Nonlinear forced convective heat transfer in a composite air/porous layer with permeable top and bottom boundaries and energy source: different penetration depth of patterns

Abstract

The paper deals with nonlinear convective heat transfer in a horizontal air layer overlaying a heat-generating porous medium saturated with air. The composite air/porous system is bounded by the top and bottom solid permeable planes of equal temperature and forced by a vertical throughflow. The upward throughflow enhances heat flux through the air-porous interface, while the downward one reduces it with increasing the flow velocity or relative air layer depth. In the presence of a uniform energy source and basic throughflow, there are favorable conditions for penetrative convection. The stationary convective patterns of different penetration depth, which originate after the basic throughflow has lost its stability, are revealed by Newton's method. The supercritical and subcritical nonlinear regimes are studied with increasing the supercriticality. All of the regimes enhance heat flux. The short-wave convective patterns localized mainly in the upper air layer appear over the upward basic throughflow. Their relative contribution to the total heat flux is much smaller than that of the basic flow. It decreases with increasing the Peclet number or relative air layer depth. The similar local patterns or patterns of a large wavelength can initiate over the downward basic throughflow. Their relative contribution to the total heat flux grows with increasing the parameters mentioned. The large-scale convective patterns which cover both air and porous layers and are typical for a strong downward throughflow and small air layer depth contribute into the total heat transfer more effectively than those located in the air layer only.