A. Introduction

Analytical solutions presented in #%SECTION_1.3.3_%# have been used to build an engineering approach to the simplified heat exchanger design. The modelling described in Section 97, and Section 101 offers at least two major, alternate routes for resolving this task. These involve the so called (i) the F correction factor method [see Equation 97.10], and (ii) the NTU-effectiveness method [see Equation 97.15 and Equation 97.20]. The variation of these methods called, θ – P [see Equation (1.2.4(30)] or ψ – P, have also been promoted. In this section, we will emphasize in more detail how one executes the first two methods in resolving the major engineering task (determining the heat exchanger thermal size). The approaches will be applicable irrespective of the magnitude of the heat capacity rate ratio and flow arrangement, with constraints mentioned next.

Analytical solutions involving fluids with finite heat capacity rates are rigorously valid under conditions of adopted idealizations for the heat exchangers without a change of a fluid phase, i.e., not necessarily valid for condensers, evaporators and/or boilers — unless the phase change takes place throughout the heat exchanger. If a stream enters and leaves at the same temperature, having changed phase meanwhile, the temperature distribution analytical solutions can still be used. In general, the heat transferred between the fluids must be equal to the enthalpy change of each fluid stream (see Section 100), i.e.

\[\label{eq134_1} \dot{Q}=\Delta \dot{H}_{1,2} =\left( {\dot{M}\Delta h} \right)_{1,2} \tag{1}\]

In Equation 1, indices 1 or 2 denote Fluid 1 and Fluid 2. In case of the absence of phase transformations the heat transfer rate is