Flow characteristics in a parallel-plate porous channel under convective boundary conditions and triple diffusion for the non-Darcy porous matrix

Abstract

This article inspects the effect of triple diffusion in a vertical conduit encapsulated with porous matrix and subjected to third kind boundary conditions. Third kind boundary condition is a combination of Dirichlet and Neumann boundary conditions which specifies a linear combination of function and its derivative values on the boundary. Homogeneous chemical reaction along with viscous and Darcy dissipation effects are included. Adapting the Boussinesq approximation, the soultal buoyancy effects due to concentration gradients of the dispersed components are taken into account. Applying suitable transformations, the conservation equations are reduced into dimensionless form and the dimensionless parameters evolved are thermal Grashof number (0≤Λ1≤20), solutal Grashof number (for species 1 and 2, 0≤Λ2,Λ3≤20), porous (2≤σ≤8) and inertial parameters (0≤I≤6), Biot numbers (at the left and right walls, 1≤Bi1,Bi2≤10), Brinkman number (0≤Br≤1), Schmidt numbers (0≤Sc1,Sc2≤6), Soret numbers (Sr1=Sr2=1) and temperature difference ratio (RT=1). Adopting perturbation technique, the analytical solutions which are applicable only when the Brinkman number is less than one is appraised. However for any values of the Brinkman number, Runge-Kutta shooting method is operated. The impact of selected parameters on the momentum, heat and dual species concentration fields are presented in the form of pictures. The solutions computed by numerical method are justified by comparing with the analytical method. The numerical and analytical solutions are equal in the absence of Darcy and viscous dissipations and the discrepancy advances as the Brinkman number expands. Further the solutions obtained are also justified by comparing the results with Zanchini [1] in the absence of chemical reaction for clear fluid. The thermal field is augmented with the Brinkman number for symmetric and asymmetric Biot numbers. However the profiles are highly distinct at the cold plate for unequal Biot numbers in comparison with equal Biot numbers. The conclusions are admissible to materials processing and chemical transport phenomena.