EXPERIMENT NO# 2
EXPERIMENT NAME: DETERMINATION OF THERMAL CONTACT CONDUCTANCE
OBJECTIVE:
In addition to thermal properties of the contact materials and the interstitial fluids the thermal contact
conductance is also a function of contact geometry parameters such as surface roughness, hardness of
mating surfaces and contact pressure. The experiment has the following objectives:
1. Determine the thermal conduct conduce at different pressures.
2. Plot pressure vs. contact conduce curve.
3. Plot temperature vs. distance curve at different pressures.
THEORY:
When two surfaces are brought into contact, they actually touch only at a limited number of spots. The
remainder of the space between the surfaces may be filled with air or other fluid or may be in vacuum.
Thus when heat flows from one surface to the other, it experiences a resistance at the contact surface.
This resistance is known as contact resistance and the inverse of contact resistance is known as the
contact conductance. The unit of thermal conductance is W/m2K.
When two mating surface of materials having thermal conductivity of KC and KS are put under a pressure
of P (MPa), the X-section area of each of the mating surfaces is A (m2), the effective gap thickness
between then is δ. Meyer hardness number of the softer material is M, then the following numbers can be
defined as:
A
Interface size number, S = , where δ=15 microns
P
Constriction number, C = , where M= Meyer hardness number of Copper, 250 MPa
M
Gap number B = 0.335C 0.315S
0.137
K (K + K c )
Conductivity number, K = f s .
2K s K c
Where Kf= Equivalent Conductivity of air. Here Kf=KA+ 5.164x10-13 (Tm)3
Ka= Conductivity of air
Ks = Conductivity of steel
Kc= Conductivity of copper
Thus the ratio B/K can be calculated. Charts are used for calculating thermal contact conductance for the
specified constriction number C to find conductance number. Finally thermal contact conductance per
Uk 1
unit area uc may be obtained from, u c =
ASSUMPTION:
a. Heat transfer is one-dimensional.
b. Steady state condition.
c. Interstitial fluid is air only.
EXPERIMENTAL SETUP AND PROCEDURE:
Steel
Copper
Water in Water out
Figure-1: Experimental setup
PROCEDURE:
The cylindrical surface is insulated to ensure one dimensional heat flow. One metal is made of pure
copper and the other metal is carbon steel (0.5%C). They are insulated circumferentially. The top end of
the upper test piece (steel) is heated by an electric heater. The bottom end of the lower test piece is cooled
by water circulation. Iron constantan thermocouples are embedded at different locations on each metal
piece. A spring balance has been used to apply and indicate the force applied on the system.
Set the load force at 600 N. Switch on the heater and start the circulation of water. Allow sometime for
temperature distribution to reach the steady state condition. This can be checked by plotting temperature
vs. time curve for any one of the thermocouples. When steady state is attained, record the readings of all
the thermocouples and fill up the data sheet. Repeat the above procedure with spring.
Table-1:
Load Deflection
(N) (mm)
100 3.66
200 6.81
300 9.94
400 13.02
500 16.03
600 18.83
700 22.41
750 24.11
950 28.45
Table-2:
For conductivity Values of Copper, Steel and Air (W/mk)
Temperature (°C) Copper, KC Steel, KS Air, KA
0 386 55 0.0242
50 --- --- ---
100 379 52 ---
150 --- --- ---
200 374 48 0.0313
300 396 45 ---
400 --- --- 0.0388
DATA COLLECTION:
Table-3:
No. of obs Forces, FR Temperature (°C)
(kg)
For Steel fin For Copper fin Water Water
Inlet Outlet
TC-1 TC-2 TC-3 TC-4 TC-5 TC-6
1
2
3
4
5
Table-4:
No of obs. 1 2 3 4 5 6 7 8
Items of calculation
Resultant force, FR (kg)
FR
Pressure, P = (MPa)
A
Average gap Temp. Tm (°C)
A
Interface size number, S =
P
Constriction number, C=
M
Gap number, B = 0.335C
0.315S0.137
Conductivity of Air, KA at temp. Tm (W/mK)
Conductivity of Copper, KC at temp. Tm (W/mK)
Conductivity of Steel, KS at temp. Tm (W/mK)
Equivalent Conductivity of air, Kf=KA+ 5.164x10-13(Tm)3
K f (K s + K c )
Conductivity number, K = (W/mK)
2K s K c
B/K
U from graph
uc (W/m2K)
CALCULATION:
Record data and complete the calculation as described below:
a. Find FR
F
b. Find P form P = R where A is the X -section area of the rod, m2
A
c. For each pressure plot distance vs. steady state temperature and find the mean gap
temperature, Tm (K)
d. Find S, C and B from their respective definitions.
e. Find ka, kb and ks at temperature Tm from table for conductivity values given below.
f. Find kf and K
B
g. Find .
K
B
h. Find U from graph of U vs. .
K
Uk 1
i. Determine uc using u c =
DISCUSSION:
Discuss the variation of temperature gradient along the axis of the steel and copper rod and give suitable
differences. Discuss also the temperature gap at the contact surface and explain the cause behind it.
CONCLUSION:
a. Comment on the variation of contact conductance with pressure
b. Comment on the variation of temperature gap with pressure at the contact surface.
