Abstract

The natural convection and entropy generation during double-diffusive MHD natural convection in a tilted sinusoidal corrugated porous enclosure is investigated numerically in this work by using heatline visualization technique. The top and bottom horizontal walls are assumed as adiabatic and non-diffusive, while the left and right vertical corrugated sidewalls are maintained at a constant hot and cold temperatures and concentrations respectively. The flow in the enclosure is subjected to an inclined magnetic field. The enclosure is filled with an electrically conducting fluid [Pr = 0.024] saturated with a porous media. The numerical computations are presented for various values of Rayleigh number (Ra), Hartmann number (Ha), Lewis number (Le), Darcy number (Da), buoyancy ratio (N), magnetic field orientation angle (φ) and enclosure inclination angle (Φ). In addition, the entropy generation due to fluid friction, thermal gradients, diffusion, and magnetic field beside the total entropy generation are studied and discussed. It is found that the flow circulation decreases strongly when the magnetic field applied horizontally and the enclosure is considered vertical. Heatline visualization concept is successfully applied to the considered problem. The average Nusselt number decreases when the Lewis number increases, while the average Sherwood number increases when the Lewis number increases. Also, both average Nusselt and Sherwood numbers increase when the Darcy number and buoyancy ratio increase. Moreover, the results show that the entropy generations due to magnetic field when the enclosure is subjected to the horizontal magnetic field are higher than the corresponding values when it subjected to the vertical magnetic field.

Abstract

In this study we analyzed the influence of thermal radiation and chemical reaction on two dimensional steady magnetohydrodynamic flow of a nanofluid past a permeable stretching/shrinking sheet in the presence of suction/injection. We considered nanofluid volume fraction on the boundary is submissive controlled, which makes the present study entirely different from earlier studies and physically more realistic. The equations governing the flow are solved numerically. Effects of non-dimensional governing parameters on velocity, temperature and concentration profiles are discussed and presented through graphs. Also, coefficient of skin friction and local Nusselt number is investigated for stretching/shrinking and suction/injection cases separately and presented through tables. Comparisons with existed results are presented. Present results have an excellent agreement with the existed studies under some special assumptions. Results indicate that the enhancement in Brownian motion and thermophoresis parameters depreciates the nanoparticle concentration and increases the mass transfer rate. Dual solutions exist only for certain range of stretching/shrinking and suction/injection parameters.

Abstract

In this study, we investigated the effects of nonlinear thermal radiation and non-uniform heat source/sink in unsteady three-dimensional flow of Carreau and Casson fluids past a stretching surface in the presence of homogeneous–heterogeneous reactions. The transformed governing equations are solved numerically using Runge–Kutta based shooting technique. We obtained good accuracy of the present results by comparing with the already published literature. The influence of dimensionless governing parameters on velocity, temperature and concentration profiles along with the friction factors, local Nusselt and Sherwood numbers is discussed and presented graphically. We presented dual solutions for flow, heat and mass transfer in Carreau and Casson fluids. It is found that the heat and mass transfer rate in Casson fluid is significantly high while compared with the Carreau fluid.

Abstract

The effect of transpiration on magnetohydrodynamic stagnation-point flow of a Carreau nanofluid toward a stretching/shrinking sheet in the presence of thermophoresis and Brownian motion was investigated numerically. The transformed governing partial differential equations are solved using Runge–Kutta coupled with shooting technique. The effect of pertinent parameters on velocity, temperature and concentration profiles along with the friction factor, local Nusselt and Sherwood numbers is presented graphically and through tables. It is observed that, increasing values of the thermophoresis parameter enhances the heat and mass transfer rate, whereas the Weissenberg number enlarges the momentum boundary layer thickness along with the heat and mass transfer rate. A good agreement of the present results has been observed by comparing with the published results.

Abstract

The objective of the present study was to investigate the partial slip effect on an unsteady two-dimensional mixed convection stagnation point flow towards a permeable shrinking sheet. The governing equations are reduced to a system of non-dimensional partial differential equations using a semi-similarity transformation, before being solved numerically by using Keller-box method. The features of the flow characteristics for different values of the governing parameters are analysed and discussed. The results indicate that the momentum, thermal and concentration boundary layer thicknesses increase with increasing mixed convection parameter for opposing flow, whereas the opposite effect is observed for assisting flow. The results also show that the surface velocity is higher when there is slip at a sheet compared to its absent. Further, the study indicates that the boundary layer thicknesses become thicker and thicker with increasing shrinking parameter, while the opposite effect is observed with increasing Hartmann number. Comparison with previously published work for special cases is performed and found to be in excellent agreement.

Abstract

This paper examines the effect of heat generation or absorption on the free convection flow of an incompressible, electrically conducting fluid about an isothermal truncated cone in the presence of a transverse magnetic field. The non-linear coupled partial differential equations governing the flow and heat transfer have been solved numerically, using an efficient implicit finite-difference scheme along with quasilinearization technique. The nonsimilar solutions have been obtained for the problem overcoming numerical difficulties near the leading edge and in the downstream regime, for air (Pr = 0.72). The effects of various physical parameters on skin friction and heat transfer coefficients and, on velocity and temperature are shown graphically for different values of magnetic parameter (M) and heat generation/absorption parameter (Q). It is observed that, magnetic field decreases both skin friction and heat transfer coefficients. The effect of heat generation or absorption is found to be very significant on heat transfer, but its effect on skin friction is negligible.

Abstract

Magnetohydrodynamic instability (MHD) in an aluminum reduction cell is due to the interactions between the conductive liquid currents and the magnetic field generated by very high currents flowing through current feeding circuit buses. Such phenomenon creates oscillations in this fluid, compromising the efficiency of the process aluminum reduction. The reduction cells consist, in their usual configuration, of a container with flat walls that accommodates the liquid. In this work, a new geometry is proposed for the container based on periodic structures, with the aim of to mitigate such oscillations. The analysis of oscillations of fluid in both configurations is made with a software developed in this work to numerically simulate the process in two dimensions. The numerical formulation employed is based on the finite-difference time-domain method to solve the Navier-Stokes equations (N-S) explicitly through the Chorin projections method. The volume and surface of the fluid are mapped using the MAC method. The liquid is treated as incompressible and viscous, in addition to being electrically conductive. The accelerations caused by magnetic field and the electric currents are coupled to N-S by calculating the Lorentz Force. The results are analyzed by calculating differences between liquid heighs obtained at rest and by applying electric currents.