Hydromagnetic convection at a continuous moving surface

Summary Exact solution for hydromagnetic convection at a continous moving surface with uniform suction is obtained. Flow of this type represents a new class of boundary-layer problems, with solutions substantially different from those for boundary-layer flow at a surface of finite length. Moreover, this is an exact solution of the complete Navier-Stokes equations (including, buoyancy force-term). The solutions for the velocity and skin friction are evaluated numerically for several sets of values of the parameters;G, the Grashof number,P, the Prandtl number, andM, the Hartmann number. It is observed that there is a reverse flow in the boundary-layer due to heating of the fluid (close to the moving surface). That is, whenT _w>T , the fluid in the boundary-layer will be heated up and thus the free convection currents will set in. Also, it is observed that, there is an increase in the skin friction (absolute) with increasingG, P andM.With 7 Figures     

Electrothermal convection in a rotating dielectric fluid layer: Effect of velocity and temperature boundary conditions

The simultaneous effect of a vertical AC electric field and rotation on the onset of thermal convective instability in a horizontal rotating dielectric fluid layer is studied by performing linear stability analysis. The lower and upper boundaries of the fluid layer are considered to be either rigid or free and either isothermal or insulated to temperature perturbations. The resulting eigenvalue problem is solved exactly for free–free isothermal boundaries. It is observed that the oscillatory convection is not a preferred mode of instability for dielectric fluids and the necessary conditions for its occurrence are independent of applied vertical AC electric field. For the other combinations of velocity and temperature boundary conditions, the problem is solved numerically using the Galerkin method. The similarities and differences between the results of isothermal and insulated boundaries are highlighted. It is noted that the effect of increasing AC electric Rayleigh number is to increase the transfer of heat more effectively and hence to hasten the onset of convection. To the contrary, the effect of rotation is to delay the electrothermal convection for a fixed type of boundary conditions. Although the rigid–rigid boundaries enhance the stability when compared to rigid–free and free–free boundaries up to moderate values of Taylor number, the situation is reversed at high Taylor number domain. This trend depends on the temperature boundary conditions as well.     

Hydromagnetic flow and heat transfer over a continuous,moving, porous,flat surface

Summary Exact solutions for hydromagnetic boundary-layer flow and heat transfer over a continuous, moving, flat surface with uniform suction and internal heat generation/absorption are obtained. Flow of this type represents a new class of boundary-layer problems, with solutions substantially different from those for boundary-layer flow on a flat surface of finite length. These solutions are even exact solutions of the complete Navier-Stokes equations and the energy equation.With 3 Figures     

Existence and uniqueness results for a nonlinear differential equation arising in stagnation point flow in a porous medium

We establish existence and uniqueness results over the semi-infinite interval [0, ∞) for a class of nonlinear third-order ordinary differential equations arising in the stagnation point flow in a porous medium.     

Flow and heat transfer in a moving fluid over a moving non-isothermal surface

Heat transfer characteristics for a boundary layer forced convective flow past a moving parallel flat non-isothermal surface in the presence of heat source/sink are obtained. The cases of surface temperature varying directly or inversely with power-law exponent are considered. The similarity solutions are obtained. The numerical results are validated by comparing them with the available results in the literature for some special cases. It is found that dual solutions exist when the surface and the fluid move in the opposite directions. Furthermore, exact and analytical solutions are provided for some parametric regimes.     

Effects of thermal nonequilibrium and non-uniform temperature gradients on the onset of convection in a heterogeneous porous medium

The simultaneous effect of local thermal nonequilibrium (LTNE), vertical heterogeneity of permeability, and non-uniform basic temperature gradient on the criterion for the onset of Darcy-Benard convection is studied. The eigenvalue problem is solved numerically using the Galerkin method. The interaction of various types of permeability heterogeneity and non-uniform basic temperature gradient functions on the stability characteristics of the system is analyzed. It is observed that the linear variation (about the mean) of the permeability and the basic temperature gradient with depth has no added effect on the criterion for the onset of convection. However, the concurrent variation in heterogeneous permeability and non-uniform basic temperature gradient functions has more stabilizing effect on the system, while opposite is the trend when the effect of non-uniform basic temperature gradient alone is present.     

Diffusion of chemically reactive species in Casson fluid flow over an unsteady permeable stretching surface

In this paper we investigate the two-dimensional flow of a non-Newtonian fluid over an unsteady stretching permeable surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First-order constructive/destructive chemical reaction is considered. With the help of a shooting method, numerical solutions for a class of nonlinear coupled differential equations subject to appropriate boundary conditions are obtained. For the steady flow, the exact solution is obtained. The flow features and the mass transfer characteristics for different values of the governing parameters are analyzed and discussed in detail.     

Heat transfer in a second-order fluid over a continuous stretching surface

Summary The heat transfer characteristics of a second-order fluid over a continuous stretching surface with internal heat generation or absorption is analyzed. Two cases are studied, namely (i) the sheet with prescribed surface temperature (PST-case) and (ii) the sheet with prescribed wall heat flux (PHF-case). The solution and heat transfer characteristics are obtained in terms of Kummer's functions. For large values of Prandtl number a uniform approximation is given in terms of parabolic cylinder functions with a boundary layer of width in both the PST and PHF cases. It is also shown that no boundary layer type solution exists for small Prandtl number.     

Hydromagnetic flow and heat transfer of a non-Newtonian power law fluid over a vertical stretching sheet

We consider the steady state, viscous, incompressible two-dimensional magneto hydrodynamic flow of an electrically conducting power law fluid over a vertical stretching sheet. The stretching of the surface velocity and the prescribed surface temperature are assumed to vary linearly with the distance from the slit. The coupled partial differential equations governing the flow and heat transfer are transformed into non-linear coupled ordinary differential equations by a similarity transformation. The transformed boundary layer equations are solved numerically by Keller-Box method for several sets of values of the parameters governing the flow and heat transfer. The flow and heat transfer characteristics are analysed and discussed for different values of the parameters. We observe that the local skin friction coefficient and the local Nusselt number decrease as the magnetic parameter Mn increase for fixed value of the buoyancy parameter λ. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.     

Hall effect on MHD flow and heat transfer over a stretching sheet with variable thickness

We investigate the MHD flow and heat transfer of an electrically conducting fluid over a stretching sheet with variable thickness. The wall temperature and the wall velocity are assumed to vary. The effects of external magnetic field along the sheet and the Hall currents are considered. The governing equations are solved numerically using an implicit finite difference scheme. The obtained numerical results are compared with the available results in the literature for some special cases and the results are found to be in very good agreement. The effects of the physical parameters on the velocity and temperature fields are presented graphically and analyzed. The effect of the Hall current gives rise to a cross flow. Moreover, the Hall current and the magnetic field have strong effect on the flow and heat transfer characteristics, i.e., shear stress and the Nusselt number.