conduct heat. Conduction is poorest in gases because their molecules are relatively far apart and so
interact less frequently than in solids and liquids. Metals are the best conductors of heat because
some of their electrons are able to move about relatively freely and can interact frequently by
collisions.

Without the guard heater, cooler air surrounding the edge of the main heater would be heated by
conduction and convection. Thus some of the heat supplied to the main heater would be carried
away by the surrounding air.

With the guard heater in place and adjusted to the same temperature as the main heater, the air in
the gap between is maintained at the temperature of the main heater, so no heat is lost at the edge
of the main heater. All heat lost from the main heater must flow into the test slabs.

Consider one dimensional heat conduction (Fig 2). The rate at which heat is conducted through a
slab of a particular material is proportional to the area A of the slab and to the temperature
difference ΔT between its sides and inversely proportional to the slab's thickness d.

The amount of heat Q that flows through the slab in the time t is given by

Rate of conduction

And thus

Where ΔT = T1 – T2, and k is the thermal conductivity of the material, is a measure of its ability to
conduct heat. The SI unit of k is Wm-1K-1.

Thermal conductivity: Note that a heat flow rate is involved, and the numerical value of the thermal
conductivity indicates how fast heat will flow. In general, thermal conductivity is strongly
temperature dependent. It has the units of watts per meter per Kelvin. Heat transfer by conduction
in a solid can be realized through the support of phonons, electrons and photons. The individual
contributions of these carriers widely depend on material and its temperature. Thermal conductivity
is thus a second order tensor, but in a material with cubic isotropy it reduces to a scalar. It is an
intensive property (changing the amount of material does not change its thermal conductivity) and is
a function of both pressure and temperature.
The thermal resistance R of a layer of a material of thickness d and of thermal conductivity k is given
by

The greater the value of R, the greater the resistance to the flow of heat.

Applications:

Heat transfer has wide applications for the proper functioning of thermal devices and systems. This
principle is used to solve many problems in thermal mechanics.

1. Heat exchangers.

2. Building construction works.

3. Thermal energy storage devices.

4. Heat transfer in human body.

5. Thermopile and infrared thermometer.

6. Thermal resistance in electronics like thermal diode or thermal rectifier.

7. Used in laser cooling, radiative cooling, magnetic cooling, etc.

Performing Simulation:
Simulator Controls

1. The Choose Material combo box is used to select the material for the test slab.
2. The Diameter of the material slider is used set the diameter of the portion of the test slab in
contact with the main heater, in cm
3. The Thickness of material slider is used to set the thickness of the test slab, in cm.
4. The Coldwater temperature slider is used to set the temperature ( in degrees Celsius) of the
water flowing inside the outer plates.
5. The White knobs in simulator can be rotated by clicking side arrows to adjust the voltage and
corresponding current, which can be used to calculate input power.
6. The MH-GH Switch is used to set either main heater (MH) or guard heater (GH) voltage and
current as shown on the meters. Note: For the simulator to be powered on, the voltage for both
heaters must be the same.
7. The Power on button switches on the power after the initial adjustments are done.
8. The Temperature indicator is used to read the temperature at the positions of the various
thermocouples. After a steady state is reached (when the timer shows 20 minutes), click the
arrows on either side of the knob to read temperatures T1 to T8 in degrees Celsius.

Procedure for Simulation

1. Choose the material from combo box.

2. Using the sliders, fix a particular diameter for the portion of the test slab in contact with the
main heater, and a thickness for the entire slab.
3. Adjust the cold water temperature using the slider.
4. Using the white knobs, fix the value of same voltage and current for both main heater (MH) and
guard heater (GH). With the MH-GH switch set to MH, use white MH knob to set the voltage and
current for the main heater. Then click the MH-GH switch to GH and use the white GH knob to set
the voltage and current for the guard heater to the same values you set for the main heater.
5. Click the Power On switch to power the unit on.
6. After a steady state is reached (20 minutes in the timer), use the temperature indicator to read
and note down T1, T2, T3, T4, T5, T6, T7 and T8.
7. Using the work sheet and the equations from the theory page, calculate the thermal
conductivity of the test slab. Note: since the main heater is in contact with a test slab on both
sides, the area A in equation

(1)
where d is the diameter of the MH, not , as might first be assumed.
Procedure for Real lab
The procedure for the real lab is quite similar. The main differences are (1) the guard heater can
be set to a slightly different temperature, as needed, to keep the temperature of the main heater
uniform, and (2) the calculations can be extended to allow for and/or find the dependence
of k on ΔT.

