A conductive heat transfer of 15 W is applied to a metal bar whose length is 0.50- m. The hot end of the bar is at 80oC. Determine the temperature at the other end of the bar for (a) a copper bar (? = 401 W/m-K) with a cross-sectional area of 0.0005 m2, (b) a copper bar (? = 401 W/m-K) with a cross-sectional area of 0.005 m2, and (c) a zinc bar (? = 116 W/m-K) with a cross-sectional area of 0.005 m2.
Given: Q?cond=150 W; ?x = 0.50 m; T1 = 80°C
What will be an ideal response?
From Qcond = ?A dT/dx = - ?A T2-T1/?x
T2 = Qcond/-?A + T1
(a) Copper, ? = 401 W/m-K, A = 0.0005 m2
T2 = 15W/-(401W/m-K) (0.0005 m2) (0.50 m) + 80° = 42.6°C
(b) Copper, ? = 401 W/m-K, A = 0.005 m2
T2 = 76.3°C
(c) Zinc, ? = 116 W/m-K, A = 0.005 m2
T2 = 54.1°C
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