The thermal effectiveness of a TEMA E shell-and-tube heat exchanger, with one shell pass and an arbitrary number of tube passes, is determined under the usual symplifying assumptions of perfect transverse mixing of the shell fluid, no phase change, and temperature independence of the heat capacity rates and the heat transfer coefficient. A purely algebraic solution is obtained for the effectiveness as a function of the heat capacity rate ratio and the number of heat transfer units. The case with M shell passes and N tube passes is easily expressed in terms of the single-shell-pass case.

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