Harmindar S. Takhar

Radiation effect on mixed convection along a vertical plate with uniform surface temperature

This paper investigates the effect of radiation on the forced and free convection flow of an optically dense viscous incompressible fluid along a heated vertical flat plate with uniform free stream and uniform surface temperature with Rosseland diffusion approximation. With appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity equations valid in the forced convection regime as well as in the free convection regime. A group of transformation is, also, introduced to reduce the boundary layer equations to a set of local nonsimilarity equations valid in both the forced and free convection regimes. Solutions of the governing equations are obtained by employing the implicit finite difference methods together with Keller box scheme and are expressed in terms of local shear stress and local rate of heat transfer for a range of values of the pertinent parameters.ZusammenfassungIn der Arbeit wird der Einfluß der Wärmestrahlung auf die erzwungene und freie Konvektionsströmung eines optisch dichten, zähen, inkompressiblen Fluids entlang einer beheizten, senkrechten Platte mit gleichförmiger Oberflächentemperatur mit Hilfe der Rosseland-Diffusionsnäherung untersucht. Durch geeignete Transformationen lassen sich die den Strömungsvorgang beschreibenden Grenzschichtgleichungen in lokale, Nichtähnlichkeits-Gleichungen überführen, die sowohl im Bereich der Zwangs- wie der Freikonvektion Gültigkeit haben. Durch Anwendung impliziter Finitdifferenzen-Methoden in Verbindung mit dem “Keller-Box” Schema wurden Lösungen der Grundgleichungen gewonnen und in Form lokaler Schubspannungen und Wärmeübergangsintensitäten in einem weiten Bereich der Haupteinflußparameter dokumentiert werden.

Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species

An analysis has been carried out to obtain the flow and mass transfer characteristics of a viscous electrically conducting fluid on a continuously stretching surface with non-zero slot velocity. The motion is caused solely by the stretching surface which introduces non-similarity in the velocity and concentration fields. The partial differential equations governing the boundary layer flow and mass transfer are solved by using an implicit finite-difference scheme. The magnetic field significantly increases the surface skin friction, but slightly reduces the surface mass transfer. The surface mass transfer strongly depends on the Schmidt number and the reaction rate and it increases with their increasing values. The surface mass transfer for the first-order reaction is more than that for the second- or-third-order reaction.

Effect of thermal radiation on MHD flow

An analysis of the steady MHD asymmetric flow of an electrically conducting fluid past a semi-infinite stationary plate is considered in the presence of radiation. Numerical solutions for the temperature field have been derived and the effect of the radiation parameter is discussed.

Radiation effects on free convection flow past a semi-infinite vertical plate with mass transfer

Laminar free convection flow of air past a semi-infinite vertical plate in the presence of chemical species concentration and thermal radiation effects is studied. This type of problem finds application in many technological and engineering fields such as rocket propulsion systems, spacecraft re-entry aerothermodynamics, cosmical flight aerodynamics, plasma physics, glass production and furnace engineering. The governing boundary-layer equations for this problem are reduced to a non-similar form and are solved numerically by an implicit finite-difference technique. Representative velocity, temperature and concentration profiles are shown graphically and the numerical values of the wall slopes of the velocity, temperature and concentration profiles (which are related to the dimensionless skin-friction coefficient, wall heat transfer and the Sherwood number, respectively) are also shown graphically. The effects of the radiation parameter, buoyancy ratio, Schmidt number and the dimensionless distance from the leading edge of the plate on the numerical solutions are presented and discussed.

