A plane wall is a composite of

i.  A plane wall is a composite of two materials, A and B. The wall of material A (k = 75 W/m K) has uniform heat generation 1.5 X 106 W/m3, and thickness 50 mm. The wall material B has no generation with (k = 150 W/m K) and thickness 20 mm. The inner surface of material A is well insulated, while the outer surface of material B is cooled by a water stream with 30°C and heat transfer coefficient 1000 W/m2 K.

1.Sketch the temperature distribution that exists in the composite under steady-state conditions.
2.Determine the maximum temperature T1 of the insulated surface and the temperature of the cooled surface T2.
 
 
ii.  The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA  20 W/m  K and kC50 W/m  K, and known thickness, LA 0.30 m and LC  0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB  0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o  20°C, an inner surface temperature of Ts,i  600°C, and an oven air temperature of T  800°C. The inside convection coefficient h is known to be 25 W/m2  K. What is the value of kB?

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