The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

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Numerical Heat Transfer And Fluid Flow

The flow of homogeneous fluids through porous media: analogies with other physical problems

Boundary Integral and Singularity Methods for Linearized Viscous Flow: Green's functions

Life at Low Reynolds Number

The effect of double dispersion on free convection heat and mass transfer from a vertical surface embedded in a non-Darcy electrically conducting fluid saturated porous medium with Soret and Dufour effects is studied using similarity solution technique. The heat and mass transfer coefficients are effected greatly due to these secondary effects and also due to the complex interaction among the dispersion parameters Ra γ . Ra ξ , and Lewis number Le and buoyancy ratio N. In both aiding and opposing buoyancies, D f and S r have significant influence on the Nusselt and Sherwood numbers in the presence and absence of thermal and solutal dispersion in the medium. It is also observed that the magnetic field parameter lowered heat and mass transfer coefficients. The results are presented through comparison tables and plots.

Soret and Dufour Effects in a Non-Darcy Porous Medium

An arbitrary Stokes flow of a viscous, incompressible fluid inside a sphere with internal singularities, enclosed by a porous spherical shell, using Brinkman’s equation for the flow in the porous region is discussed At the interface of the clear fluid and porous region stress jump boundary condition for tangential stresses is used The drag and torque are found by deriving the corresponding Faxen’s laws It is found that drag and torque not only change with the varying permeability, but also change for different values of stress jump coefficient Critical permeability is found for which drag and torque change their behavior As a limiting case the corresponding Faxen’s laws for the rigid spherical shell with internal singularities has been obtained

Stokes flow inside a porous spherical shell: Stress jump boundary condition

Viscous flow past a porous sphere with an impermeable core : effect of stress jump condition

The present article investigates the overall bed permeability of an assemblage of porous particles. For the bed of porous particles, the fluid-particle system is represented as an assemblage of uniform porous spheres fixed in space. Each sphere, with a surrounding envelope of fluid, is uncoupled from the system and considered separately. This model is popularly known as cell model. Stokes equations are employed inside the fluid envelope and Brinkman equations are used inside the porous region. The stress jump boundary condition is used at the porous-liquid interface together with the continuity of normal stress and continuity of velocity components. On the surface of the fluid envelope, three different possible boundary conditions are tested. The obtained expression for the drag force is used to estimate the overall bed permeability of the assemblage of porous particles and the behavior of overall bed permeability is analyzed with various parameters like modified Darcy number (Da*), stress jump coefficient (β), volume fraction (e), and effective viscosity.

Stokes flow of an assemblage of porous particles: stress jump condition

The problem of non-isothermal fluid flow in and around a liquid drop has been studied The temperature of the fluid is assumed to be non-constant, steady and hence is governed by the Laplace's equation The thermal and hydrodynamic problems have been solved under nonisothermal boundary conditions assuming Stokes equations for the flow inside and outside the drop The drag and torque on the droplet in the form of Faxen's laws are presented The use of the drag formula has been demonstrated by few particular cases Some important asymptotic limiting cases have been discussed

G. P. Raja Sekhar

Papers

Soret and Dufour Effects in a Non-Darcy Porous Medium

Stokes flow inside a porous spherical shell: Stress jump boundary condition

Viscous flow past a porous sphere with an impermeable core : effect of stress jump condition

Stokes flow of an assemblage of porous particles: stress jump condition

Thermocapillary drift on a spherical drop in a viscous fluid