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(Solution Download) 1.14 A wall is made from an inhomogeneous (nonuniform) material for which the thermal...

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1.14   A wall is made from an inhomogeneous (nonuniform) material for which the thermal conductivity varies through the thickness according to k = ax + b, where a and b are constants. The heat flux is known to be con- stant. Determine expressions for the temperature gradi- ent and the temperature distribution when the surface at x = 0 is at temperature T1.

1.15   The 5-mm-thick bottom of a 200-mm-diameter  pan may be made from aluminum (k = 240 W/m · K) or copper (k = 390 W/m · K). When used to boil water, the surface of the bottom exposed to the water is nomi- nally at 110°C. If heat is transferred from the stove to the pan at a rate of 600 W, what is the temperature of the surface in contact with the stove for each of the two materials?

1.16   A square silicon chip (k = 150 W/m · K) is of width w = 5 mm on a side and of thickness t = 1 mm. The chip is mounted in a substrate such that its side and back surfaces are insulated, while the front surface is exposed to a coolant. If 4 W are being dissipated in cir- cuits mounted to the back surface of the chip, what is the steady-state temperature difference between back and front surfaces?



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