Observations and Calculations

Voltmeter Ammeter Main heater Temperature Cold Plate Guard Plate
Reading Reading (˚C) Temperature Temperature
(V) (A) (˚C) (˚C)
T1˚C T2˚C T3˚C T4˚C T5˚C T6˚C T7˚C T8˚C
110 0.31 14.39 14.77 14.13 14.77 14.00 14.00 14.13 14.77
120 0.40 23.74 23.98 23.81 23.98 16.00 16.00 23.81 23.98
110 0.31 24.10 24.81 24.20 24.81 24.00 24.00 24.20 24.81
120 0.40 25.44 25.55 24.92 25.55 19.00 19.00 24.92 25.55

Test 1
Material used: Glass
Result:

T1: 14.39°C

T2: 14.77°C
T3: 14.13°C

T4: 14.77°C
T5: 14.00°C

T6: 14.00°C
T7: 14.13°C

T8: 14.77°C
Mean temperature at the surface of the specimen on the heater side,

= 14.515 °C

Mean temperature at the surface of the specimen on cold plate side,

= 7 °C

Area of heat transfer,

= 0.049 m2
In above equation, d is the diameter of the specimen

Heat transferred,

Δx is the thickness of the specimen

Thermal conductivity k =0.3237Wm-1K-1

Result:
Thermal conductivity of the given specimen by conduction = 0.3237Wm-1K-1
Test 2

Material used: Cardboard

Result
T1: 23.74°C

T2: 23.98°C
T3: 23.81°C

T4: 23.98°C
T5: 16.00°C

T6: 16.00°C
T7: 23.81°C

T8: 23.98°C
Mean temperature at the surface of the specimen on the heater side,

= 23.8775°C

Mean temperature at the surface of the specimen on cold plate side,

= 16°C

Area of heat transfer,

= 0.0572m2
In above equation, d is the diameter of the specimen

Heat transferred,

Δx is the thickness of the specimen

Thermal conductivity k =0.2113Wm-1K-1

Result:
Thermal conductivity of the given specimen by conduction = 0.2113Wm-1K-1
Test 3

Material used: Mica

Result:
T1: 24.10°C

T2: 24.81°C
T3: 24.20°C

T4: 24.81°C
T5: 24.00°C

T6: 24.00°C
T7: 24.20°C

T8: 24.81°C
Mean temperature at the surface of the specimen on the heater side,

= 24.48°C

Mean temperature at the surface of the specimen on cold plate side,

= 24°C

Area of heat transfer,

= 0.0962m2
In above equation, d is the diameter of the specimen

Heat transferred,

Δx is the thickness of the specimen

Thermal conductivity k =2.4001Wm-1K-1

Result:
Thermal conductivity of the given specimen by conduction = 2.4001Wm-1K-1
Test 4

Material used: Ebonite Solid

Result:
T1: 25.44°C

T2: 25.55°C
T3: 24.92°C

T4: 25.55°C
T5: 19.00°C

T6: 19.00°C
T7: 24.92°C

T8: 25.55°C
Mean temperature at the surface of the specimen on the heater side,

= 25.365°C

Mean temperature at the surface of the specimen on cold plate side,

= 19°C

Area of heat transfer,

= 0.0754m2
In above equation, d is the diameter of the specimen

Heat transferred,

Δx is the thickness of the specimen

Thermal conductivity k =0.3499Wm-1K-1

Result:
Thermal conductivity of the given specimen by conduction = 0.3499Wm-1K-1
Conclusion
In this experiment, we found out that each materials that we used to check through thermal
conductivity shows that the value material different. Besides, Thermal Conductivity is a measure
of a materials ability to transfer heat through itself and is one of the 3 variables in Thermal
resistance. Thermal Resistance is analogous to Electrical Resistance in that it is inversely
proportional to the flow of heat. The materials that we used is glass, cardboard, mica and
ebonite solid shows the resistance temperature is difference and mostly used in food industries
to ensure the quality remains forever.