(a) The inside of a hollow cylinder is maintained at a temperature , and the outside is at a lower temperature, (Fig. 19.45). 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 . A radial energy current passes through a concentric cylinder of area .
(b) The passenger section of a jet airliner is in the shape of a cylindrical tube with a length of and an inner radius of . Its walls are lined with an insulating material in thickness and having a thermal conductivity of . A heater must maintain the interior temperature at while the outside temperature is . What power must be supplied to the heater?
