Counter-flow vs parallel-flow · temperature profiles · LMTD & effectiveness–NTU
Two fluid streams flow through the exchanger separated by a wall, and heat passes from the hot stream to the cold one. In a parallel-flow unit both streams enter at the same end and run side by side; in a counter-flow unit they run in opposite directions. The right-hand plot shows the temperature of each stream along the length. The key idea is the capacity rate C = ṁ·c_p (in W/K): the stream with the smaller C changes temperature the most, because Q = C_hot·(T_h,in − T_h,out) = C_cold·(T_c,out − T_c,in).
The classic design equation is the LMTD method: Q = U·A·ΔT_lm, where the log-mean temperature difference is ΔT_lm = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂) using the end temperature differences. Counter-flow keeps a more even ΔT along the whole length, giving a larger ΔT_lm and more heat transfer for the same hardware — which is why it almost always beats parallel-flow.
The effectiveness–NTU method avoids iterating on unknown outlet temperatures. With NTU = UA / C_min and the capacity ratio Cr = C_min/C_max, the effectiveness ε (actual heat / maximum possible heat) follows a closed form: for counter-flow ε = (1 − e^(−NTU(1−Cr))) / (1 − Cr·e^(−NTU(1−Cr))). When one stream changes phase (a condenser or boiler) its capacity rate is effectively infinite, so Cr → 0 and both arrangements give the same simple ε = 1 − e^(−NTU).