Theoretical magnetohydrodynamic analysis of mixed convection boundary-layer flow over a wedge with uniform suction or injection

Summary The purpose of this work is to study the effects of an applied magnetic field on the mixed convection boundary-layer flow over a wedge with suction or injection. The fluid is assumed to be viscous, incompressible and electrically conducting, and the magnetic field is applied transversally to the direction of the flow. Such a flow model has great significance not only of its own theoretical interest, but also for applications to aerodynamics and engineering. The governing partial differential equations of this problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary-layer analysis. Numerical calculations are carried out for different values of the dimensionless parameters of the problem, and the analysis of the obtained results showed that the flow field is appreciably influenced by the applied magnetic field.     

Free convection boundary layer flow with uniform suction or injection over a cone

Summary The effect of uniform suction or injection on free convection boundary layer over a cone was theoretically investigated. The non-linear ordinary differential equations were obtained by the difference-differential method after transforming it to an equivalent two-dimensional problem by Mangler's transformation. The solutions of the resulting equations can be expressed in the form of integral equations. Numerical calculations were performed solving the integral equations by the iterative numerical quadrature. The velocity profiles, temperature profiles, skin friction parameters and heat transfer parameters with constant wall temperature were computed for various values of suction/injection parameter and cone angle parameter.     

Forced and free mixed convection boundary layer flow with uniform suction or injection on a vertical flat plate

Summary A laminar forced and free mixed convection flow on a flat plate with uniform suction or injection was theoretically investigated. Nonsimilar partial differential equations are transformed into nonsimilar ordinary ones by means of difference-differential method. The solutions of the resulting equations are obtained with integral forms, and are calculated by the method of successive iteration. The velocity profiles, temperature profiles, friction coefficient and heat transfer coefficient are obtained for various values of suction/injection parameter and buoyancy parameter.     

Thermal boundary layers over a wedge with uniform suction or injection in forced flow

Summary The behavior of incompressible laminar boundary layers in forced flow over a wedge with uniform suction or injection was theoretically investigated. The boundary layer equations along a wedge are transformed into non-similar partial differential ones, and the ordinary differential equations were obtained by means of the difference-differential method. The solutions of the resulting equations are expressed in a form of integral equations which are in turn solved by iterative numerical quadratures. The numerical results are given for the velocity distribution, temperature distribution and the coefficient of skin friction and heat transfer for various values of suction/injection parameter.     

Effect of uniform suction or injection on a magnetohydrodynamic boundary layer flow along a flat plate with pressure gradient

Summary The effect of uniform suction or injection on the flow of an incompressible electrically conducting fluid past a flat plate with pressure gradient in the presence of a transverse magnetic field was theoretically investigated. The boundary layer equations were transformed into non-similar ones, and the numerical calculations of the resulting equations were performed by the difference differential method. The velocity profiles, the coefficient of skin friction, and the displacement thickness were given for various values of the pressure gradient, the magnetic and suction/injection parameters. The neutral stability curves for wavelike disturbances of Tollmien-Schlichting type and the critical Reynolds numbers were then presented for the velocity profiles obtained above.With 13 Figures     

Free convection in the laminar boundary layer flow of a thermomicropolar fluid past a vertical flat plate with suction/injection

Summary The effect of suction/injection in the laminar free convection flow of a thermomicropolar fluid past a nonuniformly heated vertical flat plate has been considered. The conditions under which similarity exists have been examined. The resulting system of non-linear ordinary differential equations has been solved numerically after transforming the infinite domain of boundary layer coordinate into a finite domain. The effects of variation of the boundary condition parameter and suction/injection parameter on the velocity, microrotation and temperature fields and the heat transfer coefficient have been studied graphically. The skin-friction parameter and the gradient of microrotation on the wall have been tabulated. It is found that there is significant increase in velocity, skin-friction and the heat transfer coefficient with the decreasing concentration of microelements.With 4 Figures     

