Heat is generated uniformly in a large plate at a rate of Egen=e0(12x+1). the inside of the plate is fully insulated while the midpoint of the plate has a temperature of Tm. If the plate has a thickness of L and a thermal conductivity of k, express the temperature profile across the plate.

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.