Mixed convection in horizontal fluid-superposed porous layers

Abstract

Mixed convection in horizontal fluid-superposed porous layers is studied in the following work. Much research has been done in the field of natural, mixed, and forced convection in a porous layer. Several studies have investigated natural and forced convection in a two-domain system that includes a porous and a fluid layer, but mixed convection has not been addressed. This problem can be found in many natural and engineering applications. Some examples include beach sand, human lungs, bread, gravel, soil, rock, packed bed reactors, fiberglass insulation, thermal energy storage systems, electronic cooling, crude oil extraction, nuclear reactors, and the list goes on. The present study is motivated by the wide range of applications and seeks to fill the gap in the literature regarding mixed convection. The problem considers a long, narrow channel that is partially filled with a porous layer and has a fluid layer above the porous layer. The channel is partially heated on the bottom and cross flow along the length of the channel is added in varying degrees. The problem is studied at a fundamental level, with the governing equations being derived, non-dimensionalized, discretized, and solved numerically. The two layers are treated as a single domain and the porosity is used as a switching parameter, causing the governing equations to transition from an extended form of the Darcy-Brinkman-Forchheimer equation in the porous layer to the Navier-Stokes equations in the fluid layer. This method avoids the need for interfacial boundary conditions to be explicitly defined at the interface between the two domains. Several dimensionless numbers are varied and their effects on the overall Nusselt number of the system are documented. The parameters varied include the Peclet number, the Rayleigh number, the porous layer height ratio, the Darcy number, the Prandtl number, and the conductivity ratio between the solid and fluid phases. In addition, the impact of the various additional terms in the extended form of Darcy's law is investigated and documented as well. The conductivity ratio, Darcy number, porous layer height ratio, Rayleigh number, and Peclet number all have a strong effect on the overall Nusselt number of the system, while the Prandtl number, the Brinkman term, the Forchheimer term, and the convective terms have a negligible effect. A critical Peclet number was observed, where the Nusselt number is a minimum, and was shown to be proportional to the Rayleigh-Darcy number and inversely proportional to the porous layer height ratio. A critical porous layer height ratio was also found, where the Nusselt number is a minimum, and was shown to be proportional to the Rayleigh-Darcy number and inversely proportional to the Peclet number. The streamlines capture the transition from the natural convection regime to the forced convection regime. In the transition region the flow patterns have characteristics of both domains. The isotherms capture the plume flow and show the influence of the cross flow on the shape and character of the plume. An experimental apparatus is designed in order to collect data over a similar range of parameters as explored numerically. The average error between the numerical and experimental results is 30%, with a peak of 67%. The numerical results show good agreement with the experimental data within the bounds of uncertainty. The experimental results confirm the presence of a critical Peclet number. However, they do not show the same trends at intermediate porous layer height ratios. The effect of the porous layer height ratio, η=h_p⁄H, on the Nusselt number is shown to be small in the range of η = 0.5 to η = 1 and large in the range of η = 0 to η = 0.5. Also, the transition to the forced convection regime occurs earlier for the numerical results than it does for the experimental results. This points towards future research opportunities that focus on the lower range of porous layer height ratio values.