Thermoconvective flow in a saturated, isotropic, homogeneous porous medium using Brinkman’s model: numerical study

Abstract

Numerical results generated by a highly efficient finite‐difference method (originated by Keller for aerodynamical flows at the California Institute of Technology in 1970), and a robust double shooting Runge‐Kutta‐Merson scheme are presented for the boundary layer equations representing the convection flow of a viscous incompressible fluid past a hot vertical flat plate embedded in a non‐Darcy porous medium. Viscous dissipation due to mechanical work is included in the temperature field equation. The computations for both solution techniques are compared at the leading edge (ξ = 0.0) and found to be in excellent agreement. The effects of the viscous heating parameter (Ec), thermal conductivity ratio (λ) and a Darcy porous parameter (Re/GrDa) on the fluid velocities, temperatures, local shear stress and wall heat transfer rate are discussed with applications to geothermal and industrial flows.

Numerical solutions for unsteady rotating high-porosity medium channel Couette hydrodynamics

“…Fs > 0) and the model as used here has been implemented successfully by the authors in a wide spectrum of transport phenomena studies over the past decade. These include hydromagnetic convective non-Darcian flows [26], thermal radiation-convection dissipative non-Darcian boundary layer gas dynamics [27], variable-viscosity non-Darcian thermo-convection with viscous heating effects [28], hydromagnetic viscoelastic non-Darcian free, forced and mixed convection flows past a wedge [29], free convective non-Darcian MHD boundary layers from a vertical porous isothermal surface with suction/injection effects [30], combined radiation-convection flow in a non-Darcian boundary layer regime [31], second-order viscoelastic non-Darcian stagnation point and wedge thermal convection [32], radiation-convection non-Newtonian thermal boundary layers in non-Darcian porous regimes [33], thermally stratified Darcy-Forchheimer rotating convection flows [34], biomagnetic micro-structural physiological fluid flow through Darcy-Forchheimer models of tissue regimes [35], and most recently periodic hydromagnetic flow and mass transfer in Darcy-Forchheimer porous filtration materials [36]. The present study therefore constitutes an important addition to the scientific literature and simultaneously provides a benchmark for extension to non-Newtonian fluid cases.…”