Unsteady mixed convection flow in stagnation region adjacent to a vertical surface

AbstractsThe unsteady two-dimensional laminar mixed convection flow in the stagnation region of a vertical surface has been studied where the buoyancy forces are due to both the temperature and concentration gradients. The unsteadiness in the flow and temperature fields is caused by the time-dependent free stream velocity. Both arbitrary wall temperature and concentration, and arbitrary surface heat and mass flux variations have been considered. The Navier-Stokes equations, the energy equation and the concentration equation, which are coupled nonlinear partial differential equations with three independent variables, have been reduced to a set of nonlinear ordinary differential equations. The analysis has also been done using boundary layer approximations and the difference between the solutions has been discussed. The governing ordinary differential equations for buoyancy assisting and buoyancy opposing regions have been solved numerically using a shooting method. The skin friction, heat transfer and mass transfer coefficients increase with the buoyancy parameter. However, the skin friction coefficient increases with the parameter λ, which represents the unsteadiness in the free stream velocity, but the heat and mass transfer coefficients decrease. In the case of buoyancy opposed flow, the solution does not exist beyond a certain critical value of the buoyancy parameter. Also, for a certain range of the buoyancy parameter dual solutions exist.ZusammenfassungDie zweidimensionale laminare Mischkonvektionsströmung im Staubereich einer vertikalen Oberfläche, in der Temperatur- und Konzentrationsgradienten die Auftriebskräfte erzeugen, wurde untersucht. Die Unstetigkeiten im Strömungs- und im Temperaturfeld liegen in der zeitabhängigen freien Strömungsge-schwindigkeit begründet. Die willkürliche Wandtempereratur und Konzentration sowie die willkürliche Oberflächenwärme- und die Massenstromschwankungen wurden in Betracht gezogen. Die Navier-Stokes-Gleichung, die Energiegleichung und die Konzentrationsgleichung, die drei nicht lineare, partielle Differentialgleichungen mit drei unabhängigen Variablen darstellen, sind auf eine Gruppe von nicht linearen, gewöhnlichen Differentialgleichungen reduziert worden. Die Berechnung ist auch mit der Grenzflächenap-proximation gemacht worden und die Unterschiede der Ergebnisse wurden diskutiert.Die bestehenden gewöhnlichen Differentialgleichungen für auftriebsuntertützte und auftriebshemmende Bereiche sind numerisch mit dem Shooting-Verfahren gelöst worden. Die Oberflächenreibung, die Wärme- und Stoffübertragungskoeffizienten steigen mit dem Auftriebsparameter. Der Oberflächenreibungskoeffizient steigt mit dem Parameter, der auch für die Unstetigkeit der freien Strömungsgeschwindigkeit verantwortlich ist. Die Wärme- und Stoffübertragungskoeffizienten sinken dann. Im Fall der auftriebsgehemmten Strömung, existiert nach einem bestimmten kritischen Wert des Auftriebsparameters keine Lösung mehr. Für eine bestimmte Reihe von Auftriebsparametern gibt es zwei Lösungen.

Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface

SummaryThe development of velocity and temperature fields of an incompressible viscous electrically conducting fluid, caused by an impulsive stretching of the surface in two lateral directions and by suddenly increasing the surface temperature from that of the surrounding fluid, is studied. The partial differential equations governing the unsteady laminar boundary-layer flow are solved numerically using an implicit finite difference scheme. For some particular cases, closed form solutions are obtained, and for large values of the independent variable asymptotic solutions are found. The surface shear stresses inx-andy-directions and the surface heat transfer increase with the magnetic field and the stretching ratio, and there is a smooth transition from the short-time solution to the long-time solution.

Short communication radiation effects on MHD free convection flow of a gas past a semi—infinite vertical plate

Free convection heat transfer due to the simultaneous action of buoyancy, radiation and transverse magnetic field is investigated for a semi‐infinite vertical plate. Solutions are derived by expanding the stream function and the temperature into a series in terms of the parameter ζ = x1/2 L–1/2, where L is the length of the plate. Velocity and temperature functions are shown on graphs and the numerical values of functions affecting the shear stress and the rate of heat transfer are entered in a table. The effects of the magnetic field parameter λ and the radiation parameter F on these functions are discussed.

Finite element solution of mixed convection micropolar flow driven by a porous stretching sheet

This paper presents a finite element solution for the mixed convection micropolar flow driven by a porous stretching sheet with uniform suction. The governing partial differential equations are solved numerically by the using finite element method and the results have been compared with those obtained by using the quasi-linearization method. The effect of surface conditions on the velocity, microrotation as well as for temperature functions has been studied. It is noticed that the micropolar fluids help in the reduction of drag forces and also act as a cooling agent.

