An analytical model of a matrix heat exchanger with longitudinal heat conduction in the matrix in application for the exchanger dynamics research

The paper presents an analytical method for the solution of the problem of a fixed matrix heat exchanger with axial heat conduction within the matrix. The small parameter method and Laplace transform have been applied. A general solution has been obtained for the unsteady state in the form of function series, using single and double convolutions of functions, as well as a particular solution for both the uniform and non-uniform initial temperature of the matrix and for an arbitrary function of the fluid temperature at the inlet. Particular solutions have been used in the study of the matrix dynamics in determining dynamic characteristics for the standard input signals in the form of: Dirac δ pulse, Heaviside function and the function of sinusoidal variable temperature of the fluid at the inlet. The results obtained both illustrate and enable the assessment of the effect of axial heat conduction in the matrix on the dynamic properties of the heat exchanger.