Numerical calculation of heat transfer processes in the case of laminar, free, convection flows in arbitrary, fixed or time-dependent, two-dimensional geometries

The present investigation is concerned with the theoretical study of heat transfer processes in the case of laminar, natural convection flows involving incompressible fluids. A finite difference procedure is proposed for the solution of the equations representing the conservation of mass, momentum, and energy. The formulation of the considered procedure makes it possible to employ arbitrary curvilinear coordinate systems which are adapted to the boundaries of the flow region. The coordinate systems are generated as the numerical solution of an elliptic, partial differential equation system. This approach makes it possible to examine flow processes in cases in which the flow region depends on the thermal and hydrodynamic behavior of the fluid medium. Such flows are found in many technical, biological, and geophysical systems. The numerical solution of the conservation equations is discussed, taking into account the Navier-Stokes equations. Applications of the new method are also considered, giving attention to the melting of ice, and processes of interest for the fabrication of alloys and single crystals under the environmental conditions of space.