The rate of energy conduction from inner surface to outer surface in radial direction is d Q d t = 2 π L k [ T a − T b ln ( b / a ) ] .

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Chapter 20, Problem 84CP

(a)

To determine

The rate of energy conduction from inner surface to outer surface in radial direction is dQdt=2πLk[Ta−Tbln(b/a)].

(b)

To determine

The power supplied to the heater.

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(a) The inside of a hollow cylinder is maintained at a tem- perature T, and the outside is at a lower temperature, T, (Fig. P19.45). The wall of the cylinder has a thermal conduc- tivity k. Ignoring end effects, show that the rate of energy conduction from the inner surface to the outer surface in the radial direction is [T.- T, dQ = 2Lk dt In(b/a) Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 27rL. (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 insulat- ing material 6.00 cm in thickness and having a thermal conductivity of 4.00 x 10-5 cal/s · cm · °C. A heater must maintain the interior temperature at 25.0°C while the out- side temperature is –35.0°C. What power must be supplied to the heater? T. Figure P19.45

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