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Two-phase flow problem has attracted considerable attention of many researchers due to its potential in investigating the flow characteristics of binary mixture of fluid and solid particles. In line with this, a mathematical model of convective flow of Casson fluid embedded with solid particles (dust) is formulated in order to study the interaction between the fluid phase and dust phase under the influences of non-linear thermal radiation and convective boundary condition (CBC) which is moving over a vertical stretching sheet. Through the use of similarity transformations, governing equations of fluid and dust phases are reduced into ordinary differential equations, which are then solved numerically by employing the Runge-Kutta Fehlberg (RKF45) method. The effects of radiation parameter and temperature ratio on velocity and temperature profiles, together with skin friction coefficient and Nusselt number are presented graphically as well as in tabular form. Findings reveal that, both effects improve the motion and temperature of fluid and dust phases, respectively. [ABSTRACT FROM AUTHOR]

The problem of steady laminar magnetohydrodynamic (MHD) mixed convection stagnation-point flow of an incompressible viscous fluid over a vertical stretching sheet is studied. The effect of an externally magnetic field is taken into account. The transformed boundary layer equations are solved numerically by using an implicit finite-difference scheme. Numerical results are obtained for various values of the mixed convection parameter, Hartmann number, and Prandtl number. The effects of an externally magnetic field on the skin friction coefficient, local Nusselt number, velocity, and temperature profiles for both A > 1 and A < 1, where A is the velocity ratio parameter, are presented graphically and discussed in detail. Both assisting and opposing flows are considered, and it is found that dual solutions exist for the opposing flow. [ABSTRACT FROM AUTHOR]

The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of non-uniform temperature gradient and magnetic field on Marangoni convection in a horizontal fluid layer heated from below and cooled from above with a constant heat flux. A linear stability analysis is performed. The influence of various parameters on the convection onset is analyzed. Six non-uniform basic temperature profiles are considered, and some general conclusions about their destabilizing effects are presented. [ABSTRACT FROM AUTHOR]

Linear stability theory is applied to the problem of the onset of oscillatory Marangoni convection in a horizontal layer of electrically conducting fluid heated from below in the presence of a vertical magnetic field. The fluid layer is bounded from below by a rigid boundary and from above by a deformable free surface. The critical Marangoni number M[subc], the critical wavenumber a[subc] and the critical frequency w[subc] are obtained for wide ranges of the Prandtl number P[sub1], the magnetic Prandt[subl] number P[sub2], the crispation number C[subr] and the Chandrasekhar number Q. We present numerically a necessary and sufficient condition for oscillatory Marangoni convection to occur. [ABSTRACT FROM AUTHOR]

Combined effect of magnetic field and internal heat generation on the onset of Rayleigh-Bénard convection in a horizontal micropolar fluid layer is studied. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid, and free-free with combination isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. The influence of various parameters on the onset of convection has been analyzed. It is shown that the presence of magnetic field always has a stability effect on the Rayleigh-Bénard convection in micropolar fluid. [ABSTRACT FROM AUTHOR]

In this paper, the steady magnetohydrodynamic (MHD) mixed convection stagnation point flow of an incompressible, viscous, and electrically conducting fluid over a vertical flat plate is investigated. The effect of induced magnetic field is taken into account. Numerical results are obtained using an implicit finite-difference scheme. Both assisting and opposing flows are considered. The results for skin friction, heat transfer, and induced magnetic field coefficients are obtained and discussed for various parameters. The velocity, temperature, and induced magnetic field profiles are also presented. For the case of the opposing flow, it is found that dual solutions exist for a certain range of the buoyancy parameter. Dual solutions are also obtained for the assisting flow. [ABSTRACT FROM AUTHOR]