Vertical Free Convective Boundary-Layer Flow in a Bidisperse Porous Medium

In this article, we study the effect of adopting a two-temperature and two-velocity model, appropriate to a bidisperse porous medium (BDPM), on the classical Cheng–Minkowycz study of vertical free convection boundary-layer flow in a porous medium. It is shown that the boundary-layer equations can be expressed in terms of three parameters: a modified volume fraction, a modified thermal conductivity ratio, and a third parameter incorporating both thermal and BDPM properties. A numerical simulation of the developing boundary layer is guided by a near-leading-edge analysis and supplemented by a far-field analysis. The study is completed by a presentation of numerical simulations of the elliptic equations in order to determine how the adoption of the BDPM model affects the thermal fields in the close vicinity of the origin.

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NATURAL CONVECTION BOUNDARY LAYER FLOW ALONG A SPHERE EMBEDDED IN A POROUS MEDIUM FILLED WITH A NANOFLUID

Latin American Applied Research - An international journal ◽

10.52292/j.laar.2014.433 ◽

2014 ◽

Vol 44 (2) ◽

pp. 149-157

Author(s):

A. M. RASHAD

Keyword(s):

Boundary Layer ◽

Porous Medium ◽

Boundary Layer Flow ◽

Volume Fraction ◽

Skin Friction Coefficient ◽

Convection Boundary Layer ◽

Physical Parameters ◽

Extended Model ◽

Local Skin ◽

Layer Flow

A boundary-layer analysis is presented for the natural convec tion boundary layer flow about a sphere embedded in a porous medium filled with a nanofluid using Brinkman-ForchheimerDarcy extended model. The model used for the nanofluid incorporates the ef fects of Brownian motion and thermophoresis. The governing partial differential equa tions are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature, and nanoparticles volume fraction profiles as well as the local skin-friction coefficient, local Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.

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Mixed Convection Boundary Layer Flow Near the Lower Stagnation Point of a Cylinder Embedded in a Porous Medium Using a Thermal Nonequilibrium Model

Journal of Heat Transfer ◽

10.1115/1.4033164 ◽

2016 ◽

Vol 138 (8) ◽

Cited By ~ 6

Author(s):

Haliza Rosali ◽

Anuar Ishak ◽

Ioan Pop

Keyword(s):

Boundary Layer ◽

Porous Medium ◽

Differential Equations ◽

Mixed Convection ◽

Stagnation Point ◽

Boundary Layer Flow ◽

Thermal Conductivity Ratio ◽

Convection Boundary Layer ◽

Convection Boundary ◽

Layer Flow

The present paper analyzes the problem of two-dimensional mixed convection boundary layer flow near the lower stagnation point of a cylinder embedded in a porous medium. It is assumed that the Darcy's law holds and that the solid and fluid phases of the medium are not in thermal equilibrium. Using an appropriate similarity transformation, the governing system of partial differential equations are transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. We investigate the dependence of the Nusselt number on the solid–fluid parameters, thermal conductivity ratio and the mixed convection parameter. The results indicate that dual solutions exist for buoyancy opposing flow, while for the assisting flow, the solution is unique.

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