(a) The inside of a hollow cylinder is maintained at atemperature Ta, and the outside is
Chapter 20, Problem 84(choose chapter or problem)
(a) The inside of a hollow cylinder is maintained at atemperature Ta, and the outside is at a lower temperature,Tb (Fig. P20.84). The wall of the cylinder has athermal conductivity k. Ignoring end effects, show thatthe rate of energy conduction from the inner surfaceto the outer surface in the radial direction isdQdt5 2pLk cTa 2 Tbln1b/a2 Suggestions: The temperature gradient is dT/dr. Aradial energy current passes through a concentriccylinder of area 2prL. (b) The passenger section ofa jet airliner is in the shape of a cylindrical tube witha length of 35.0 m and an inner radius of 2.50 m. Itswalls are lined with an insulating material 6.00 cmin thickness and having a thermal conductivity of4.00 3 1025 cal/s ? cm ? C. A heater must maintainthe interior temperature at 25.0C while the outsidetemperature is 235.0C. What power must be suppliedto the heater?
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