Aspherical particle of radius r1 experiences uniform thermal generation at a rate of q. the particle is encapsulated by a spherical shell of outside radius r2 that is cooled by ambient air. the thermal conductivities of the particle and shell are k1 and k2, respectively, where k1 = 2k2. by applying conservation of energy principle to spherical control volume a, which is placed at ar arbitrary location within the sphere, determine a relationship between the temperature gradient dt/dr and the local radius r, for o < r

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.