Boundary Layer Partial Differential Equations Research Articles

Analytical and Numerical Study for MHD Radiating Flow over an Infinite Vertical Surface Bounded by a Porous Medium in Presence of Chemical Reaction

The study of non-linear MHD flow with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting and Newtonian fluid over a vertical oscillating porous plate embedded in a porous medium in presence of homogeneous chemical reaction of first order and thermal radiation effects have been analyzed. The fluid considered here is a gray, absorbing/emitting radiation, but a non-scattering medium. At time , the plate temperature and concentration levels near the plate raised linearly with time . The dimensionless governing coupled, non-linear boundary layer partial differential equations are solved by an efficient, accurate, and extensively validated and unconditionally stable finite difference scheme of the Crank-Nicolson type as well as by the Laplace Transform technique. An increase in porosity parameter is found to depress the fluid velocities and shear stress in the regime. Also it has been found that, when the conduction-radiation increased, the fluid velocities as well as temperature profiles were decreased. It has been found that, when the chemical reaction parameter increased, the fluid velocities as well as concentration profiles were decreased. Applications of the study arise in materials processing and solar energy collector systems.

Numerical Study of Stagnation Point Flow and Heat Transfer of Micropolar Fluid towards a Surface with Viscous Dissipation Effects

In this paper, we present numerical investigation of the problem of steady laminar two dimensional boundary layer stagnation point flow and heat transfer of a Micropolar fluid towards a heated surface in the presence of viscous dissipation. The governing boundary layer partial differential equations are reduced to a set of ordinary ones using similarity transformations. The solutions for different values of Eckert number, Micropolar parameters and Prandtl number are computed, analyzed and discussed. The study reveals that the reverse flow of heat near the surface may occur due to viscous dissipation which may further be enhanced by the increasing values of the Prandtl number. It may be recommended that the viscous dissipation should not be simply ignored while studying the boundary layer stagnation point flows.

Free Convection Heat Transfer From A Sphere In A Porous Medium Using A Thermal Non-equilibrium Model

This work studies the free convection heat transfer from a sphere with constant wall temperature embedded in a fluid-saturated porous medium using a thermal non-equilibrium model. The governing equations are transformed into boundary-layer partial differential equations by the coordinate transform, and the obtained governing equations are then solved by the cubic spline collocation method. The temperature distributions for fluid and solid phases are shown for different values of the porosity scaled thermal conductivity ratio, the interphase heat transfer parameter, and the streamwise coordinate. The effects of the porosity scaled thermal conductivity ratio and the interphase heat transfer parameter between solid and fluid phases on the local Nusselt numbers for fluid and solid phases are examined. Results show the local Nusset number for the porous medium can be increased by increasing the porosity scaled thermal conductivity ratio. Moreover, the thermal non-equilibrium effect is more significant for low values of the porosity scaled thermal conductivity ratio or the interphase heat transfer parameter.

Dual solutions in MHD flow on a nonlinear porous shrinking sheet in a viscous fluid

In this paper, the problem of magnetohydrodynamic (MHD) flow of a viscous fluid on a nonlinear porous shrinking sheet is studied. The boundary layer partial differential equations are first transformed into an ordinary differential equation, which is then solved numerically by the shooting method. The features of the flow for various governing parameters are presented and discussed in detail. It is found that dual solutions only exist for positive values of the controlling parameter. MSC: 34B15, 76D10.

Similarity Solution of Unsteady Combined Free and Force Convective Laminar Boundary Layer Flow about a Vertical Porous Surface with Suction and Blowing

Abstract In this paper the unsteady laminar combined free and forced convective boundary layer flow about a vertical porous plate in viscous incompressible fluid with suction and blowing is considered. The governing non-dimensional boundary layer partial differential equations are simplified first by using Boussinesq approximation. Secondly, similarity transformations are introduced on the basis of detailed analysis in order to transform the simplified coupled partial differential equations into a set of ordinary differential equations. The transformed complete similarity equations are then solved numerically by using Nachtsheim-Swigert shooting iteration technique along with sixth order Runga-Kutta method. The flow phenomenon has been characterized with the help of obtained flow controlling parameters such as suction parameter, buoyancy parameter, Prandtl number and the other driving parameter. The effects of the involved parameters on the velocity and temperature fields across the boundary layer are investigated. Numerical results for the velocity and temperature distributions are presented graphically. It is found that a small suction or blowing can play a significant role on the patterns of flow and temperature fields.