Forced convection over a continuous sheet with suction or injection moving in a flowing fluid

Summary The analysis of forced convection flow and heat transfer about a flat sheet with suction or injection continuously moving in a quiescent or flowing fluid has been carried out. This kind of problem finds applications in a variety of manufacturing processes such as hot rolling, extrusion of plastic sheets, continuous casting, and cooling of a metallic plate in a cooling bath. The governing differential equations are reduced to nonlinear ordinary differential equations by similarity transformations. These equations are solved numerically based on a finite difference algorithm. Representative velocity and temperature profiles within the boundary layer are presented at selected values of free stream velocity and injection parameter. The friction factor and Nusselt number are illustrated for a wide range of governing parameters. For the same injection parameter, Prandtl number, and normalized velocity difference |U _w–U |, higher values of the Nusselt number and friction factor result fromU _w>U than fromU _w<U . Also, an increase in the velocity ratioU /U _w results in an increase in the heat transfer rate, but a decrease in the friction factor. Furthermore, the heat transfer is enhanced due to increasing the values of the free stream velocity, the injection parameter, and Prandtl number; while it is reduced due to increasing the velocity difference.Nomenclature C _f friction factor, _w/(u_r ²/2) - F dimensionless stream function - F _w injection parameter - h local heat transfer coefficient - k thermal conductivity - Nu Nusselt number,hx/k - Pr Prandtl number, / - q _w wall heat flux - Re Reynolds number,u _rx/ - T temperature - T _w temperature at the fluid-sheet interface - T free stream temperature - U _w normalized velocity of the sheet,u _w/u_r - U normalized free stream velocity,u /u _r - u fluid velocity component inx-direction - u _r reference velocity, Eq. (8) - u _w velocity of the continuous sheet - u free stream velocity - v fluid velocity component iny-direction - v _w fluid velocity component iny-direction at the fluid-sheet interface - x streamwise coordinate - y cross-stream coordinate Greek symbols thermal diffusivity - boundary-layer thickness - dimensionless cross-stream coordinate - dimensionless temperature - kinematic viscosity - _w wall shear stress - stream function     

Stability of fluid flow in a plane channel with uniform injection or suction through porous walls

The stability of laminar flow in a channel with porous walls is analyzed within the scope of the linear theory.Notation x distance from entrance cross section - y transverse coordinate measured from axis - u_x, u_y longitudinal and transverse velocity components of main flow - h half-width of channel - kinematic viscosity coefficient - U₀ average velocity in entrance cross section - V suction or injection rate (positive for suction) - U=U₀–V_x/h local average velocity - amplitude of flow disturbances - wave number - c complex phase velocity of disturbances - c_r real propagation velocity of disturbances, =y/h - Re=Uh/ Reynolds number of main flow - R=Vh/ injection or suction Reynolds number - m=U/¦V¦ injection rate parameter Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 436–440, September, 1981.     

Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection

Van Dyke's singular perturbation technique has been used to study the heat transfer in the flow of a micropolar fluid past a curved surface with suction and injection. The conditions for similar solutions of the thermal boundary layer equations have been obtained. In addition to the usual “no slip” condition for velocity, the two types of boundary conditions used for microrotation are: (i) no relative spin on the boundary; (ii) the anti-symmetric part of the stress tensor vanishes at the boundary. The effect of suction or injection on velocity, microrotation, temperature, skin friction coefficient, wall couple stress coefficient, displacement and momentum thicknesses, rate of heat transfer and adiabatic wall temperature have been studied. It is observed that with the increase of injection velocity, the thickness of the boundary layer is increased and the local drag is reduced. A comparison with the results obtained for a Newtonian fluid reveals that the microelements present in the fluid reduce the velocity and frictional drag, and cool the boundary.     

Free convection boundary layer flow of a thermomicropolar fluid with stretch

The free convective boundary layer of a micropolar fluid with stretch has been studied numerically. The governing equations and boundary conditions are stated and solved in the case of a flow past a vertical flat plate. Steady state and transient developments of the flow field are given along with a detailed study of the effect of microstructure on heat transfer.     

