A. INTRODUCTION

The differential equations given in Section 98 are useful if the two fluids flow in parallel or counter flow, or in some combination of these. They cannot be used, however, in cross-flow situations, for these give rise to 2D or 3D temperature variations, see Section 101.

The task of the present section is to develop the differential equations that govern the temperature distribution in more complex situations. Mass transfer and phase-change effects will be neglected for simplicity; a more advanced treatment, allowing for these effects, is to be found in Spalding (1980).

It has been common practice for heat exchanger theorists to suppose that they know quantitatively the pattern of flow adopted by the fluids in the equipment, and that their task is to predict the resulting temperature distributions. This is the first level at which the differential equations can be approached: the velocities appearing in them can be regarded as known functions of position.

However, knowledge of actual flow patterns in, say, baffled shells, is in fact very unreliable; little more is known than that the common assumptions are considerably at fault. It therefore becomes desirable to be able to calculate the velocity fields on the basis of the best general information that is available concerning flows in media containing distributed resistances (such as baffles per banks of tubes).