Transient Temperature Fields in Crossflow Heat Exchangers With Finite Wall Capacitance

Solutions are provided in nondimensional form for the transient analysis of direct-transfer crossflow heat exchangers, with both fluids unmixed and finite wall heat capacity. The two-dimensional transient temperature distributions of core wall and both fluids are determined by analytical methods for any externally applied variation of the primary fluid inlet temperature. The general solutions are derived by the local energy balance equations, and are presented as simple integrals of the Green’s functions, which represent the pulse response following a deltalike perturbation in the inlet temperature of the primary fluid, and are deduced using the Laplace transform method. The Green’s functions are expressed as integrals of modified Bessel functions, in terms of the heat capacity ratios, number of transfer units, heat transfer resistance and flow capacitance ratios.