A section of a composite wall with the dimensions shown below has uniform temperatures of 200°C and 50°C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA = 70 W/(m K), kB = 60 W/(m K), kc = 40 W/(m K) and kD = 20 W/(m K), determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces.

Question

GIVEN

• A section of a composite wall

• Thermal conductivities

? kA = 70 W/(m K)

? kB = 60 W/(m K)

? kC = 40 W/(m K)

? kD = 20 W/(m K)

• Surface temperatures

? Left side (TAs) = 200°C

? Right side (TDs) = 50°C

FIND

(a) Rate of heat transfer through the wall (q) (b) Temperature at the interfaces

ASSUMPTIONS

• One dimensional conduction

• The system is in steady state

• The contact resistances between the materials is negligible

SKETCH

Answer 1

The thermal circuit for the composite wall is shown below



(a) Each of these thermal resistances has a form given by



Evaluating the thermal resistance for each component of the wall



The total thermal resistance of the wall section, is.



The total rate of heat transfer through the composite wall is given by



(b) The average temperature at the interface between material A and materials B and C (TABC) can be

determined by examining the conduction through material A alone





The average temperature at the interface between material D and materials B and C (TBCD) can be

determined by examining the conduction through material D alone