Conjugate Free Convection From Vertical Fins Embedded in a Porous Medium

Conjugate free convection from a vertical plate fin with a rounded tip embedded in a porous medium

“…For the purpose of comparison of the results with those presented by Vaszi et al [9], we introduce the conduction-convection parameter N cc , which is defined as N cc ¼ 2Ra 1=2 kk .…”

“…This half cylindrically shaped part of the fin makes it possible to avoid the necessity of prescribing a boundary condition at the tip of the fin. In the work by Vaszi et al [9] it was assumed that the heat loss from the end face of the fin is negligible, but this is an assumption that is only valid if the fin is very long. For convenience, the coordinate system is chosen such that X measures the distance along the surface of the fin from the lowest point and being measured positive along the right hand side of the fin.…”

“…Liu and Minkowycz [7] and Liu et al [8] studied the natural convection from a plate and cylindrical shaped fin, respectively, and they assumed that the heat conduction in the fin is one-dimensional along the axis of the fin. Vaszi et al [9] extended the analysis on both of these papers by considering twodimensional heat conduction in the fin and solving the conjugate problem by a finite-difference approach. In their work they assumed the tip of the fin to be insulated, and they also investigated the validity of this boundary condition.…”

“…These similarity transformations were introduced by Merkin [10] for the free convection boundary-layer around an isothermal cylinder surrounded by a porous medium. In the case of fins with a flat tip, Vaszi et al [9] employed the artificial, but frequently assumed, boundary condition of an insulating fin tip, which may be restrictive, and it introduces mathematical inaccuracies when dealing with the heat and fluid flow in the vicinity of the tip in practical situations. These authors also studied analytically the mathematical singularity that appears at the fin surface near the fin tip which, of course, does not occur in practice and the present work avoids it.…”

“…In order to illustrate the computational procedure, we have taken the end of the fin to be half of a cylinder of diameter the width of the rectangular section of the fin, thus extending the problem of free convection from a vertical plate fin studied by Vaszi et al [9]. The two-dimensional heat conduction in the fin is coupled to the convection boundary-layer in the porous medium by the conditions of the continuity of the temperature and the heat flux at the porous medium-solid interface.…”