Natural Convection from a Permeable Sphere Embedded in a Variable Porosity Porous Medium Due to Thermal Dispersion

The laminar natural convection boundary-layer flow of an electricallyconducting fluid from a permeable sphere embedded in a porous medium with variable porosity is considered. The non-Darcy effects including convective, boundary, inertial and thermal dispersion effects are included in this analysis. The sphere surface is maintained at a constant heat flux and is permeable to allow for possible fluid wall suction or blowing. The resulting governing equations are nondimensionalized and transformed into a nonsimilar form and then solved numerically by using the secondlevel local non-similarity method that is used to convert the non-similar equations into a system of ordinary differential equations. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity and temperature profiles as well as the local skin-friction coefficient and the Nusselt number are illustrated graphically to show interesting features of Darcy number, inertia coefficient, the magnetic parameter, dimensionless coordinate, dispersion parameter, the Prantdl number and suction/blowing parameter

Heat transfer in MHD flow of Carreau ternary-hybrid nanofluid over a curved surface stretched exponentially

This investigation aims to study Magnetohydrodynamics (MHD)two-dimensional incompressible boundary layer performing non-Newtonian Carreau ternary-hybrid nanofluid flow with heat transfer through an exponential stretching curved surface. The ternary-hybrid nanofluid has been synthesized with titanium oxide, aluminum oxide, and silver dispersionin the base fluid water. TheNavier Stokes equation and Carreau ternary-hybrid nanofluid model govern the partial differential equations (PDEs), and appropriate similarity transformations are utilized to transfer these PDEs into ordinary differential equations (ODEs). The effects of the pertinent parameters on the dimensionless velocity and temperature profiles are analyzed withfigures. This study provides new insights and solutions to previously unsolved problems related to heat transfer in the MHD flow of a Carreau Ternary-Hybrid Nanofluid over a curved surface stretched exponentially, or it could contribute to the existing knowledge and literature by refining existing models or methods. The surface drag force and Nusselt numbers are studied for the different values of the governing parameters throughgraphs. It is demonstrated that the heat transfer rate and skin friction increase from base fluid to mono, hybrid, and ternary nanofluids. Both heat transfer rate and skin friction increase with the addition of nanoparticles