G. P. Raja Sekhar

Soret and Dufour Effects in a Non-Darcy Porous Medium

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.

Two-dimensional viscous flow in a granular material with a void of arbitrary shape

The effect of the presence of a void of characteristic size R0 in a granular material with permeability k on an otherwise undisturbed uniform flow U∞ is investigated analytically. The cavity region is assumed to be two-dimensional, and its cross section is slightly deformed from a circle. The entire flow field is determined by matching the solution of the Stokes equation inside the hole with that of the generalized Darcy’s equation (or Brinkman’s equation) in the granular material. The effect of the hole increases with the value of ζ0=R0/k. When ζ0 is much larger than unity, which corresponds to the case for typical groundwater flow, the velocity at the center of the circular cylindrical hole U0 becomes 3U∞. In addition this velocity depends on the shape and orientation of the cavity, and attains still larger value. The volume flux Q0 flowing into the hole from the upstream side also depends on ζ0 and its configuration, which is typically two times for a circular cavity in comparison with Q∞ that would ot...

Thermocapillary drift on a spherical drop in a viscous fluid

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 Laplaces 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 Faxens laws are presented. The use of the drag formula has been demonstrated by few particular cases. Some important asymptotic limiting cases have been discussed.

BOUNDARY INTEGRAL EQUATIONS FOR A THREE-DIMENSIONAL STOKES–BRINKMAN CELL MODEL

The purpose of this paper is to prove the existence and uniqueness of the solution in Sobolev or Holder spaces for a cell model problem which describes the Stokes flow of a viscous incompressible fluid in a bounded region past a porous particle. The flow within the porous particle is described by the Brinkman equation. In order to obtain the desired existence and uniqueness result, we use an indirect boundary integral formulation and potential theory for both Brinkman and Stokes equations. Some special cases, which refer to the cell model for a porous particle with large permeability, or to the exterior Stokes flow past a porous particle, are also presented.

Stokes flow past a porous sphere with an impermeable core

Abstract Stokes flow of a viscous, incompressible fluid past a porous sphere with an impermeable core using Darcy law for the flow in the porous region is discussed. The formulae for drag and torque are found by deriving the corresponding Faxens laws. It is found that torque is always less than that on a solid sphere and it does not depend on the radius of the impermeable core. Some illustrative examples are discussed.

Thermocapillary migration of a spherical drop in an arbitrary transient Stokes flow

The present problem is concerned with an arbitrary transient Stokes flow past a viscous drop. The interfacial tension gradient is assumed to be dependent on temperature which is unsteady and hence governed by unsteady heat conduction equation. Solenoidal decomposition method is used to solve the hydrodynamic problem. The unknown coefficients have been computed by using non-isothermal boundary conditions. The drag force and torque exerted on the surface of the drop are computed in the form of Faxen’s laws. Some special cases like flow due to an unsteady Stokeslet and thermal field due to a heat source have been discussed. Asymptotic expansions for drag and torque have been calculated. Further, we have computed migration velocity.

OVERALL BED PERMEABILITY FOR FLOW THROUGH BEDS OF PERMEABLE POROUS PARTICLES USING THE EFFECTIVE MEDIUM MODEL-STRESS JUMP CONDITION

An effective medium model is used for predicting the overall bed permeability (OBP) for the flow through beds of permeable porous spherical particles. The effective medium model used here assumes that a single permeable porous spherical particle is surrounded by a hypothetical fluid envelope and an effective medium beyond the envelope. Stokes equations are used in the fluid region and Brinkman equations are used inside the porous regions. At the porous-liquid interfaces, the stress-jump condition is used together with the continuity of velocity components and the continuity of normal stress. Fa[xacute]ens law for drag and torque acting on the surface of permeable porous sphere is determined and hence the overall bed permeability is calculated as an implicit relation. This model converges to the existing models in various limiting cases.

EXISTENCE AND UNIQUENESS RESULT FOR THE PROBLEM OF VISCOUS FLOW IN A GRANULAR MATERIAL WITH A VOID

The purpose of this paper is to obtain an indirect boundary integral formulation for the three-dimensional viscous flow problem in a granular material with a void. The corresponding existence and uniqueness result of the classical solution to this problem is proved by using the theory of hydrodynamic potentials.

Lifting a large object from an anisotropic porous bed

An analytical study of two dimensional problem of lifting an object from the top of a fully saturated rigid porous bed is discussed. It is assumed that the porous bed is anisotropic in nature. The flow within the gap region between the object and the porous bed is assumed to be governed by Stokes equation while the flow within the porous bed is governed by Brinkman equation. The breakout phenomenon for different kinds of soil is reported. The effect of mechanical properties like anisotropic permeability, grain diameter size, and porosity on streamlines, velocity, and force is analyzed. Relevant comparison with C. C. Mei, R. W. Yeung, and K. F. Liu [“Lifting a large object from a porous bed,” J. Fluid. Mech. 152, 203–215 (1985)] and Y. Chang, L. H. Huang and F. P. Y. Yang [“Two-dimensional lift-up problem for a rigid porous bed,” Phys. Fluids, 27, 053101 (2015)] is done.

Expansions at small Reynolds numbers for the flow past a porous circular cylinder

The purpose of this article is to use the method of matched asymptotic expansions (MMAE) in order to study the two-dimensional steady low Reynolds number flow of a viscous incompressible fluid past a porous circular cylinder. We assume that the flow inside the porous body is described by the continuity and Brinkman equations, and the velocity and boundary traction fields are continuous across the interface between the fluid and porous media. Formal expansions for the corresponding stream functions are used. We show that the force exerted by the exterior flow on the porous cylinder admits an asymptotic expansion with respect to low Reynolds numbers, whose terms depend on the characteristics of the porous cylinder. In addition, by considering Darcys law for the flow inside the porous circular cylinder, an asymptotic formula for the force on the cylinder is obtained. Also, a porous circular cylinder with a rigid core inside is considered with Brinkman equation inside the porous region. Stress jump condition is used at the porous–liquid interface together with the continuity of velocity components and continuity of normal stress. Some particular cases, which refer to the low Reynolds number flow past a solid circular cylinder, have also been investigated.