How this calculator works
Capacity rates are mass flow times specific heat. Their smaller value limits the largest possible duty for the given inlet temperature difference. The selected flow arrangement maps NTU = UA/Cmin and capacity ratio to effectiveness. Design modes invert that map numerically and reject targets above its finite limit. Both-mixed crossflow is performance-only because its inverse can be nonunique; the both-unmixed expression is an engineering approximation. Properties and U are constant, with no external heat loss or phase change.
Formula
C = mdot cp; Cr = Cmin/Cmax; NTU = UA/Cmin; epsilon = Q/[Cmin(Thi - Tci)]. Counterflow at Cr = 1: epsilon = NTU/(1 + NTU). Parallel: epsilon = [1 - exp(-NTU(1 + Cr))]/(1 + Cr).
Worked example
For counterflow with both capacity rates 1000 W/K, inlets 400 K and 300 K, and UA = 1000 W/K, NTU = 1 and effectiveness = 0.5. Duty is 50000 W and both outlets are 350 K. Target effectiveness 0.75 requires NTU = 3 and three times the area at fixed U.
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Frequently asked questions
Can outlet temperatures cross?
Counterflow can have a cold outlet warmer than the hot outlet, while local heat still flows down a temperature gradient.
Why can a design target be rejected?
Some arrangements have a maximum effectiveness below one for a given capacity ratio; no finite area reaches a target beyond it.
What does the shell-pass count mean?
The model uses n shell passes with the standard 2n, 4n or higher compatible tube-pass arrangement.