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.