Project ForgeConsider a parallel-flow heat exchanger with area Ap and a counter-flow heat exchanger with area Ac. In both, the hot stream flowing at 1 kg/s cools from 80°C to 50°C, and the cold stream (2 kg/s, both same fluid) enters at 10°C. Both heat exchangers have the same overall heat transfer coefficient. The ratio Ac/Ap is __________.
Explanation
Energy balance gives cold-stream exit temp: 1×30 = 2×(Tc_out-10) → Tc_out=25°C. Parallel-flow LMTD: ΔT1=70, ΔT2=25, LMTD_p=(70-25)/ln(70/25)≈43.7°C. Counter-flow LMTD: ΔT1=55, ΔT2=40, LMTD_c=(55-40)/ln(55/40)≈47.1°C. Since Q=UA·LMTD is the same Q and U, A∝1/LMTD, so Ac/Ap=LMTD_p/LMTD_c≈43.7/47.1≈0.93.
Source: GATE ME 2016 Set-2 (2016)
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