Conjugate convective-conductive heat transfer in a rectangular region with forced flow and a heat source is simulated numerically. Distributions of the thermal and hydrodynamic characteristics of the flow regimes studied are obtained. The evolution of the process analyzed is shown.Introduction. The joint analysis of convection in a gas cavity and conductive heat transfer in solid blocks is of great theoretical significance [1, 2] and applied significance [3][4][5][6][7][8][9][10][11][12][13]. Recently, there has been increased interest in this problem [2][3][4][5][6][7][8][9][10][11][12][13] due to the possibility of using the theory of conjugate heat transfer in modern and promising technological systems. Results have been obtained that describe various flow regimes and configurations of solution regions. Lykov [1] considered a class of conjugate problems of convective heat transfer (simple geometry, external boundary conditions mainly of the first and second kind), analyzed conditions under which the conjugate formulation is the most correct, and found significant singularities of this class of problems. Great attention has been given to the problem of formulating conjugate problems. Liaqat and Baytas [2] performed numerical simulations of natural convection in a closed square region with heat-conducting walls of finite thickness. The obtained results indicate that the thermohydrodynamic parameters differ considerably from the same parameters in the nonconjugate formulation. Aydin [3], using a finite-difference method, analyzed conjugate heat transfer in a double-glazing window (thermal conductivity in only one direction was considered). Optimum thicknesses of the air layer between the glazing layers in a window for various climatic conditions were determined, and the effect of heat-transfer conditions on the boundaries on the thermohydrodynamic state of the object studied was analyzed. Yapici et al.[4] studied conjugate heat transfer in completely developed laminar flow in a channel heated on the outer contour. The channel considered had walls of silicon carbide and contained liquid metals (lithium and sodium). The cases of flow in a channel with constant thermal properties and temperature-dependent properties were analyzed. Characteristic distributions of temperature and thermal stress were obtained. Merrikh and Lage [5] performed a numerical study of natural convection in a closed rectangular region filled with a liquid flowing over several uniformly distributed heatconducting blocks. The solution region is an analog for both accommodation facilities and typical radio electronic devices. The effect of the number of blocks and their dimensions on the heat transfer process in the enclosure was determined. Polat and Bilgen [6] studied conjugate heat transfer in half-opened cavities (solar collectors, geothermal tanks, electronic chips), in which one of the walls of finite thickness was subjected to thermal flux and the other walls were thermally insulated. Distributions of thermal and hydrodynamic parameters we...