Approximately 106  discrete electrical components can be  placed  on  a  single  integrated  circuit  (chip),  with electrical heat dissipation as high as 30,000 W/m2. The chip, which is very thin, is exposed to a dielectric liq- uid  at  its  outer  surface,  with  ho  = 1000  W/m2 · K and Too,o  = 20°C, and is joined to a circuit board at its inner surface.  The  thermal  contact  resistance  between  the chip  and  the board  is  10-4  m2 · K/W,  and  the  board thickness and thermal conductivity are Lb  = 5 mm and kb  = 1 W/m · K, respectively. The other surface of the board  is  exposed  to  ambient  air  for  which  hi  = 40 and kB = 0.04 W/m · K and thicknesses LA = 10 mm and LB = 20 mm. The contact resistance at the interface between the two materials is known to be 0.30 m2 · K/W. Material A adjoins a fluid at 200°C for which h = 10 W/m2 · K, and material B adjoins a fluid at 40°C for which h = 20 W/m2 · K.

(a) What is the rate of heat transfer through a wall that is 2 m high by 2.5 m wide?

(b) Sketch the temperature distribution.