Two-Dimensional Transient Solutions for Crossflow Heat Exchangers With Neither Gas Mixed

The two-dimensional transient behavior of gas-to-gas crossflow heat exchangers is investigated, solving by analytical methods the thermal balance equations in order to determine the transient distribution of temperatures in the core wall and in both the unmixed gases. Assuming large wall capacitance, the general solutions are deduced by the Laplace transform method and are presented as integrals of modified Bessel functions on space and time, for a transient response with any arbitrary initial and inlet conditions, in terms of the number of transfer units, capacity rate and conductance ratio. Specializing the entrance temperature and assuming constant initial conditions, the most meaningful transient conditions (such as step, ramp, and exponential responses) have been simulated and the relevant solutions, expressed by means of either integrals or series, have been accurately computed with extremely low computational time. The temperature responses are then presented in graphic form for a wide range of the number of transfer units.