1) Deduce an expression for generalized heat conduction equation in the Cartesian coordinates.

2) An electric current is passed through a composite wall made up of two layers. First layer is steel of 10 cm thickness and second layer is brass of 8 cm thickness. The outer surface temperature of steel and brass are maintained at 120°C and 65°C respectively. Suppose that the contact between two slab is perfect and the heat generation is 1,65,000 W/m³

a) Heat flux through the outer surface of brass slab

b) Interface temperature

3) Ten thin brass fins (K = 100 W/m K), 0.75 mm thick are placed axially on a 1m long and 60 mm diameter engine cylinder which is surrounded by 27°C. The fins are extended 1.5 cm from the cylinder surface and the heat transfer co-efficient between cylinder and atmospheric air is 15 W/m²k. Compute the rate of heat transfer and the temperature at the end of fins when the cylinder surface is at 160°C.

4) A large steel plate 5cm thick is initially at a uniform temperature of 400°C. It is abruptly exposed on both sides to a surrounding at 60°C with convective heat transfer co-efficient of 285 W/m²k. Compute the centre line temperature and the temperature inside the plate 1.25 cm from the mid plane after 3 minutes. Consider K for steel = 42.5 W/m²k, α for steel = 0.043 m²/hr.

5) Air at 30°C flows over a flat plate at a velocity of 4 m/s. The plate is maintained at 90°C. The plate dimension is 90 X 30 cm². Determine the heat transfer for the following condition:

a) First half of the plate,

b) Full plate,

c) Next half of the plate.