Mixed Convection Boundary-Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium: Brinkman Model with Slip

Abstract

The steady boundary-layer flow near the stagnation point on an impermeable vertical surface with slip that is embedded in a fluid-saturated porous medium is investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary differential equations. This system is then solved numerically. The features of the flow and the heat transfer characteristics for different values of the governing parameters, namely, the Darcy-Brinkman, , mixed convection, λ, and slip, γ , parameters, are analysed and discussed in detail for the cases of assisting and opposing flows. It is found that dual solutions exist for assisting flows, as well as those usually reported in the literature for opposing flows. A stability analysis of the steady flow solutions encountered for different values of the mixed convection parameter λ is performed using a linear temporal stability analysis. This analysis reveals that for γ = 0 (slip absent) and = 1 the lower solution branch is unstable while the upper solution branch is stable.

Mixed convection and thermodynamic irreversibilities in MHD nanofluid stagnation-point flows over a cylinder embedded in porous media

“…Harris et al [22] built a similarity solution for the boundary layer developed near the stagnation point on a porous plate positioned vertically. A numerical work on mixed convection in jet impingement on a flat porous plate revealed that increasing the jet width and the Reynolds number lead to the magnification of the average Nusselt number [23].…”

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The stagnation-point flow towards a shrinking sheet with homogeneous – heterogeneous reactions effects: A stability analysis

“…On the other hand, if an initial decomposition, then the flow is declared as stable when the smallest eigenvalue is a positive value. As it has been recommended by Harris et al [20], as a result of relaxing a boundary condition on 0 ( ) …”