N. Rudraiah

Asymptotic analysis of natural convection through horizontal porous layer

Two-dimensional cellular convection in a fluid saturated horizontal porous layer is studied using a simple asymptotic analysis. Based on the physical grounds, supported by experiments, the entire region of study is divided into no-slip regime governed by the Brinkinan equations and slip regime governed by the Darcy equations. Self-consistent solutions for velocity and temperature are obtained in a closed form using the technique of matched asymptotic expansion. The transition from the no-slip regime to the slip regime is followed exactly and the maximum value of velocity is obtained. It is shown that the point of maximum velocity gets close to the bounding walls as the permeability parameter decreases. This exhibits the boundary layer behaviour. It is: also shown that permeability has negligible effect on the temperature distribution. Close agreement between analytical and numerical results is observed.

Natural convection through vertical porous stratum

Abstract The combined effect of Darcy and viscous resistances on the fully developed natural convection of a fluid between two heated vertical plates is investigated. When Darcy and viscous dissipations, in the energy equation, are negligible the energy and momentum equations become decoupled and we obtain the modified Poiseuille flow distribution through porous media. The deviation of the velocity and temperature distributions from those existing in modified Poiseuille flow are presented for various porous number σ = b k , b is the spacing between the plates and k is the permeability of the porous medium) when dissipations are not neglected. It is shown that the increase in porous number rapidly decreases the influence of both viscous and Darcy dissipations on velocity and temperature profiles. Therefore, by suitable adjustment of dissipation terms, it is possible to control the temperature distribution which will be of some use in plant physiology.

Convective diffusion in steady flow through a tube with a retentive and absorptive wall

This is a study on the mass transport, accomplished by reaction, advection, and dispersion, of a solute in steady Poiseuille flow through a circular tube with a reactive wall layer. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer and an irreversible component due to absorption into the wall. First, the generalized dispersion model is employed to deduce asymptotic steady-state values of the first three transport coefficients in terms of the strengths and kinetics of the two reactions, which can be of any magnitude. Second, a numerical simulation is performed to examine the time development of the fluid- and wall-phase concentration profiles starting from the initial release of the solute into the tube. The analytical deduction brings out not only results relevant to the asymptotic state when the transport coefficients become independent of time but also criteria that can be used to estimate the significance of the asymptotic steady state in the whole course of mass transport. The numerical simulation generates time-developing concentration profiles that can be used to explain some paradoxical behaviors exhibited by the transport coefficients under certain conditions.

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.

Modeling of Smart Materials of Nanostructure in a Poorly Electrically Conducting Fluid Saturated Composite Materials

To meet the demands of technology for the development of new materials with tailormade properties, we propose the use of smart materials of nanostructure synthesized by solidifying a poorly conducting alloy in a microgravity environment in the presence of an electric field and surface tension. Energy method combined with a single term Galerkin expansion is used to find the condition for the onset of Marangoni marginal electroconvection (MMEC) in a composite material modeled as a porous layer. It is shown that a proper choice of electric parameter and the ratio of Brinkman viscosity to viscosity of the fluid λ control Marangonielectroconvection (MEC).

Effect of Artificial Cartilage Made up of Smart Material of Nanostructure on Dispersion in Poorly Conducting Macromolecular Components in Synovial Joints

Electrohydrodynamic (EHD) dispersion of macromolecular components in a biological bearing consisting of a poorly conducting synovial fluid both in the cavity of the bones and in the bounding porous cartilage of finite thickness is investigated using Taylor’s [4] dispersion model . It is shown that artificial joints involving smart materials of nanostructure discussed here work more efficiently than the natural joints.

Effect of couple-stress on the ultrafiltration process

The effects of couple-stress and suction-Reynolds number on velocity and concentration distribution in the ultrafiltration process of a gel-polarization model are investigated. Both analytical and numerical techniques are used. The numerical method is based on an implicit finite difference scheme, and the analytical technique makes use of a regular perturbation. The calculations show that the effect of couple-stress is to inhibit the diffusive transport of solute molecules from the membrane surface to the bulk solution, in contrast to the suction effect. The ramification of the couple-stress in predicting the flux rates during ultrafiltration is examined.<<ETX>>

Influence of electric field on the control of haemolysis

The influence of an electric field on unsteady convective diffusion in coupled-stress flow is studied using a time-dependent dispersion model. The electric field is shown to increase the axial dispersion coefficient, which is useful in the control of hemolysis caused by implanted or extracorporeal artificial organs. The contribution of pure convection in the dispersion of concentration is singled out and investigated in detail. The results obtained are compared with those in the absence of electric field, and some important conclusions are drawn.<<ETX>>