Abstract:
The effects of magnetic force, acting vertically downward, on natural convection
within a porous trapezoidal enclosure saturated with an electrically conducting fluid
have been investigated numerically. The bottom wall of the enclosure is subjected to
a constant hot temperature and the top wall experiences a constant cold temperature
whereas the remaining sidewalls are kept adiabatic. The physical problems are
represented mathematically by different sets of governing equations along with the
corresponding boundary conditions. Using Galerkin weighted residual method of
finite element formulation; the non-dimensional governing equations are discritized.
For natural convection in a porous medium or two horizontally layered porous media
of different permeabilities, the influential parameters are the modified Rayleigh
number, Ram, the fluid Rayleigh number, Raj, the inclination angle of the sidewalls of
the cavity, y, the rotational angle of the enclosure, (/J, the pernleability ratio, K" and
the Hartmann number, Ha, through which different thermo-fluid characteristics
inside the enclosure are obtained. In the present study, the obtained results are
presented in ternlS of streamlines, isotherms and average Nusselt number along the
hot wall. The results show that with increasing Ha, the diffusive heat transfer
becomes prominent even though the modified Rayleigh number increases. Optimum
heat transfer rate is obtained at higher values of Ram in the absence of magnetic
force. In case of horizontal layered porous media, the small difference of the
permeabilities of two layers shows the dominancy of convective currents over the
diffusive one.
