M. Kumari

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.

MHD boundary-layer flow of a non-Newtonian fluid over a continuously moving surface with a parallel free stream

SummaryThe MHD flow and heat transfer of a non-Newtonian power-law fluid over a continuously moving surface with a parallel free stream have been investigated. The partial differential equations governing the non-similar flow have been solved numerically using an implicit finite-difference scheme. The skin friction and heat-transfer coefficients increase with the magnetic parameter, and they are more for the pseudoplastic fluid than for the dilatant fluid. The heat-transfer coefficient increases significantly with the Prandtl number. The gradient of the velocity at the surface is negative when the wall velocity is greater than the free stream velocity, and it is positive when the wall velocity is less than the free stream velocity.

Unsteady free convection flow over a continuous moving vertical surface

SummaryThe problem of heat transfer in the unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid has been investigated. Both constant surface temperature and constant surface heat flux conditions have been considered. The nonlinear coupled partial differential equations governing the flow have been solved numerically using the Keller box method and the Nakamura method which both give closely similar solutions. The results indicate that the cooling rate of the sheet can be enhanced by increasing the buoancy parameter or the velocity of the sheet. It is found that a better cooling performance could be achieved by using a liquid as a cooling medium rather than a gas. The overshoot in the velocity occurs near the surface when the buoyancy parameter exceeds a certain critical value.

Free-convection boundary-layer flow of a non-Newtonian fluid along a vertical wavy surface

A theoretical analysis of laminar free-convection flow over a vertical isothermal wavy surface in a non-Newtonian power-law fluid is considered. The governing equations are first cast into a nondimensional form by using suitable boundary-layer variables that substract out the effect of the wavy surface from the boundary conditions. The boundary-layer equations are then solved numerically by a very efficient implicit finite-difference method known as the Kelter-Box method. A sinusoidal surface is used to elucidate the effects of the power-law index, amplitude wavelength, and Prandtl number on the velocity and temperature fields, as well as on the local Nusselt number. It is shown that the local Nusselt number varies periodically along the wavy surface. The wavelength of the local Nusselt number variation is half that of the wavy surface, irrespective of whether the fluid is a Newtonian fluid or a non-Newtonian fluid. Comparisons with earlier works are also made, and the agreement is found to be very good.

Conjugate MHD flow past a flat plate

SummaryA boundary layer solution for the conjugate forced convection flow of an electrically conducting fluid over a semi-infinite flat plate in the presence of a transverse magnetic field is presented. The governing nonsimilar partial differential equations are solved numerically using the Keller box method. Values of the temperature profiles of the plate are obtained for various values of the parameters entering the problem and are given in a table and shown on graphs.

Mixed convection along a vertical cone

An analysis is performed to study the flow and heat transfer characteristics for the case of laminar mixed convection along a vertical circular cone. A mixed-convection parameter is introduced in the formulation of the problem such that smooth transition from one convective limit to the other is possible. The transformed conservation equations of the nonsimilar boundary layers are solved by an efficient finite-difference method.

Effect of variable viscosity on non-Darcy free or mixed convection flow on a horizontal surface in a saturated porous medium

Abstract The effect of the variable viscosity is considered for non-Darcy free or mixed convection boundary-layer flow on a horizontal surface in a saturated porous medium. The viscosity of the fluid is assumed to be an inverse linear function of the temperature. The partial differential equations governing the nonsimilar flow have been solved numerically using an implicit finite-difference scheme developed by Keller. For the forced convection flow, the self-similar solution exists for the constant free stream velocity and for isothermal and non-isothermal walls, but for the free convection flow self-similar solution exists for only λ = 1 2 (non-isothermal wall).

MHD flow over a wedge with large blowing rates

The effect of large blowing rates on the unsteady laminar incompressible electrically conducting fluid flow over an infinite wedge with an aligned magnetic field has been studied. The effects of the induced magnetic field and the heat transfer are included in the analysis. The boundary layer equations and the Maxwells equations governing the flow are reduced to a system of ordinary differential equations by using similarity transformations. These equations are solved numerically by using an implicit finite-difference scheme (with nonuniform step length) in combination with the quasilinearization technique. Also, we have carried out an asymptotic analysis using the method of matched asymptotic expansion. The asymptotic analysis, although approximate, allows the numerical results to be extended to indefinitely large rates of blowing and circumvents the difficulties in numerical analysis which become progressively more severe as the blowing rate increases. For large blowing rates the results of the asymptotic analysis are found to be in very good agreement with those of the numerical method. The boundary layer thickness increases rapidly with the blowing rate or the magnetic parameter. The location of the dividing streamline moves away from the boundary as the blowing rate or the magnetic parameter increases. The surface heat transfer and the x-component of the induced magnetic field on the surface tend to zero for large blowing rates, but the surface skin friction remains finite.

Variable viscosity effects on free and mixed convection boundary-layer flow from a horizontal surface in a saturated porous medium - variable heat flux

In recent years, the study of convective heat transfer from surfaces embedded in porous media has received considerable attention in the literature. The interest for such studies is motivated by several thermal engineering applications, such as geothermal systems, the storage of nuclear wastes, oil extraction, ground water pollution and thermal insulation. The boundary-layer mixed convection flow over horizontal surface with constant or variable wall temperature or heat flux has been studied by many investigators [1-8]. Recently, the flow over an horizontal surface in saturated porous media for the entire regime of forced to free convection has been investigated by Aldoss et al. [9], Chen [10] for Newtonian fluids and by Kumari et al. [11] for non-Newtonian fluids. In all these studies, it was assumed that the thermophysical properties of the fluid are constant. However, it is known that these properties may change with temperature, especially for fluid viscosity. Variable viscosity effects on the stability of flow and temperature fields were considered by Kassoy and Zebib [12], Strans and Schubert [13], Horne and Sullivan [14] and Gary et al. [15]. The effect of variable viscosity for mixed convection flow over a vertical plate with constant wall temperature in saturated porous media has been investigated by Lai and Kulacki [16]. The free or mixed convection flow taking in to account the effect of variable viscosity over a horizontal surface with variable heat flux has not been studied so far.

Non-Darcy mixed convection in power-law fluids along a non-isothermal horizontal surface in a porous medium

Abstract The non-similar non-Darcy mixed convection from a horizontal surface in a porous medium saturated with a power-law type non-Newtonian fluid has been studied. Non-similarity solutions have been obtained for the case of a variable surface temperature of the form T w ( x )= T ∞ ± Ax λ , λ ≠1/2. It has been found that for λ =1/2, self-similar solution exists. A single mixed convection parameter has been used which covers the entire regime of mixed convection from pure forced convection to pure free convection limits. Both these limiting flows admit self-similar solutions. The partial differential equations governing the non-similar flow and the ordinary differential equations governing the self-similar flow have been solved numerically. The buoyancy force and the wall temperature have significant influence on the heat transfer and the velocity at the wall. For a fixed buoyancy force, the heat transfer and the velocity at the wall decrease with increasing non-Newtonian parameter, non-Darcy parameter and Peclet number.