For the simple case of condensation at constant temperature and constant overall coefficient in a singlepass arrangement, the logarithmic mean temperature difference is used. When stepwise calculations are made, the local temperature difference is used with the local overall coefficients and is integrated numerically. In a multipass arrangement it is necessary to use the local overall coefficient and local temperature difference for each pass. Iterative calculations are required in order to have the stream temperatures match at the turn-around. Computers can be programmed to perform such calculations. For shell-side condensation and assuming that the overall coefficient is constant for each pass at a given location along the shell, Butterworth (1977) has proposed the following calculation procedure.

The presentation assumes that temperature-enthalpy curves for the two fluid streams are already available. Capital letters are used to denote the shell-side stream and lowercase letters denote the tube side. Figure 1 shows a typical T-H curve for the shell-side stream. The tube-side temperatures may be plotted on this diagram by integrating numerically the equation

\[\label{eq1} \frac{dh^{II}}{dh^{I}} = \frac{T - t^{II}}{T - t^{I}}\tag{1}\]

A simple numerical form of this is

\[\label{eq2} {h^{II}_{\rm new}} = {h^{II}_{\rm old}} - \Delta h^{I} \frac{T - t^{II}}{T - t^{I}}\tag{2}\]