Analytical solutions of the equations for the transient temperature field in the three-fluid parallel-channel heat exchanger with three thermal communications

The partial differential equations for the general case of the three-fluid parallel-channel heat exchanger are solved analytically by formulating them into boundary control systems. Both the co- and the counter-flow cases with three thermal communications between the channels are considered. Based on the analytical solution formula for the transient case, the steady state and the time to reach the steady state are studied. Illustrating examples and numerical simulations are given.