Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
Three straight metal wires AC, BC, CD (same length, diameter, thermal conductivity) are connected as a Y; heat flows from A and B to C, then from C to D. T_A=100°C, T_B=100°C, T_D=40°C. Find T_C (°C), steady state, no heat loss. (Answer in integer)
Official Answer Key:
80
Step-by-Step Solution & Explanation
Since all wires have identical length/diameter/conductivity, each has the same thermal resistance R. Energy balance at node C: (T_A−T_C)/R + (T_B−T_C)/R = (T_C−T_D)/R ⇒ (100−T_C)+(100−T_C) = (T_C−40) ⇒ 240 = 3T_C ⇒ T_C = 80°C.
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