Effects of Homogeneous–Heterogeneous Reactions on the Viscoelastic Fluid Toward a Stretching Sheet

The effects of homogeneous–heterogeneous reactions on the steady viscoelastic fluid toward a stretching sheet are numerically investigated in this paper. The model developed by Chaudhary and Merkin for homogeneous–heterogeneous reactions in stagnation-point boundary-layer flow with equal diffusivities for reactant and autocatalyst is used for present stretching sheet problem in a viscoelastic fluid. The basic boundary layer partial differential equations of motion and concentration are reduced to ordinary differential (similarity) equations, which then are numerically solved using an implicit finite difference method in the case when the diffusion coefficients of both reactant and autocatalyst are equal. It is found that the concentration at the surface decreases with an increase in the viscoelastic parameter and strengths of the homogeneous, while heterogeneous reactions increase.

Hydromagnetic flow and heat transfer over a bidirectional stretching surface in a porous medium

In this study, we present a steady three-dimensional magnetohydrodynamic (MHD) flow and heat transfer characteristics of a viscous fluid due to a bidirectional stretching sheet in a porous medium. The heat transfer analysis has been carried out for two heating processes namely (i) the prescribed surface temperature (PST) and (ii) prescribed surface heat flux (PHF). In addition the heat transfer rate varies along the surface. The similarity solution of the governing boundary layer partial differential equations is developed by employing homotopy analysis method (HAM). The quantities of interest are velocity, temperature, skin-friction and wall heat flux. The results obtained are presented through graphs and tabular data. It is observed that both velocity and boundary layer thickness decreases by increasing the porosity and magnetic field. This shows that application of magnetic and porous medium cause a control on the boundary layer thickness. Moreover, the results are also compared with the existing values in the literature and found in excellent agreement.

TRANSIENT FREE CONVECTION ABOUT A VERTICAL FLAT PLATE EMBEDDED IN A SATURATED POROUS MEDIUM

An analysis is presented of the transient, buoyancy-induced flow and heat transfer in a Darcian fluid-saturated porous medium adjacent to a suddenly heated semi-infinite vertical wall. Transient profiles of the temperature field and the local Nusselt number are obtained by solving the unsteady boundary layer partial differential equations numerically. It is shown that the governing equations are of a singular parabolic type and can be solved accurately in a semi-similar, finite elliptic domain using a successive relaxation method. The solution thus obtained is compared with a solution obtained in the physical domain using an explicit upwind method. The results confirm that during the initial stage, before the effects of the leading edge are influential at a location, heat transfer and flow phenomena in porous media are governed by transient one-dimensional conduction. New data are presented for the transition from this initial conduction stage to a fully two-dimensional transient, which ultimately termina...

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation T W − T ∞ = Nx n . The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Convective Flow Of Micropolar Fluids Along An Inclined Flat Plate With Variable Electric Conductivity And Uniform Surface Heat Flux

Magnetohydrodynamic (MHD) twodimensional steady convective flow and heat transfer of micropolar fluids flow along an inclined flat plate with variable electric conductivity and uniform surface heat flux has been analyzed numerically in the presence of heat generation. With appropriate transformations the boundary layer partial differential equations are transformed into nonlinear ordinary differential equations. The local similarity solutions of the transformed dimensionless equations for the velocity flow, microrotation and heat transfer characteristics are assessed using Nachtsheim- Swigert shooting iteration technique along with the sixth order Runge-Kutta-Butcher initial value solver. Numerical results are presented graphically in the form of velocity, microrotation, and temperature profiles within the boundary layer for different parameters entering into the analysis. The effects of the pertinent parameters on the local skin-friction coefficient (viscous drag), plate couple stress and the rate of heat transfer (Nusselt number) are also discussed and displayed graphically. Keywords: Convective flow; Micropolar fluid; Heat transfer; Electric conductivity; Inclined plate; Locally self-similar solution DOI: http://dx.doi.org/10.3329/diujst.v6i1.9336 DIUJST 2011; 6(1): 69-79