You are stoking a fire in a furnace, and leave the stoker inside the furnace for several minutes. The end of the stoker inside the furnace reaches a temperature of 300°C, while the other end of the stoker in the air is cooled sufficiently to maintain a temperature of 60°C. The length of the stoker between these two ends is 2.0 m. If the cross-sectional area of the stoker is 0.0010 m2, determine the rate of heat transfer that occurs if (a) the stoker is made of aluminum (? = 237 W/m-K), (b) iron (? = 80.2 W/m-K), and (c) granite (? = 2.79 W/m-K).
Given: T1 = 300°C; T2 = 60°C; ?x = 2.0 m; A = 0.0010 m2
For the each material, approximate: dT/dx = T2-t1/?x
Qcond=-?A dT/dx = ?A T2 - T1/?x
(a) Aluminum: ? = 237 W/m-K
Qcond = -(237 W/m-K)(0.0010 m2)(60°C-300°C)/2.0m = 28.4 W
(b) Iron: ? = 80.2 W/m-K
Qcond = -(80.2 W/m-K)(0.0010 m2)(60°C-300°C)/2.0m = 9.62 W
(c) Granite: ? = 2.79 W/m-K
Qcond = - (2.79 W/m-K)(0.0010 m2)(60°C-300°C)/2.0m = 0.335 W
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