Magnetohydrodynamic Natural Convection Flow on a Sphere in Presence of Heat Generation

The present work describes the effect of magnetohydrodynamic natural convection flow on a sphere in presence of heat generation. The governing boundary layer equations are first transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations arethen solved numerically using the Keller-box method. Here we have focused our attention on the evolution of the surface shear stress in terms of local skin friction and the rate of heat transfer in terms of local Nusselt number, velocity distribution as well as temperature distribution for a selection of parameter sets consisting of heat generation parameter Q (= 0.0, 0.5, 1.0, 2.0) and the magnetic parameter M (= 0.0, 0.2, 0.5, 0.8, 1.0). Numerical solutions have been considered for Prandtl number Pr (= 0.7, 1.0, 2.0)

Viscous Dissipation Effects on MHD Natural Convection Flow Over a Sphere in the Presence of Heat Generation

In this paper, the viscous dissipation effects on magnetohydrodynamic natural convection flow over a sphere in the presence of heat generation have been described. The governing boundary layer equations are first transformed into a nondimensional form and the resulting nonlinear system of partial differential equations are then solved numerically using finite-difference method together with Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles are shown graphically and tabular form for a selection of parameters set consisting of heat generation parameter Q, magnetic parameter M, viscous dissipation parameter N and the Prandlt number Pr

Simulation of second-order velocity slip of magnetohydrodynamic (MHD) flows

Abstract: The influence of second-order velocity slip of magnetohydrodynamic flow involved in liquid-metal was numerically investigated. A commercial Computational Fluid Dynamics (CFD) code, STAR-CCM+ 13 was used. The MHD flow of Galinstan (GaInSn - Gallium-Indium-Tin) an electrically conducting liquid-metal fluid in the presence of a magnetic field was investigated. The variations of velocity within the second-order velocity slip parameters were found to be influenced by the local variations of the magnetic field. It was determined that the second-order velocity slip persists due to an increase in the thermal boundary layer. The numerical results were compared to published literature and were in good agreement

A Study of MHD Free Convection Flow Past an Infinite Inclined Plate

In the present article, we have studied the magnetohydrodynamic (MHD) free convection flow past an infinite inclined plate. In order to explore the effects of velocity, temperature and concentration, Laplace transform technique has been used in this study. This method is adapted to accomplish the analytical solution of governing equation. The impact of various embedded parameter on concentration, velocity and temperature such as chemical reaction, magnetic parameter, radiation and inclination angle has been discussed graphically with numerical results

Radiative and magnetohydrodynamics flow of third grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

A mathematical analysis is presented to investigate the nonlinear, isothermal, steady-state, free convection boundary layer flow of an incompressible third grade viscoelastic fluid past an isothermal inverted cone in the presence of magnetohydrodynamic, thermal radiation and heat generation/absorption. The transformed conservation equations for linear momentum, heat and mass are solved numerically subject to the realistic boundary conditions using the second-order accurate implicit finite-difference Keller Box Method. The numerical code is validated with previous studies. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and low-density polymer materials processing

Instabilities in extreme magnetoconvection

Thermal convection in an electrically conducting fluid (for example, a liquid metal) in the presence of a static magnetic field is considered in this chapter. The focus is on the extreme states of the flow, in which both buoyancy and Lorentz forces are very strong. It is argued that the instabilities occurring in such flows are often of unique and counter-intuitive nature due to the action of the magnetic field, which suppresses conventional turbulence and gives preference to two-dimensional instability modes not appearing in more conventional convection systems. Tools of numerical analysis suitable for such flows are discussed

Radiative heat transfer in MHD mixed convection flow of nanofluids along a vertical channel

Over the past few decades, nanofluids have emerged as a promising technology for the enhancement of the intrinsic thermophysical properties of many convectional heat transfer fluids such as water and oil. Many researchers have been investigated the merits of dispersing nanometer-sized particles into base fluids to enhance heat transfer, thermal conductivity and viscosity of the fluids. Therefore, this research focused on radiative heat transfer in magnethohydrodynamics mixed convection flow in a channel filled with nanofluids containing different type of nanoparticles. Five types of nanoparticles (Al2O3, 3 4Fe O , Cu, 2 TiO , and Ag) with five different shapes (platelet, blade, cylinder, brick and spherical) were used in water 2 (H O) and ethylene glycol 2 6 2 (C H O), as conventional base fluid. An important subtype of nanofluids called ferrofluids 3 4 (Fe O in water based nanofluids) was also studied. Four different problems were modelled as partial differential equations with physical boundary conditions. In the first three problems, the channel walls were taken rigid, while the fourth problem the walls were chosen permeable where suction or injection was taking place. Perturbed type analytical solutions for velocity and temperature were obtained and discussed graphically in various graphs. Results for skin friction and Nusselt number were also computed and presented in tabular forms. This study showed that 2 6 2 C H O was the better convectional base fluid compared to 2 H O because of the higher viscosity and thermal conductivity. Ag nanoparticles had the highest thermal conductivity and viscosity compared to other type of nanoparticles. Increasing nanoparticles size had caused variation in velocity. It was also observed that, variation in velocity for Ag nanoparticles was obtained at low volume concentration, whereas for 2 3 Al O nanoparticles, this variation was observed only at high volume concentration. Velocity increases with increasing Grashof number, radiation, heat generation and permeability parameters, but decreases with increasing magnetic parameter and volume fraction of nanoparticles. However, the effects of these parameters were quite different in the case of suction and injection. Results had also shown that, temperature increases with increasing radiation and heat generation parameters. In this study, the temperature of ferrofluids was found smaller when compared to the temperature of nanofluids

Chemical Reaction Effects on an Unsteady MHD Mixed Convective and Radiative Boundary Layer Flow over a Circular Cylinder

A mathematical model is presented for an optically dense fluid past an isothermal circular cylinder with chemical reaction taking place in it. A constant, static, magnetic field is applied transverse to the cylinder surface. The cylinder surface is maintained at a constant temperature. New variables are introduced to transform the complex geometry into a simple shape and the boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, Crank-Nicolson finite difference scheme. Numerical computations are made and the effects of the various material parameters on the velocity, temperature and concentration as well as the surface skin friction and surface heat and mass transfer rates are illustrated graphs and tables. Increasing magnetohydrodynamic body force parameter (M) is found to decelerate the flow but enhance temperatures. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing radiation parameter

Finite element analysis of rotating oscillatory magneto-convective radiative micropolar thermo-solutal flow

Micropolar fluids provide an alternative mechanism for simulating micro-scale and molecular fluid mechanics which require less computational effort. In the present paper, a numerical analysis is conducted for the primary and secondary flow characterizing dissipative micropolar convective heat and mass transfer from a rotating vertical plate with oscillatory plate velocity, adjacent to a permeable medium. Owing to high temperature, thermal radiation effects are also studied. The micropolar fluid is also chemically-reacting, both thermal and species (concentration) buoyancy effects and heat source/sink are included. The entire system rotates with uniform angular velocity about an axis normal to the plate. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. The partial differential equations governing the flow problem are rendered dimensionless with appropriate transformation variables. A Galerkin finite element method is employed to solve the emerging multi-physical components of fluid dynamics problem are examined for a variety of parameters including rotation parameter, radiation-conduction parameter, micropolar coupling parameter, Eckert number (dissipation), reaction parameter, magnetic body force parameter and Schmidt number. A comparison with previously published article is made to check the validity and accuracy of the present finite element solutions under some limiting case and excellent agreement is attained. The current simulations may be applicable to various chemical engineering systems, oscillating rheometry, and rotating MHD energy generator near-wall flows