(6 points) A cylinder has a radius of 12 mm and a length of 2.5 m. It is made of steel with a thermal conductivity of LaTeX: 53.4 \frac{\mathrm{W}}{\mathrm{m K}}53.4 W m K. One end of the cylinder is held at a temperature of LaTeX: 361^{\circ}\text{C}361 ∘ C, the other at LaTeX: 105^{\circ}\text{C}105 ∘ C. In steady state how much power will flow through the cylinder in the form of heat?

2.46 W

Explanation:

Thermal conductivity k = 53.4 W/m-K

Radius r = 12 mm = 12x10^-3 m

Lenght = 2.5 m

T1 = 361 °C

T2 = 105 ∘C

Area A = ¶r^2 = 3.142 x (12x10^-3)^2

= 0.00045 m^2

Power P = -AkdT/dx

Where dT = 361 - 105 = 256

dx = lenght of heat travel = 2.5 m

P = -0.00045 X 53.4 X (256/2.5)

= -0.024 X 102.4 = -2.46 W

The negative sign indicates that heat is lost from the metal.

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