Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic (MHD), incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted

Homotopy and adomian semi-numerical solutions for oscillatory flow of partially ionized dielectric hydrogen gas in a rotating MHD energy generator duct

Hydrogen-based MHD power generators offer significant advantages over conventional designs. The optimization of these energy devices benefits from both laboratory scale testing and computational simulation. Motivated by this, in the current work, a mathematical model is developed for MHD pumping of partially ionized hydrogen in a rotating duct with oscillatory, Maxwell displacement and magnetic induction effects under an inclined static magnetic field. Perfectly electrically conducting duct walls are assumed. The non-dimensional conservation equations are solved using the power-series based Homotopy Analysis Method (HAM) with an appropriate embedding parameter. Detailed graphical visualization of the impact of emerging parameters on the non-dimensional primary and secondary velocity components (u, v) and magnetic induction components ( , ) x y b b across the duct is presented. Average squared residual errors for all key variables , , , ( and ) u v bx by with associated CPU times at various orders of the HAM iteration are also included. Validation with an Adomian Decomposition Method (ADM) is also conducted, and excellent agreement is obtained (tabulated). The computations have shown that with increasing inverse Ekman number strong damping is observed in the primary flow whereas the secondary flow is accelerated, in particular in the core region of the duct. With elevation in Maxwell displacement effect (for the case of a 45 degrees inclined magnetic field i.e. = /4) there is a strong decrease in primary magnetic induction at the lower wall of the duct and elevation in magnitudes at the upper duct wall; however, in the core region no tangible modification is computed. The opposite trend is observed for the secondary magnetic induction. With increasing magnetic Prandtl number (i.e. ratio of magnetic Reynolds number to ordinary Reynolds number) in the presence of strong Maxwell displacement current, strong magnetic field and high inverse Ekman number, the primary velocity is accelerated in both the left and right half space of the duct with a dip in magnitude at the centreline. However, the secondary velocity exhibits a much lower enhancement in both zones with only weak acceleration near the duct walls. Both velocity components achieve symmetrical distributions about the duct centreline. A significant depletion in primary magnetic induction is computed near the lower duct wall with enhancement near the upper duct wall; the contrary behaviour is exhibited by the secondary induced magnetic field. Applications of the study arise in hybrid rotating hydrogen based MHD energy generators and furthermore the computations provide a good basis for generalization to 3-dimensional flows with commercial multi-physical fluid dynamic codes e.g. ADINA-F, COMSOL, ANSYS FLUENT-Maxwell wherein further phenomena may be explored including Alfven wave effects and dielectric losses

Second law analysis of flow in a circular pipe with uniform suction and magnetic field effects

The present paper investigates analytically the two-dimensional heat transfer and entropy generation characteristics of axi-symmetric, incompressible viscous fluid flow in a horizontal circular pipe.The flow is subjected to an externally applied uniform suction across the wall in normal direction and a constant radial magnetic field. Constant wall temperature is considered as the thermal boundary condition.The reduced Navier-Stokes equations in a cylindrical coordinate system are solved to obtain the velocity and temperature distributions. The velocity distributions are expressed in terms of stream function and thesolution is obtained using the Homotopy Analysis Method (HAM). Validation with earlier non-magnetic solutions in the literature is incorporated. The effects of various parameters on axial and radial velocities, temperature, axial and radial entropy generation numbers, and axial and radial Bejan numbers and are presented graphically and interpreted at length. Streamlines, isotherms, pressure, entropy generation number and Bejan number contours are also visualized. Increasing magnetic body force parameter shifts the peak of the velocity curve near to the axis where as it accelerates the radial flow. The study is relevant to thermodynamic optimization of magnetic blood flows and electromagnetic industrial flows featuring heat transfer