The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a heated vertical plate is studied for high Rayleigh numbers. Similarity solutions are obtained within the frame work of boundary layer theory for a power law variation in surface temperature,T Wpropx lambda and surface injectionv Wpropx(lambda–1/2). The analysis incorporates the expression connecting porosity and permeability and also the expression connecting porosity and effective thermal diffusivity. The influence of thermal dispersion on the flow and heat transfer characteristics are also analysed in detail. The results of the present analysis document the fact that variable porosity enhances heat transfer rate and the magnitude of velocity near the wall. The governing equations are solved using an implicit finite difference scheme for both the Darcy flow model and Forchheimer flow model, the latter analysis being confined to an isothermal surface and an impermeable vertical plate. The influence of the intertial terms in the Forchheimer model is to decrease the heat transfer and flow rates and the influence of thermal dispersion is to increase the heat transfer rate.

Unsteady laminar compressible swirling flow with massive blowing

THE study of swirling boundary layers is of considerable importance in many rotodynamic machines such as rockets, jet engines, swirl generators, swirl atomizers, arc heaters, etc. For example, the introduction of swirl in a flow acceleration device such as a nozzle in a rocket engine promises efficient mass flow control. In nuclear rockets, swirl is used to retain the uranium atoms in the rocket chamber. With these applications in mind, Back1 and Muthanna and Nath2 have obtained the similarity solutions for a low-speed three-dimensional steady laminar compressible boundary layer with swirl inside an axisymmetric surface of variable cross section. The aim of the present analysis is to study the effect of massive blowing rates on the unsteady laminar swirling compressible boundary-layer flow of an axisymmetric body of arbitrary cross section when the freestream velocity and blowing rate vary with time. The type of swirl considered here is that of a free vortex superimposed on the longitudinal flow of a compressible fluid with variable properties. The analysis is applicable to external flow over a body as well as internal flow along a surface. For the case of external flow, strong blowing can have significant use in cooling the surface of hypervelocity vehicles, particularly when ablation occurs under large aerodynamic or radiative heating, but there may not be such an important application of strong blowing in the case of internal flow. The governing partial differential equations have been solved numerically using an implicit finite difference scheme with a quasilinearization technique.3 High temperature gas effects, such as radiation, dissociation, and ionization, etc., are not investigated. The nomenclature is usually that of Ref. 4 and is listed in the full paper.

Unsteady compressible boundary layer flow in the stagnation region of a sphere with a magnetic field

Abstract: An analysis is performed to study the unsteady compressible laminar boundary layer flow in the forward stagnation-point region of a sphere with a magnetic field applied normal, to the surface. We have considered the case where there is an initial steady state that is perturbed by the step change in the total enthalpy at the wall. The nonlinear coupled parabolic partial differential equations governing the flow and heat transfer have been solved numerically using a finite-difference scheme. The numerical results are presented, which show the temporal development of the boundary layer. The magnetic field in the presence of variable electrical conductivity causes an overshoot in the velocity profile. Also, when the total enthalpy at the wall is suddenly increased, there is a change in the direction of transfer of heat in a small interval of time.

Unsteady three-dimensional stagnation point flow of a viscoelastic fluid

The unsteady three-dimensional stagnation point Bow of a viscoelastic fluid has been studied. Both nodal and saddle point regions of How have been considered. The unsteadiness in the Bow field is caused by the free stream velocity which varies arbitrarily with time. The governing boundary layer equations represented by a system of nonlinear partial differential equations have been solved numerically using a finite-difference scheme along with the quasilinearization technique in the nodal point region and a finite-difference scheme in combination with the parametric differentiation technique in the saddle point region. The skin friction coefficients for the viscoelastic fluid are found to be significantly less than those of the Newtonian fluid. The skin friction and heat transfer increase due to suction and reduce due to injection. The heat transfer at the wall increases with the Prandtl number. There is a flow reversal in the y-component of the velocity in the saddle point region. The absolute value of c (<<<0) for which reversal takes place is less than that of the Newtonian fluid. (C) 1997 Elsevier Science Ltd.

Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t = 0) steady and then at t > 0 it becomes unsteady. The semi-similar solution of the unsteady Navier-Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier-Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier-Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time. (C) 1999 Elsevier Science Ltd. All rights reserved.

Unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field

The unsteady laminar boundary layer flow of an electrically conducting fluid past a semi-infinite flat plate with an aligned magnetic field has been studied when at time t > 0 the plate is impulsively moved with a constant velocity which is in the same or opposite direction to that of free stream velocity. The effect of the induced magnetic field has been included in the analysis. The non-linear partial differential equations have been solved numerically using an implicit finite-difference method. The effect of the impulsive motion of the surface is found to be more pronounced on the skin friction but its effect on the x-component of the induced magnetic field and heat transfer is small. Velocity defect occurs near the surface when the plate is impulsively moved in the same direction as that of the free stream velocity. The surface shear stress, x-component of the induced magnetic field on the surface and the surface heat transfer decrease with an increasing magnetic field, but they increase with the reciprocal of the magnetic Prandtl number. However, the effect of the reciprocal of the magnetic Prandtl number is more pronounced on the x-component of the induced magnetic field. (C) 1999 Elsevier Science Ltd. All rights reserved.

A study on determining the theoretical dispersion curve for Rayleigh wave propagation

A method has been presented to establish the theoretical dispersion curve for performing the inverse analysis for the Rayleigh wave propagation. The proposed formulation is similar to the one available in literature, and is based on the finite difference formulation of the governing partial differential equations of motion. The method is framed in such a way that it ultimately leads to an Eigen value problem for which the solution can be obtained quite easily with respect to unknown frequency. The maximum absolute value of the vertical displacement at the ground surface is formed as the basis for deciding the governing mode of propagation. With the proposed technique, the numerical solutions were generated for a variety of problems, comprising of a number of different layers, associated with both ground and pavements. The results are found to be generally satisfactory. (C) 2011 Elsevier Ltd. All rights reserved.

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation. (C) 2002 Published by Elsevier Science Ltd.

Direct numerical simulation of turbulent spots

A group of high-order finite-difference schemes for incompressible flow was implemented to simulate the evolution of turbulent spots in channel flows. The long-time accuracy of these schemes was tested by comparing the evolution of small disturbances to a plane channel flow against the growth rate predicted by linear theory. When the perturbation is the unstable eigenfunction at a Reynolds number of 7500, the solution grows only if there are a comparatively large number of (equispaced) grid points across the channel. Fifth-order upwind biasing of convection terms is found to be worse than second-order central differencing. But, for a decaying mode at a Reynolds number of 1000, about a fourth of the points suffice to obtain the correct decay rate. We show that this is due to the comparatively high gradients in the unstable eigenfunction near the walls. So, high-wave-number dissipation of the high-order upwind biasing degrades the solution especially. But for a well-resolved calculation, the weak dissipation does not degrade solutions even over the very long times (O(100)) computed in these tests. Some new solutions of spot evolution in Couette flows with pressure gradients are presented. The approach to self-similarity at long times can be seen readily in contour plots.

Three-dimensional laminar compressible boundary layers with large injection

The effect of large mass injection on the following three-dimensional laminar compressible boundary-layer flows is investigated by employing the method of matched asymptotic expansions: (i) swirling flow in a laminar compressible boundary layer over an axisymmetric surface with variable cross-section and (ii) laminar compressible boundary-layer flow over a yawed infinite wing in a hypersonic flow. The resulting equations are solved numerically by combining the finite-difference technique with quasi-linearization. An increase in the swirl parameter, the yaw angle or the wall temperature is found to be capable of bringing the viscous layer nearer the surface and reducing the effects of massive blowing.

