P. V. S. N. Murthy

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.

NATURAL CONVECTION HEAT TRANSFER FROM A HORIZONTAL WAVY SURFACE IN A POROUS ENCLOSURE

Abstract The effect of surface undulations on the natural convection heat transfer from an isothermal surface in a Darcian fluid-saturated porous enclosure has been numerically analyzed using the finite element method on a graded nonuniform mesh system. The flow-driving Rayleigh number Ra together with the geometrical parameters of wave amplitude a, wave phase φ, and the number of waves N considered in the horizontal dimension of the cavity are found to influence the flow and heat transfer process in the enclosure. For Ra around 50 and above, the phenomenon of flow separation and reattachment is noticed on the waits of the enclosure. A periodic shift,n the reattachment point from the bottom wall to the adjacent walls in the clockwise direction, leading to the manifestation of cycles of unicellular and bicellular clockwise and counterclockwise flows, is observed, with the phase varying between 0° and 350°. The counterflow in the secondary circulation zone is intensified with the increase in the value of Ra...

Soret-driven thermosolutal convection induced by inclined thermal and solutal gradients in a shallow horizontal layer of a porous medium

The stability of Soret-driven thermosolutal convection in a shallow horizontal layer of a porous medium subjected to inclined thermal and solutal gradients of finite magnitude is investigated theoretically by means of a linear stability analysis. The horizontal components of these gradients induce a Hadley circulation, which becomes unstable when vertical components are sufficiently large. We employed a two-term Galerkin approximation for various modes of instability. The effect of the Soret parameter on the mechanism of instability of the thermosolutal convection is investigated. Results are presented for various values of the governing parameters of the flow. It is observed that the Soret parameter has a significant effect on convective instability and this is discussed.

Effect of Double Dispersion on Mixed Convection Heat and Mass Transfer in Non-Darcy Porous Medium

Similarity solution for the problem of hydrodynamic dispersion in mixed convection heat and mass transfer from vertical surface embedded in porous media has been presented. The flow induced by the density variations is comparable with the freestream flow. The heat and mass transfer in the boundary layer region for aiding and opposing buoyancies in both aiding and opposing flows has been analyzed. The structure of the flow, temperature, and concentration fields in the Darcy and non-Darcy porous media are governed by complex interactions among the diffusion rate (Le) and buoyancy ratio (N) in addition to the flow driving parameter (Ra/Pe). The flow, temperature, and concentration fields are analyzed and the variation of heat and mass transfer coefficients with the governing parameters are presented

Effect of viscous dissipation on a non-Darcy natural convection regime

The effect of viscous dissipation on non-Darcy natural convection flow along an isothermal vertical wall embedded in a saturated porous medium is initiated. The flow field is divided into non-Darcy G = 0, intermediate G = 0(1), and limit Darcy regimes G → ∞ using the inertia-buoyancy scales. Thermal dispersion effects are also taken into consideration. It is observed that the viscous dissipation effect reduces the heat transfer rate by about 10% in all three flow regimes. It is also found that the effect of viscous dissipation greater as the value of the parameter G increases. The effect of viscous dissipation in all three flow regimes increases with the dispersion parameter.

FREE CONVECTION HEAT TRANSFER FROM AN ISOTHERMAL WAVY SURFACE IN A POROUS ENCLOSURE

The coupled streamfuction–temperature equations governing the Darcian flow and convection process in a fluid-saturated porous enclosure with an isothermal sinusoidal bottom sun face, has been numerically analyzed using a finite element method (FEM). No restrictions have been imposed on the geometrical non-linearity arising from the parameters like wave amplitude (a), number of waves per unit length (N), wave phase (Φ), aspect ratio (A) and also on the flow driving parameter Rayleigh number (Ra). The numerical simulations for varying values of Ra bring about interesting flow features, like the transformation of a unicellular flow to a multicellular flow. Both with increasing amplitude and increasing number of waves per unit length, owing to the shift in the separation and reattachment points, a row–column pattern of multicellular flow transforms to a simple row of multicellular flow. A cycle of n celluar and n+1 cellular flows, with the flow in adjacent cells in the opposite direction, periodically manifest with phase varying between 0 and 360°. The global heat transfer into the system has been found to decrease with increasing amplitude and increasing number of waves per unit length. Only marginal changes in the global heat flux are observed, either with increasing Ra or varying Φ. Effectively, sinusoidal bottom surface undulations of the isothermal wall of a porous enclosure reduces the heat transfer into the system.

Soret and Dufour Effects on Free Convection Heat and Mass Transfer From a Horizontal Flat Plate in a Darcy Porous Medium

The effect of Soret and Dufour parameters on the non-Darcy natural convection over a horizontal flat plate in saturated porous medium is studied using similarity technique. Forchheimer extension is considered in the flow equations. Wall temperature and concentration distributions are assumed to be of the form Ax1/2 and Bx1/2 respectively, where x is the distance from the leading edge. The effect of Soret parameter Sr, Dufour parameter Df, diffusivity ratio Le, buoyancy ratio parameter N and the inertia parameter Gr on non-dimensional temperature and concentration, heat and mass transfer coefficients are analyzed. The variation of heat and mass transfer coefficients with these second order effects is presented for various values of the flow governing parameters.

Free Convective Heat and Mass Transfer in a Doubly Stratified Non-Darcy Porous Medium

Free convective heat and mass transfer from a vertical surface embedded in a doubly stratified non-Darcy porous medium has been analyzed. The wall temperature and concentration are constant and the medium is linearly stratified in the vertical direction with respect to both temperature, and concentration. A series approximation is made for stream function, temperature, and concentration in terms of the stratification parameter The flow, temperature, and concentration fields are affected by the complex interactions among the diffusion ratio Le, buoyancy ratio N and stratification ratio Sr in addition to the inertia parameter F c . The effect of double stratification of the medium on nondimensional heat and mass transfer coefficients is discussed.

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

Abstract In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.

Magnetic targeting in the impermeable microvessel with two-phase fluid model—Non-Newtonian characteristics of blood

The present investigation deals with finding the trajectories of the drug dosed magnetic carrier particle in a microvessel with two-phase fluid model which is subjected to the external magnetic field. The radius of the microvessel is divided into the endothelial glycocalyx layer in which the blood is assumed to obey Newtonian character and a core and plug regions where the blood obeys the non-Newtonian Herschel-Bulkley character which is suitable for the microvessel of radius 50 microm. The carrier particles, bound with nanoparticles and drug molecules are injected into the vascular system upstream from malignant tissue, and captured at the tumor site using a local applied magnetic field. The applied magnetic field is produced by a cylindrical magnet positioned outside the body and near the tumor position. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel are considered in the present problem. An algorithm is given to solve the system of coupled equations for trajectories of the carrier particle in the invasive case. The trajectories of the carrier particle are found for both invasive and noninvasive targeting systems. A comparison is made between the trajectories in these cases. Also, the present results are compared with the data available for the impermeable microvessel with single-phase fluid flow. Also, a prediction of the capture of therapeutic magnetic nanoparticle in the impermeable microvasculature is made for different radii, distances and volume fractions in both the invasive and noninvasive cases.