Study of nonlinear convection in a sparsely packed porous medium using spectral analysis

Nonlinear study cellular convection in a sparsely packed fluid saturated porous medium is investigated, considering the Brinkman model, using the technique of spectral analysis. It is established how the Brinkman model with free-free boundaries generalizes the study of convection in a porous medium in the sense that it yields the results tending to those of viscous and Darcy flows respectively for very small and very large values of the permeability parameter �2. It also provides results for the transition zone (i.e. 102<�2<103). The cross-interaction of the linear modes caused by non-linear effects are considered through the modal Rayleigh number Rγ. The possibility of the existence of steady solution with two self-excited modes in certain regions is predicted. The similarities of present analysis with and advantages over that of the power integral technique are brought out. A detailed discussion of the heat transport, with the effect of permeability thereon, is made. The theoretical values of the Nusselt number are found to be in good agreement with experimental results. © 1983 Martinus Nijhoff Publishers

Fluid movement in a channel of varying gap with permeable walls covered by porous media

Blood flow in arteries idealized into a channel of varying gap bounded by porous layer is studied. Analytical solutions are obtained using Beavers and Joseph slip condition by three approximate methods depending upon the geometrical configuration. The general solutions are applied to a particular problem of smooth constriction idealized into an artery with stenosis. The resistance of the porous layer to the flow in the channel and the shear stress at the nominal surface are discussed in detail. It is shown that for a given porous layer, depending on the value of the porous parameter ασ0, this may lead to an increase or decrease in the resistance and the shear stress may be used in evaluating the performance of various prosthetic devices which ultimately may be implanted in the living system

Electrohydrodynamic Dispersion with Interphase Mass Transfer in a Poorly Conducting Couple Stress Fluid Bounded by Porous Layers

Exact analysis of miscible dispersion of solute with interphase mass transfer in a poorly conducting couple stress fluid flowing through a rectangular channel bounded by porous layers is considered because of its application in many practical situations. The generalized dispersion model of Sankarasubramanian and Gill is used, which brings into focus the exchange coefficient, the convective coefficient and the dispersion coefficient. The exchange coefficient comes into picture due to the interphase mass transfer and independent of solvent fluid viscosity. It is observed that the convective coefficient increases with an increase in the porous parameter while it decreases with an increase in the couple stress parameter. The dispersion coefficient is plotted against wall reaction parameter for different values of porous parameter and couple stress parameter. It is noted that the dispersion coefficient decreases with an increase in the value of couple stress parameter but increases with porous parameter

Oberbeck convection through vertical porous stratum

Natural convection through a vertical porous stratum is investigated both analytically and numerically. Analytical solutions are obtained using a perturbation method valid for small values of buoyancy parameter N and the numerical solutions are obtained using Runge-Kutta-Gill method. It is shown that analytical solutions are valid for N < 1 and several features of the effect of large values of N are reported. The combined effects of increase in the values of temperature difference between the plates and the permeability parameter on velocity, temperature, mass flow rate and the rate of heat transfer are reported. It is shown that higher temperature difference is required to achieve the mass flow rate in a porous medium equivalent to that of viscous flow

Electro-osmotic flow of couple stress fluids in a microchannel propagated by peristalsis

A mathematical model is developed for electro-osmotic peristaltic pumping of a non-Newtonian liquid in a deformable micro-channel. Stokes’ couple stress fluid model is deployed to represent realistic working liquids. The Poisson-Boltzmann equation for electric potential distribution is implemented owing to the presence of an electrical double layer (EDL) in the micro-channel. Using long wavelength, lubrication theory and Debye-Huckel approximations, the linearized transformed dimensionless boundary value problem is solved analytically. The influence of electro-osmotic parameter (inversely proportional to Debye length), maximum electro-osmotic velocity (a function of external applied electrical field) and couple stress parameter on axial velocity, volumetric flow rate, pressure gradient, local wall shear stress and stream function distributions is evaluated in detail with the aid of graphs. The Newtonian fluid case is retrieved as a special case with vanishing couple stress effects. With increasing couple stress parameter there is a significant elevation in axial pressure gradient whereas the core axial velocity is reduced. An increase in electro-osmotic parameter induces both flow acceleration in the core region (around the channel centreline) and also enhances axial pressure gradient substantially. The study is relevant to simulation of novel smart bio-inspired space pumps, chromatography and medical microscale devices

Natural convection in a square cavity with uniformly heated and/or insulated walls using marker-and-cell method

In this study, a numerical investigation has been performed using the computational Harlow-Welch MAC (Marker and Cell) finite difference method to analyse the unsteady state two-dimensional natural convection in lid-driven square cavity with left wall maintained at constant heat flux and remaining walls kept thermally insulated. The significant parameters in the present study are Reynolds number (Re), thermal Grashof number (Gr) and Prandtl number (Pr) and Peclét number (Pe =PrRe). The structure of thermal convection patterns is analysed via streamline, vorticity, pressure and temperature contour plots. The influence of the thermophysical parameters on these distributions is described in detail. Validation of solutions with earlier studies is included. Mesh independence is also conducted. It is observed that an increase in Prandtl number intensifies the primary circulation whereas it reduces the heat transfer rate. Increasing thermal Grashof number also decreases heat transfer rates. Furthermore the isotherms are significantly compressed towards the left (constant flux) wall with a variation in Grashof number while Peclét number is fixed. The study is relevant to solar collector heat transfer simulations and also crystal growth technologies