Nonlinear Magneto-Heat Transfer in a Fluid-Particle Suspension Flowing in a Non-Darcian Channel with Heat Source and Buoyancy Effects: Numerical Study

Abstract. We consider the steady, laminar nonlinear naturalconvection heat transfer of a particulate suspension in an electricallyconductingfluid through a two-dimensional channel containing a non-Darcian porous material in the presence of a transverse magnetic field.The transport equations for both fluid and particle phases areformulated using a two-phase continuum model and a heat sourceterm is included which simulates either absorption or generation. A setof variables is implemented to reduce the ordinary differentialequations for momentum and energy conservation (for both phases)from a two-dimensional coordinate system to a one-dimensionalsystem. Finite element solutions are obtained for the dimensionlesssystem under appropriate boundary conditions. A comprehensive parametric study of the effects of heat source parameter (E), Prandtlnumber (Pr), Grashof number (Gr), momentum inverse Stokes number(Skm), Darcy number (Da), Forchheimer number (Fs), particle loadingparameter (PL), buoyancy parameter (B), Hartmann number (Ha) andtemperature inverse Stokes number (SkT) on the dimensionless fluidphase velocity (U), dimensionless particle phase velocity (Up),dimensionless fluid phase temperature (Φ) and the dimensionlesstemperature of particle phase (Φp) are presented graphically. Fluidphase velocities are found to be strongly reduce by magnetic field,Darcian drag and also Forchheimer drag; a lesser reduction isobserved for the particle phase velocity field. Prandtl number is shownto depress both fluid temperature and particle phase temperature in theleft hand side of the channel but to boost both temperatures at the righthand side of the channel (0.5 ≤ η ≤ 1). Inverse momentum Stokesnumber is seen to reduce fluid phase velocities and increase particlephase velocities. The influence of other thermophysical parameters isdiscussed in detail and computations compared with previous studies.The model finds applications in MHD plasma accelerators,astrophysical flows, geophysics, geothermics and industrial materialsprocessing.