On cavity flow at high Reynolds numbers

The flow in a square cavity is studied by solving the full Navier–Stokes and energy equations numerically, employing finite-difference techniques. Solutions are obtained over a wide range of Reynolds numbers from 0 to 50000. The solutions show that only at very high Reynolds numbers (Re [gt-or-equal, slanted] 30000) does the flow in the cavity completely correspond to that assumed by Batchelor's model for separated flows. The flow and thermal fields at such high Reynolds numbers clearly exhibit a boundary-layer character. For the first time, it is demonstrated that the downstream secondary eddy grows and decays in a manner similar to the upstream one. The upstream and downstream secondary eddies remain completely viscous throughout the range of Reynolds numbers of their existence. It is suggested that the behaviour of the secondary eddies may be characteristic of internal separated flows.

Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents

The unsteady free convection flow over an infinite vertical porous plate, which moves with time-dependent velocity in an ambient fluid, has been studied. The effects of the magnetic field and Hall current are included in the analysis. The buoyancy forces arise due to both the thermal and mass diffusion. The partial differential equations governing the flow have been solved numerically using both the implicit finite difference scheme and the difference-differential method. For the steady case, analytical solutions have also been obtained. The effect of time variation on the skin friction, heat transfer and mass transfer is very significant. Suction increases the skin friction coefficient in the primary flow, and also the Nusselt and Sherwood numbers, but the skin friction coefficient in the secondary flow is reduced. The effect of injection is opposite to that of suction. The buoyancy force, injection and the Hall parameter induce an overshoot in the velocity profiles in the primary flow which changes the velocity gradient from a negative to a positive value, but the magnetic field and suction reduce this velocity overshoot.

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the-cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.

Unsteady MUD rotating flow over a rotating sphere near the equator

The unsteady rotating flow of a laminar incompressible viscous electrically conducting fluid over a rotating sphere in the vicinity of the equator has been studied. The fluid and the body rotate either in the same direction or in opposite directions. The effects of surface suction and magnetic field have been included in the analysis. There is an initial steady state that is perturbed by a sudden change in the rotational velocity of the sphere, and this causes unsteadiness in the flow field. The nonlinear coupled parabolic partial differential equations governing the boundary-layer flow have been solved numerically by using an implicit finite-difference scheme. For large suction or magnetic field, analytical solutions have also been obtained. The magnitude of the radial, meridional and rotational velocity components is found to be higher when the fluid and the body rotate in opposite directions than when they rotate in the same direction. The surface shear stresses in the meridional and rotational directions change sign when the ratio of the angular velocities of the sphere and the fluid lambda greater than or equal to lambda(0). The final (new) steady state is reached rather quickly which implies that the spin-up time is small. The magnetic field and surface suction reduce the meridional shear stress, but increase the surface shear stress in the rotational direction.

Swam Intelligent Based Inverse Model for Laboratory Double Reservoir Diffusion Experiments

Theoretical approaches are of fundamental importance to predict the potential impact of waste disposal facilities on ground water contamination. Appropriate design parameters are, in general, estimated by fitting the theoretical models to a field monitoring or laboratory experimental data. Double-reservoir diffusion (Transient Through-Diffusion) experiments are generally conducted in the laboratory to estimate the mass transport parameters of the proposed barrier material. These design parameters are estimated by manual parameter adjusting techniques (also called eye-fitting) like Pollute. In this work an automated inverse model is developed to estimate the mass transport parameters from transient through-diffusion experimental data. The proposed inverse model uses particle swarm optimization (PSO) algorithm which is based on the social behaviour of animals for finding their food sources. Finite difference numerical solution of the transient through-diffusion mathematical model is integrated with the PSO algorithm to solve the inverse problem of parameter estimation.The working principle of the new solver is demonstrated by estimating mass transport parameters from the published transient through-diffusion experimental data. The estimated values are compared with the values obtained by existing procedure. The present technique is robust and efficient. The mass transport parameters are obtained with a very good precision in less time