Nonlinear magneto-heat transfer in a fluid-particle suspension flowing in a non-darcian channel with heat source and buoyancy effects : numerical study

Abstract EN

We consider the steady, laminar nonlinear natural convection heat transfer of a particulate suspension in an electricallyconducting fluid 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 are formulated using a two-phase continuum model and a heat source term is included which simulates either absorption or generation.

A set of variables is implemented to reduce the ordinary differential equations for momentum and energy conservation (for both phases) from a two-dimensional coordinate system to a one-dimensional system.

Finite element solutions are obtained for the dimensionless system under appropriate boundary conditions.

A comprehensive parametric study of the effects of heat source parameter (E), Prandtl number (Pr), Grashof number (Gr), momentum inverse Stokes number (Skm), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (PL), buoyancy parameter (B), Hartmann number (Ha) and temperature inverse Stokes number (SkT) on the dimensionless fluid phase velocity (U), dimensionless particle phase velocity (Up), dimensionless fluid phase temperature (Φ) and the dimensionless temperature of particle phase (Φp) are presented graphically.

Fluid phase velocities are found to be strongly reduce by magnetic field, Darcian drag and also Forchheimer drag; a lesser reduction is observed for the particle phase velocity field.

Prandtl number is shown to depress both fluid temperature and particle phase temperature in the left hand side of the channel but to boost both temperatures at the right hand side of the channel (0.5 ≤ η ≤ 1).

Inverse momentum Stokes number is seen to reduce fluid phase velocities and increase particle phase velocities.

The influence of other thermophysical parameters is discussed in detail and computations compared with previous studies.

The model finds applications in MHD plasma accelerators, astrophysical flows, geophysics, geothermics and industrial materials processing.