Question

P6.10 A 60 cm long stel rod with a diameter of 4 cm is mated to a 40 cm long Cu rod with the same diameter. The unmated end of the steel rod (not at the interface) is connected to a 140 oC heat source, while the far end of the Cu (not at the interface) is connected to a 20 °C heat source. When the rod reaches steady-state, what is the a) temperature at th and b) heat rate through the rod. e steel-Cu interface 73

Answer 1

Given length of steel rod (l_1) = 60 cm, K_steal = 50.2 Wm^- 1 degree c^- 1 = K_1 length of copper rod (l_2) = 40 cm, K_copper = 385 Wm^- 1 degree c^- 1 = K_2 Area(A) = pi r^2 Diameter = 4 cm T_1 = 140 degree c T degree c T_2 = 20 degree c When two rods are connected in series, due to temperature difference between the free ends, the rate of heat transfer (heat current) remains same. i.e (dQ/dt)_steal = (dQ/dt)_copper rightarrow 1 right double arrow K_1(T_1 - T)A/l_1 = K_2(T - T_2)A/l_2 right double arrow K_1l_2T_1 - K_1l_2 T = K_2Tl_1 - K_2 T_2l_1 right double arrow T(K_1l_2 + K_2l_1) = K_1T_1l_2 + K_2T_2l_1 right double arrow T = K_1T_1l_2 + K_2T_2l_1/K_1l_2 + K_2l_1 Temperature at interface(T) = 50.2 times 140 times 40 times 10^- 2 + 385 times 20 times 60 times 10^- 2