A thin electrical heater is fitted between two long, concentric cylinders with inner and outer radii of 20 mm and 40 mm. The inner solid cylinder (A) has a thermal conductivity kA = 0.15 W/m-K. The outer cylinder (B) has a thermal conductivity kB = 1.5 W/m-K and its surface is subjected to convection with a fluid temperature T = -15o C and a heat transfer coefficient of 50 W/m2 -K.

The missing part of the question ; The quesion continue by saying we should calculate the heat transfer per unit lenght required to maintain and outside temperature of 5degree celsius.

Explanation:

Given kA = 0.15 W/m-K, r1 = 20 mm (0.02m), r2 = 40mm(0.04m), kB = 1.5 W/m-K, h = 50 W/m2 -K, T∞ = -15 degree celsius

from heat transfer in a cylindrical shell ;

Q/L = TA - T∞ / ln(r2/r1)/ 2πkB + 1/2πhr2

Plugging the values into the equation ;

Q/L = 5 - (-15) / (ln 0.04/0.02) / 2x3.142x1.5 + 1/2x3.142x50x0.04

Q/L = 130.614W/m is the heat transfer per unit length

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