Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow

In this paper, we will study the existence of strong solutions for a nonlinear system of partial differential equations arising in convective flow, modeling a phenomenon of mixed convection created by a heated and diving plate in a porous medium saturated with a fluid. The main tools are Schäfer’s fixed-point theorem, the Fredholm alternative, and some theorems on second-order elliptic operators.

Влияние периодической макрошероховатости на развитие турбулентной свободной конвекции у внезапно нагреваемой вертикальной пластины

The results of numerical simulation of unsteady free convection developing near a suddenly heated plate, on which protrusions in the form of adiabatic cylinders of double height with respect to the diameter are arranged in a checkerboard pattern, are presented. The calculations were performed according to the Reynolds equations using a differential model of turbulent stresses. The range of variation of the Grashof number (plotted according to the thickness of the free convective flow), in which a significant intensification of heat transfer can be achieved, has been determined. It is shown that the best conditions for intensification are created if the longitudinal pitch in the array of protrusions is approximately twenty times the diameter of the latter.