(a) The inside of a hollow cylinder is maintained at a

Chapter 20, Problem 84

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(a) The inside of a hollow cylinder is maintained at a temperature Ta, and the outside is at a lower temperature, Tb (Fig. P20.84). 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 dQ dt 5 2pLk c Ta 2 Tb ln1b/a2 d Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 2prL. (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 3 1025 cal/s ? cm ? C. A heater must maintain the interior temperature at 25.0C while the outside temperature is 235.0C. What power must be supplied to the heater?