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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.

Forced convection of Williamson fluid flow in porous media under constant surface heat flux conditions is investigated numerically. A model of Darcy–Forchheimer–Brinkman is used and the corresponding governing equations are expressed in dimensionless forms and solved numerically using bvp4c with MATLAB package. Boundary layer velocity, shear stress, and temperature profiles, in addition to the local Nusselt number parameter over a horizontal plate, are found. The effects of the Forchheimer parameter, Nusselt number, Darcy parameter, porous inertia, and Williamson parameter on the velocity profiles, temperature profiles, coefficient of friction, and coefficient of heat transfer are investigated. The results showed that as the Darcy parameter increases, boundary layer velocity and shear stress increase, while the temperature and Nusselt number decrease. In addition, as Williamson's parameter increases, velocity within the boundary layer, shear stress, and Nusselt number decrease while the temperature profile increases. Also, with larger values of the Forchheimer parameter, the velocity of the boundary layer, shear stress, temperature, and Nusselt number increase. Furthermore, the Nusselt number and the coefficient of friction are obtained on the surface of the horizontal plate. [ABSTRACT FROM AUTHOR]

Heat transfer characteristics of an incompressible viscous fluid past a plate embedded into a porous medium with a convective boundary condition are obtained by using the Darcy-Forchheimer-Brinkman model. The governing partial differential equations are reduced to nonlinear ordinary differential equations, and similarity solutions are obtained. The similarity equations are solved numerically. With increasing convective parameter, the surface temperature increases. The rate of heat transfer increases as the Prandtl number increases. [ABSTRACT FROM AUTHOR]

In the present study, fluid flow and thermal characteristics associated with forced convection cooling of an array of discrete protruding heat sources mounted on impingement plate of channel by an impinging laminar jet is investigated for various Reynolds number ( Re ) and channel height ( H / L ) . It is observed that, the magnitude of average Nusselt number for all heat sources increases with increasing Re and decreasing H / L , except the regions of heat sources covered by recirculation bubbles which may be due to accumulation of heat resulting in hot spots. In order to eliminate these hot spots, a porous layer is attached to the impingement plate. A parametric study is conducted to predict the performance of porous layer on fluid flow pattern, heat transfer and entropy generation for various values of Darcy number ( Da ) , Reynolds number ( Re ) , channel height ( H / L ) , porosity ( ∊ ) and porous layer thickness ( h / H ) . For the purpose, equations governing two-dimensional, time-dependent, incompressible and laminar flow are solved in a Cartesian framework by using Streamline Upwind Petrov–Galerkin (SUPG) Finite Element (FE) method. The generalized Darcy–Forchheimer–Brinkman model is adopted to model the flow in porous medium. The recirculation bubbles on heat sources are completely eliminated with the inclusion of porous layer at Darcy number, Da = 10 - 2 . The magnitude of overall Nusselt number and global entropy generation due to heat transfer ( S θ , Ω ‾ ) and fluid friction ( S ψ , Ω ‾ ) increases with increasing Da , Re , h / H and decreasing ∊ and H / L . The optimum configuration for maximum heat transfer and minimum entropy generation is observed at Da = 10 - 2 , Re = 1000 , H / L = 1.0 , h / H = 0.75 and ∊ = 0.5 . [ABSTRACT FROM AUTHOR]

Numerical investigation of steady natural convection flow through a fluid-saturated porous medium in a vertical rectangular duct is investigated. The Darcy-Forchheimer-Brinkman model is used to represent the fluid transport within the porous medium. One of the vertical walls of the duct is cooled to a constant temperature, while the other wall is heated to constant but different temperature. The other two sides of the duct are insulated. The finite difference method of second-order accuracy is used to solve the non-dimensional governing equations. The results are presented graphically to show the effects of the Darcy number, inertial parameter, Grashof number, Brinkman number, aspect ratio, and viscosity ratio. It is found that an increase in the Darcy number and inertial parameter reduces the flow intensity whereas an increase in the Grashof number, Brinkman number, aspect ratio, and viscosity ratio increases the flow intensity. [ABSTRACT FROM AUTHOR]