Preferred location of the porous sleeve in a concentric annulus depending on the thermal insulation

Abstract

In this work, natural convection flow in a horizontal cylindrical annulus having a porous sleeve under constant volume is numerically examined and compared with a completely filled porous annulus. Three different locations for the porous sleeve were considered as follows: adjacent to the hot inner surface, in the middle of the annulus and adjacent to the cold outer surface. At each of these locations, the volume of the porous sleeve represents half the volume of the annulus. The code adopts a non-Darcian model to represent the steady laminar flow and heat transfer within the solid porous domain using the finite difference technique. The motivation of the current simulation is to show the influence of the porous sleeve locations on thermal insulation. The influences of a wide range of modified Rayleigh numbers $(50\le R{a}^{*}\le 600)$ and three various values of the porosity $(\epsilon =0.5,0.7,\mathrm{and}0.9)$ , at $\mathrm{Pr}=0.71$ , $\mathrm{Da}=2.5\times {10}^{-3}$ , and $k_s/k_f=1$ , are examined. The results proved that the location of the fixed volume porous sleeve affects the thermal insulation. In addition, the best thermal insulation performance depends on the operating conditions of the system as well as the location of the porous sleeve and its porosity.