Heat is flowing through an annular wall of inside radius r0 and outside radius r1. The thermal conductivity varies linearly with temperature from k0 at T0 to k1 at T1. Develop an expression for the heat flow through the wall.

Air at a pressure of 1atm and a temperature of 40 c is in parallel flow over the top surface of a flat plate that is heated to a uniform temperature of 120 c. the plate has a length of 0.40m (in the flow direction) and a width of 0.15m. the reynolds number based on the plate length is 50, 000. what is the rate of heat transfer from the plate to the air? if the free stream velocity of the air is doubled and the pressure is increased to 10 atm what is the rate of heat transfer?