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Numerical simulation was carried out for nonisothermal incompressible viscous liquid in the open rectangular cavity, considering the heat loss through the channel bottom outer boundary. Liquid flow pattern and temperature profiles were obtained for solid and liquid phases. Influence of model parameters on heat carrier motion pattern and cavity cooling mode has been investigated. The interest in studies of convective flow in different heat transfer conditions and for various cavities is caused by a wide applied value of the problem. Large amount of heating devices is being used in power plants and energy systems, production processes of a various complexity level. The necessity of studying these processes is determined by development of such energy-intensive indistries as power engineering, metallurgy, chemical industry and many other (1-5). Experimental development of technologies always assumes a high probability of selecting not the best process conditions both for productivity and quality, and for implementation costs. Therefore, there arises a necessity to study theoretical hydrodynamic regularities and heat transfer during heat carrier motion in limited space. This article considers nonsteady interaction of liquid with the open cavity (Fig. 1). Process of molten metal movement in the channel is being investigated with consideration to heat exchange with its walls. Thermal and physical characteristics of the molten metal and cavity walls are identical. The purpose of this work is to investigate the hydrodynamics and conjugate heat transfer during movement of nonisothermal incompressible viscous liquid in the rectangular-type cavity in conditions of the channel's outer boundary cooling. Similar problems have been solved before (6-8) for thermal insulation conditions of the cavity outer boundaries. Study of the described process was done using a mathematical model based on the Navier-Stokes equations in the variables "vortex-stream function", the energy equation, and the heat-conduction equation for the cavity material with corresponding initial and boundary conditions + U X + V Y = 1

Conjugate heat transfer during viscous liquid movement in the open cavity, considering its cooling through outer boundary of back surface