Analytical and numerical solution of the problem on nonstationary heat exchange of counterflows

A solution was obtained to the nonstationary problem of heat transfer of counterflows that occur when a liquid flows through a loop. At the far end of the loop, temperature equality is specified and the temperature difference at the inlet and outlet is determined based on calculations at a given temperature of the incoming transfer fluid. It is shown that the formation of thermophysical processes in the heat transfer system under consideration is governed by the dimensionless convective–conductive parameter $P\nu$, which is the ratio of the contributions of convection and heat transfer to the heat exchange of the system. The solution is represented in the Laplace–Carson integral transform space. The originals were constructed using the den Iseger numerical inversion algorithm, since it is difficult to obtain them by analytical methods. The spatiotemporal dependences of temperature changes in the downstream and upstream flows are presented, which make it possible to broaden the existing understanding of physical processes for different values of the dimensionless convective–conductive parameter. It is shown that with increasing $P\nu$, the contribution of convection, as well as that of kinematic temperature waves, increases.