Convective heat transfer in a locally heated plane incompressible fluid layer

Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border

“…A brief survey of the articles and reviews, in which the possibilities of finding exact solutions to free convection equations and the research of stability of these solutions were studied [4][5][6][7][8][9][10], is given in the papers [1,2] and the reference lists.…”

“…In this case, finding the exact solution is reduced to solving the nonlinear system of one-dimensional evolution heat conduction equations like heat conductivity, and stationary equations of the gradient type. When finding the exact solutions, which describe the convective fluid flow [1][2][3][4][5][6][7][8][9][10], an ideal heat transfer on the borders is assumed. The aim of the present work is to investigate the motion of a viscous incompressible fluid with heat exchange on the upper boundary.…”

Couette - Hiemenz exact solutions for the steady creeping convective flow of a viscous incompressible fluid, with allowance made for heat recovery

“…By now, a certain stock of exact solutions to the Oberbeck-Boussinesq equations has been accumulated [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Exact solutions describing convective flows of a viscous incompressible fluid allow the qualitative and quantitative characteristics of a moving flow to be re-evaluated.…”

“…Exact solutions describing convective flows of a viscous incompressible fluid allow the qualitative and quantitative characteristics of a moving flow to be re-evaluated. With certain assumptions for highly viscous fluids, the Oberbeck-Boussinesq system can be simplified by neglecting inertial effects due to the predominance of viscous forces (the Stokes approximation) [8,[10][11][12][13][14][15][16][17][18][19].…”

“…By now, there have appeared Hiemenz exact solution modifications for isothermal flows [34][35][36] and convective flows [37][38][39][40] of a viscous incompressible fluid. The proposed generalizations of the Hiemenz exact solution family allow one to investigate counterflows in a fluid that are induced by kinematic, dynamic, and thermal perturbations of the fluid flow (boundary conditions) [8,9,[11][12][13][14][15][16][17][37][38][39][40]. Additionally, papers studying the existence of stagnant points in the flow and flows near such points are worthy of note.…”