Numerical study of heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects

A numerical solution is presented for the natural convective dissipative heat transfer of an incompressible, third grade, non-Newtonian fluid flowing past an infinite porous plate embedded in a Darcy–Forchheimer porous medium. The mathematical model is developed in an (x,y) coordinate system. Using a set of transformations, the momentum equation is rendered one-dimensional and a partly linearized heat conservation equation is derived. The viscoelastic formulation presented by Akyildiz (2001 Int. J. Non-Linear Mechanics 36 349–52) is adopted, which generates lateral mass and viscoelastic terms in the heat conservation equation, as well as in the momentum equation. A number of special cases of the general transformed model are discussed. A finite element method is implemented to solve, with appropriate boundary conditions, the coupled third-order, second degree ordinary differential equation for momentum and the second-order, fourth degree heat conservation equation. We study the influence of the third grade viscoelastic parameter (β3), Darcian parameter (inversely proportional to permeability (kp)), the Forchheimer inertial parameter (b), transpiration velocity (Vo), the transpiration parameter in the heat equation (R) and the thermal conductivity parameter (S) on momentum and heat transfer. Additionally, we study the influence of the Forchheimer inertial parameter (b) on second-order viscoelastic non-Darcy free convection flow and also the effects of the third grade parameter (β3) on Darcian free convection. Velocities increase with rising permeability (Darcian parameter) for both second and third grade viscoelastic free convection regimes and decrease with rising Forchheimer parameter. The effects of the other parameters are described at length. The flow scenario is important in chemical engineering processes.

MHD flow and heat transfer over a stretching surface with prescribed wall temperature or heat flux

The flow and heat transfer over a stretching sheet with a magnetic field in an electrically conducting ambient fluid have been studied. The effects of the induced magnetic field and sources or sinks have been included in the analysis. Both non-isothermal wall and constant heat flux conditions have been considered. The governing equations have been solved numerically using a shooting method. It is observed that for the prescribed wall temperature the skin friction, induced magnetic field at the wall and heat transfer are enhanced due to the magnetic field, but in general, they reduce as the reciprocal of the magnetic Prandtl number increases. For constant heat flux case, the temperature at the wall reduces as the magnetic field increases, but it increases with the reciprocal of the magnetic Prandtl number. The heat transfer is strongly affected by the Prandtl number, wall temperature and sink. Whenm<−2 andPr>2.5 the unrealistic temperature distributions are encountered. The present analysis is more general than any previous investigation.ZusammenfassungIn dieser Studie ist die Strömung und Wärmeübertragung über eine gedehnte Fläche mit magnetischem Feld in einem elektrisch leitenden Fluid untersucht worden. Der Einfluß des induzierten magnetischen Feldes und der Quellen oder Senken sind in die Untersuchung einbezogen. Die beiden Fälle, nicht-isotherme Wand und konstanter Wandwärmestrom, sind betrachtet worden. Mit dem Eliminationsverfahren sind bestehende Gleichungen numerisch gelöst worden. Es ist beobachtet worden, daß für eine vorgeschriebene Wandtemperatur die Oberflächenreibung, das induzierte magnetische Feld und die Wärmeübertragung aufgrund des magnetischen Feldes verbessert sind. Aber im allgemeinen reduzieren sie sich im umgekehrten Maß wie die magnetische Prandtlzahl ansteigt. Für den Fall des konstanten Wärmestromes sinkt die Wandtemperatur, wenn das magnetische Feld stärker wird. Die Temperatur steigt jedoch reziprok zur magnetischen Prandtlzahl an. Die Wärmeübertragung ist sehr stark von der Prandtlzahl, Wandtemperatur und der Senke beeinflußt. Bei Werten vonm<−2 undPr≥2.5 sind unrealistische Temperaturverteilungen eingetreten. Die gezeigte Analyse ist allgemeiner als jede vorhergehende Untersuchung.