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Question 3: Transient Heating of a Composite Wall (3 marks)

The composite wall of Q.1 consisting of two materials A and B with thermal conductivities kA =

5 W/m⋅K and kB = 1 W/m⋅K has warm air (40 °C) on one side and cold air (10 °C) on the other.

The thermal diffusivities of the materials A and B are 7.0×10-6 m2

/s and 2.0×10-6 m2


respectively. The heat transfer coefficients are 500 W/m2K and 450 W/m2K for the warm and

cold sides respectively. The thicknesses are as given in the figure below. The composite has

a uniform initial temperature of 15 °C. Neglecting contact resistance between the layers

and using the method of finite differences, calculate the wall surface temperature on the warm

side as a function of time during the first 60 seconds. Show your solution as a graph on the

spreadsheet. (Make sure you include axis labels and units on the graph). Hint: The calculation

will probably give you less trouble if you use a fully implicit time scheme rather than a time

marching scheme.

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