Mathematical Model of the Heat Circulation Path of Complex Technical Systems

Assuming that the heat-emission and heat-dissipating components of the closed circulation cooling circuit belong to elements with hydrodynamics close to ideal displacement, and the heat in them is transferred by a convective mechanism without taking into account the thermal resistances with a uniform distribution of sources and channels, a mathematical model is proposed for determining non-stationary local temperatures in the form of an initial-boundary value problem for a system of first-order partial differential equations. An analytical solution is obtained which confirms the existence of an autooscillatory mode in the circuit. The condition for the existence of a stationary regime is indicated. Average trend of the equations with respect to the axial coordinates made it possible to estimate the reference local temperatures in the circulation path and to identify the relaxation time to the stationary regime. Using the example of a circulation circuit with a porous heat exchanger and a thermoelectric cooler, the effectiveness of the proposed approach for estimating the design of such systems is shown.