Nonsimilar mixed convection flow of a non-Newtonian fluid past a vertical wedge

Summary The flow and heat transfer characteristics of a second-order fluid over a vertical wedge with buoyancy forces have been analysed. The coupled nonlinear partial differential equations governing the nonsimilar mixed convection flow have been solved numerically using Keller box method. The effects of the buoyancy parameter, viscoelastic parameter, mass transfer parameter, pressure gradient parameter, Prandtl number and viscous dissipation parameter on the skin friction and heat transfer have been examined in detail. Particular cases of the present results match exactly with those available in the literature.     

Stability of free convection with uniform suction or injection from a vertical flat plate subjected to a constant wall heat flux

Summary A theoretical study is presented for the stability characteristics of the laminar free convection boundary layer flow along a vertical porous (permeable) flat plate subjected to a constant heat flux. The disturbance equations are solved numerically on the basis of the linear stability theory for a wide range of values of the modified Grashof number,G, and some values of the suction or injection parameterX when the Prandtl number, Pr, is 0.73 (air). These solutions indicate the important role of the parametersG andX on the flow and heat transfer characteristics. It is found that the present results are in very good agreement with those from the open literature.     

Influence of radiation on mixed convection over a wedge in non-Darcy porous medium

The influences of radiation on mixed convection flow of an optically dense viscous fluid along an isothermal wedge embedded in non-Darcy porous medium, in the presence of heat source/sink are numerically investigated. The entire mixed convection regime is covered by a single parameter χ from the pure free convection limit (χ=0) to the pure forced convection limit (χ=1). Forchheimer’s extension is employed to describe the fluid flow in the porous medium and the Rosseland diffusion approximation is considered to describe the radiative heat flux in the energy equation. The governing equations, including internal heat source/sink, are first transformed into a dimensionless form by the nonsimilar transformation and then solved by the Keller box method. The effect of the radiation parameter, mixed convection parameter, Forchheimer number and heat source/sink parameter on the velocity and temperature profiles as well as on the local Nusselt number is presented and analyzed. The results are compared with those known from the literature and excellent agreement between the results is obtained.     

Variational approach to free convection boundary-layer flow with suction and injection

The Gyarmati variational principle — a significant development in the field of the thermodynamics of irreversible processes — is employed to study suction and injection effects in flow and heat transfer in a free convection boundary layer over a cone. The velocity and temperature distributions inside respective boundary layers are considered as simple polynomial functions, and with the use of the perturbation procedure the variational principle is formulated. The Euler-Lagrange equations are reduced to coupled polynomial equations in terms of boundary-layer thicknesses. The skin-friction (shear-stress) and heat-transfer (Nusselt number) values with constant wall temperature are computed for various values of the suction and injection parameters and the cone-angle parameter. The comparison of the present solution with an available numerical solution shows good agreement. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 6, pp. 109–115, November–December, 2007.     

Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge

With a comprehensive and rigorous method, this paper has successfully examined the transient heat transfer in a steady and two-dimensional (2D) laminar boundary layer flow on a wedge with sudden change of thermal boundary conditions of uniform wall temperature (UWT) and heat flux (UHF). Additionally, a correlation of unsteady forced convection was also formulated through an exact solution of transient heat conduction (ξ=0) and the similarity solutions of a steady forced convection on a wedge (ξ=1) in this study. Particularly, for the wedge with −0.198838?ξ?1, the deviation of the wall temperatures estimated by correlation is less than 7.5% within full time of 0?ξ?1 comparing with numerical results in the case of UHF ranging from Pr=10⁻⁴ to 10⁴.     

Optimal boundary layer suction on a porous plate with allowance for initial flow turbulence

It is shown that the initial flow turbulence has an appreciable influence on the optimal suction of fluid from the boundary layer on a porous flat plate.