An investigation on an unsteady MHD natural convection flow with radiative heat transfer of a viscous, incompressible, electrically conducting and optically thick fluid past an impulsively moving vertical plate with ramped temperature in a porous medium in the presence of a Hall current and thermal diffusion is carried out. An exact solution of momentum and energy equations, under Boussinesq and Rosseland approximations, is obtained in a closed form by the Laplace transform technique for both ramped temperature and isothermal plates. Expressions for the skin friction and Nusselt number for both ramped temperature and isothermal plates are also derived. The numerical values of fluid velocity and fluid temperature are displayed graphically versus the boundary layer coordinate y for various values of pertinent flow parameters for both ramped temperature and isothermal plates. The numerical values of the skin friction due to primary and secondary flows are presented in tabular form for various values of pertinent flow parameters.

Effects of Hall current on unsteady MHD natural convection flow of a viscous, incompressible, electrically conducting and heat absorbing fluid past an impulsively moving vertical plate with ramped temperature in a porous medium, in the presence of thermal diffusion, is studied. The exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique for both ramped temperature and isothermal plates. Solution is also obtained in the case of unit Prandtl number for ramped temperature plate. The expressions for skin friction due to primary and secondary flows and Nusselt number for both ramped temperature and isothermal plates are also derived. Mathematical formulation of the problem, in non-dimensional form, contains six pertinent flow parameters viz.

A numerical investigation of unsteady hydromagnetic natural convection flow of a viscous, incompressible, electrically conducting and heat absorbing fluid past an impulsively moving vertical plate with ramped temperature embedded in a porous medium in the presence of thermal diffusion is carried out. The governing equations are solved numerically by Crank-Nicolson implicit finite difference scheme. The numerical solution for fluid velocity and fluid temperature are depicted graphically whereas the numerical values of skin friction and Nusselt number are presented in tabular form for various values of pertinent flow parameters. Natural convection flow near a ramped temperature plate is also compared with the flow near an isothermal plate.

Unsteady hydromagnetic Couette flow of a viscous, incompressible and electrically conducting fluid between two parallel porous plates taking Hall current into account in a rotating system is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel and is permeated by a uniform transverse magnetic field which is fixed relative to the moving plate. Solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate due to primary and secondary flows is also derived. Asymptotic behavior of the solution valid for small and large values of time t is analyzed to gain some physical insight into the flow pattern. Numerical values of primary and secondary velocities and that of shear stress at the moving plate due to primary and secondary flows are displayed graphically for various values of Hall current parameter m, rotation parameter K2, magnetic parameter M2, suction/injection parameter S and time t.

Abstract:In this paper, authors investigate homogeneous-heterogeneous chemical reaction and heat absorption effects on a two-dimensional steady hydromagnetic Newtonian nanoliquid flow along a continuously stretching sheet. The flow field is subjected to a uniform magnetic field acting in a direction perpendicular to the direction of nanoliquid flow. A mathematical model of the physical problem is presented involving nonlinear partial differential equations with appropriate boundary conditions. These equations are then transformed into nonlinear ordinary differential equations using a suitable similarity transformation. Finally, approximate solutions of the transformed equations are obtained using the spectral quasi-linearization method. Results of fluid velocity, fluid temperature, and species concentration are depicted graphically, while the values of skin friction and Nusselt number are presented in tabular form. Fluid flow models of this kind find applications in catalytic reactors involving chemical reactions, insulation systems, and in heat exchangers. The applied magnetic field has a retarding influence on the nanofluid velocity and species concentration, while it does not have any significant effect on the nanofluid temperature. The homogeneous and heterogeneous reactions tend to decrease the species concentration.