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

Finite element computation of transient dissipative double diffusive magneto-convective nanofluid flow from a rotating vertical porous surface in porous media

This paper aimed to investigate the transient dissipative MHD double diffusive free convective boundary layer flow of electrically-conducting nanofluids from a stationary or moving vertical porous surface in a rotating high permeability porous medium, considering buoyancy, thermal radiation and first order chemical reaction. Thermo-diffusion (Soret) and diffuso-thermal (Dufour) effects are also considered. Darcy’s law is employed. The mathematical model is formulated by considering water-based nanofluids containing metallic nano-particles for both stationary and moving plate cases. Three nanofluids are examined, namely copper, aluminium oxide or titanium oxide in water. The transformed non-linear, coupled, dimensionless partial differential equations describing the flow are solved with physically appropriate boundary conditions by using Galerkin weighted residual scheme. For prescribed permeability, numerical results are presented graphically for the influence of a number of emerging parameters. Validation of finite element solutions for skin friction and Nusselt number is achieved via comparison with the previously published work as special cases of the present investigation and very good correlation obtained. Increasing rotational parameter is observed to reduce both primary and secondary velocity components. Primary and secondary velocities are consistently elevated with increasing Soret, Dufour, thermal Grashof and solutal Grashof numbers. Increasing Schmidt number, chemical reaction and suction parameter both suppress nano - particle concentration whereas the converse behavior is computed with increasing Soret number. The study is relevant to high temperature rotating chemical engineering systems exploiting magnetized nanofluids and also electromagnetic nanomaterial manufacturing processes

A New Method for Solving Singularly Perturbed Boundary Value Problems

In this paper, a new initial value method for solving a class of nonlinear singularly perturbed boundary value problems with a boundary layer at one end is proposed. The method is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems (easy to use, modest problem preparation and ready computer implementation). Using singular perturbation analysis the method is distinguished by the following fact: the original problem is replaced by a pair of first order initial value problems; namely, a reduced problem and a boundary layer correction problem. These initial value problems are solved using classical fourth order Runge–Kutta method. Numerical examples are given to illustrate the method. It is observed that the present method approximates the exact solution very well