In the present study, the transient, free convective, boundary layer flow of a couple stress fluid flowing over a vertical cylinder is investigated, and the heat and mass functions for the final steady-state of the present flow are developed. The solution of the time dependent nonlinear and coupled governing equations is obtained with the aid of an unconditionally stable Crank–Nicolson type of numerical scheme. Numerical results for the time histories of the skin-friction coefficient, Nusselt number, and Sherwood number as well as the steady-state velocity, temperature, and concentration are presented graphically and discussed. Also, it is observed that time required for the flow variables to reach the steady-state increases with the increasing values of Schmidt and Prandtl numbers, while the opposite trend is observed with respect to the buoyancy ratio parameter. To analyze the flow variables in the steady-state, the heatlines and masslines are used in addition to streamlines, isotherms, and isoconcentration lines. When the heat and mass functions are properly made dimensionless, its dimensionless values are related to the local and overall Nusselt and Sherwood numbers. Boundary layer flow visualization indicates that the heatlines and masslines are dense in the vicinity of the hot wall, especially near the leading edge.

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We report both theoretical and numerical results on convection for a binary magnetic mixture under rotation. We focus on the stationary convection for idealized boundary conditions. We obtain explicit expressions of convective thresholds in terms of the control parameters of the system. Close to bifurcation, the coefficients of the corresponding amplitude equation are determined analytically. The effect of the magnetophoresis and Kelvin force are emphasized and, finally, the nature of the bifurcation is discussed.

Thermal convection of binary mixtures in a porous medium is studied with stress-free boundary conditions. The linear stability analysis is studied by using the normal mode method. The effects of the material parameters have been studied at the onset of convection. Using a multiple scale analysis near the onset of the stationary convection, a cubic-quintic amplitude equation is derived. The influence of the Lewis number and the separation ratio on the supercritical-subcritical transition is discussed. Stationary front solutions and localized states are analyzed at the Maxwell point. Near the threshold of the oscillatory convection, a set of two coupled complex cubic-quintic Ginzburg-Landau type amplitude equations is derived, and implicit analytical expressions for the coefficients are given.

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