Heat and mass transfer past a semi - infinite vertical porous Plate in MHD flows in turbulent boundary layer
Ngesa, Joel Ochola
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Turbulent flows in electrically conducting media (MHD) remains one of the last unresolved problems in engineering industry and classical physics, but has general importance for the evolution of astro and geophysical plasmas. Turbulence in plasmas, i.e. ionized gases, also offers valuable insights into the not yet fully understood nonlinear dynamics of spectral cascades and structure formation due to the presence or generation of magnetic fields. These allow additional diagnostic access to the underlying nonlinear interaction of turbulent fluctuations. In experimental devices for thermonuclear fusion the magnetically confined hot plasma is basically collisionless and requires kinetic treatment. Exceptions are the thin and comparably cool edge layer near the vessel boundaries and plasmas in reversed-field pinch configurations. Turbulent plasmas in or beyond the earth often allow a fluid description due to the immense size of the dynamical regions and associated timescales of interest compared to the effective mean-free-path and the frequencies related to the plasma particles. Since plasma turbulence is a fully nonlinear problem comprising the dynamics of many interacting degrees of freedom, the relatively simple single fluid description of magnetohydrodynamics (MHD) represents a sensible starting point for theoretical and numerical investigations. The interesting properties of MHD turbulence lies mainly in its potential universality, that is to say the inherent properties of turbulence might well be important for the dynamics of systems involving gravity, radiation, rotation, or convection. Many authors have studied the theory of magnetohydrdynamics (MHD)flow problems as well as to various methods of solving these problems though mostly addressed heat and mass transfer with Hall and ion-slip currents in laminar boundary layer and rotating turbulent system past a semi-infinite vertical porous plate. In this research work we address the problem of heat and mass transfer of unsteady free convection incompressible fluid flow past a semi-infinite vertical porous plate in (MHD) flow in turbulent boundary layer, in the presence of a strong magnetic field inclined at an angle to the plate with Hall and Ion-Slip currents. The determination of the concentration, temperature and velocity profiles’ distribution for fluid flow, the rate of heat transfer, the skin friction, rate of mass transfer and effects of various flow parameters on the turbulent boundary layer fluid flow field are carried out. An explicit finite difference approximation method is used to analyze the partial differential equations governing the flow for a heat generating fluid with Hall and ion-slip effects. The computation of skin friction, rate of heat and mass transfers at the plate is achieved by Newton’s interpolation approximation over the first five points. In both cases when Gr < 0 (in the presence of heating of the plate by free convection currents) and Gr> 0 (in the presence of cooling of the plate by the free convection currents) have been discussed extensively. The effects of various flow parameters on the convectively cooled or convectively heated plate restricted to turbulent boundary layer is considered. The results demonstrate that, Hall current, Schmidt number, Modified Grashof number, Heat source parameter, Suction velocity, Time, Angle of inclination, Ion-Slip current on the convectively cooled or convectively heated plate affect the velocity, temperature and concentration profiles. Increases in Hall current parameter cause a decrease in both primary and secondary velocity profiles while increase in Ion Slip current, decreases primary velocity profiles but increases secondary velocity profiles. As a result, skin friction, rate of heat and mass transfers are altered by their variations.