When the far end of the copper bar in Prob. 8.9 has a 30-ft² cooling fin attached to the end of the bar and is cooled by air convection, the temperature of the fin rises to t °F. If the temperature of the air is 23°F and the coefficient of heat transfer of the surface is 0.22 BTU/h, what is the value of t?
78.35(59.4 − t) = 6.6(t − 23)
11.87 × 59.4 − 11.87t = t − 23
t = 705/12.87 = 54.8°F