(a) The inside of a hollow cylinder is maintained at a temperature Ta, and the outside is at a lower temperature Tb, as shown in the figure. The wall of the cylinder has a thermal conductivity k. Ignoring end effects, show that the rate of energy conduction from the inner surface to the outer surface in the radial direction is
(Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 2πrL.)
(b) The passenger section of a jet airliner is in the shape of a cylindrical tube with a length of 35.0 m and an inner radius of 2.50 m. Its walls are lined with an insulating material 6.00 cm in thickness and having a thermal conductivity of 4.00 x 10-5cal/s-cm-°C. A heater must maintain the interior temperature at 25.0°C while the outside temperature is -35.0°C. What power must be supplied to the heater?
