An analytical method for calculation of transient temperature field in the counter-flow heat exchangers

In this paper, we present an analytical solution to the system of partial differential equations with homogeneous initial conditions, describing transient temperature field in counter-current heat exchangers. The system of partial differential equations is Laplace-transformed and the resultant set of ordinary differential equations is solved analytically. Analytical solution in the original domain is obtained for a special case of the heat exchanger where the thermal capacities and velocities of fluids are equal in both channels. Exemplary calculations are carried out to determine the unsteady response of the heat exchanger to a step change in the inlet temperature of one fluid.