optimization of natural convection in a trapezoidal enclosure filled with a bidisperse porous medium (bdpm) using response surface methodology (rsm)

This paper concerns natural convection heat transfer in a trapezoidal enclosure with a bidisperse porous medium (bdpm). the bdpm includes the fracture phase (f-phase) and the porous phase (p-phase) where the f-phase is composed of macropores and the p-phase is the remainder of the structure. the equations governing the both phases are presented and transformed into dimensionless form. then, they are solved numerically through control volume approach. in this work, it is assumed that thermal conductivity and thermal diffusivity of the both phases are identical. thereafter, an optimization study is undertaken based on the response surface methodology (rsm) to find appropriate values for (a) porosity of the f-phase, (b) porosity of the p-phase, and (c) permeability ratio to achieve the highest value of the average nusselt number on the hot wall. it is found that the effect of the porosity of the p-phase is insignificant, as compared with the influence of the porosity of the f-phase and the permeability ratio. hence, it is concluded that the permeability of the p-phase is more influential than its porosity. based on the rsm, a correlation is developed for the average nusselt number in terms of the porosity of the f-phase and the permeability ratio.