Analytical solution to the equations for parallel-flow four-channel heat exchangers

Assuming that the thermophysical parameters of the fluids are independent on temperature, the stationary temperature field in a parallel-flow multi-channel heat exchanger can be described by a set of linear differential equations of the first order with constant coefficients. A compact analytical solution to this set is presented for the case of four-channel exchangers and simple eigenvalues of the coefficient matrix of the set.