Laminar magneto hydrodynamic (MHD) natural convection flow from an isothermal sphere immersed in a fluid with VISCOSITY proportional to linear function of TEMPERATURE has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are reduced to convenient form which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and TEMPERATURE distribution, streamlines and isotherms of the fluid as well as heat transfer characteristics, namely the local skin-friction coefficients and the local heat transfer rate for a wide range of magneto hydrodynamic paramagnet and VISCOSITY-variation parameter.

In the current study, non-Newtonian flow pattern and heat transfer in an enclosure containing a tilted square are examined. In order to numerically simulate the problem, the mesoscopic lattice Boltzmann method is utilized. The non-Newtonian Carreau-Yasuda model is employed. It is able to adequately handle the shear-thinning case. The simulation results of flow and heat transfer have been successfully verified with the previous studies. Several parameters such as Nusselt number, Drag coefficient, and Carreau number are investigated in details. Considering the TEMPERATURE-DEPENDENT VISCOSITY, it is seen that with increasing the TEMPERATURE-thinning index, the drag coefficient increases, but the Nusselt number decreases. By rotating the square obstacle, the results display that increasing the angle of inclination from zero to 45 degrees, increases both the drag coefficient and the Nusselt number. Also, the highest rate of heat transfer occur at the angle of 45 degrees (diamond); however it has a negative impact on the Drag coefficient.

A global nonlinear stability analysis is performed for a couple-stress fluid layer heated from below saturating a porous medium with TEMPERATURE-pressure DEPENDENT VISCOSITY for different conducting boundary systems. Here, the global nonlinear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. The eigenvalue problems for different conducting boundary systems are solved by using Galerkin method. The effects of couple-stress parameter F, Darcy-Brinkman number Da and variable VISCOSITY parameter G on the onset of convection are also analyzed. The use of Darcy-Brinkman model makes the system thermally more stable than the Darcy model for all the different conducting boundary systems, couple-stress parameter and medium permeability promotes stabilization, and the variable VISCOSITY destabilizes the system.

The purpose of the present communication is to investigate the flow of a radiative electromagnetic-Casson nanofluid past a stretching sheet under the impacts of a chemical reaction and nonlinear thermal radiation. To enrich the blood flow, a modulated VISCOSITY/thermal conductivity DEPENDENT TEMPERATURE/nanoparticles concentration parameter is included in the governing equations. The system of PDEs is transformed to ODEs by invoking similarity transformations and then solved numerically by the well- known fourth-order Runge-Kutta integration scheme based on shooting approach. The main factors affecting the Casson fluid’s TEMPERATURE profiles are revealed.