This workbook evaluates the effectiveness (ε) as a function of NTU (number of transfer units) for a number of common heat exchanger geometries:   counter-flow, parallel flow, shell-and-tube w/1 shell, shell-and-tube w/2 shells, crossflow unmixed, crossflow mixed and crossflow with one fluid mixed.   These may be used to check results from our heat exchanger module.

Note that as the capacity ratio (CR = Cmin/Cmax) approaches 0.0 (as in a condenser or evaporator and seen above as the light blue line), the effectiveness is maximized.  That is, the counterflow/parallel flow nature of the shell-and-tube configuration becomes less important.

The analytical solutions tabulated here may be the best way to represent a heat exchanger in an overall system model as they can be expressed easily in terms of an algebraic equation (rather than needing a graphical lookup as with the LMTD (log mean temperature difference) approach.   VBA functions used therein may be easily copied and used elsewhere.