الخلاصة:
The three-dimensional laminar convection of water in aluminum metal foam annulus between two confocal elliptic cylinders is presented. The 20 PPI aluminum foam is considered a homogeneous and isotropic porous medium. The flow field is considered axial,uniform and isothermal at the annulus entrance. The inner cylinder is uniformly heated and the outer cylinder is adiabatic. In this study, we present two parts: the first one is an analytic and a numerical solution of the thermally developing forced convection flow, with constant physical properties; the results will be compared with those of the empty annulus to assess the thermal performance of the used aluminum foam. The detailed mathematical and physical aspects of the convection are presented and discussed. The heat transfer enhancement by the use of the metal foam is demonstrated. For the considered controlling parameters of the problem, it is found that the numerical thermal field reproduces the analytic one. This reproduction is a validation of the numerical result and a demonstration of the adequacy of the spatial resolution of the used numerical grid. The validation of the numerical results of the considered forced convection is a prelude to the numerical simulation of the mixed convection in an inclined annulus with fluid variable physical properties that is presented in the second Part of this work. The results of the forced convection are considered a reference state for those of the mixed convection. In the second part of this work, the slow flow and the heat transfer through the porous annulus are modeled by the continuity equation, the Darcy-Forchheimer-Brinkman flow model, accounting for the important buoyancy, and the energy equation. In the temperature variation domain of this study, the thermophysical properties of the water are functions of temperature while those of the aluminum are constants. The model equations are numerically solved by a finite volume numerical method with a second order accurate spatiotemporal discretization. From the results obtained with the considered geometric, dynamic and thermal parameters, a small negative annulus inclination is recommended to obtain an enhanced heat transfer close to that of the horizontal annulus mounting while overcoming the total pressure drop. The qualitative aspects of the results of this study are not limited to the specific used system; they apply to any strong mixed convection system (with fluid variable physical properties), in along enough and inclined conduit, filled with any porous medium that has an effective thermal conductivity higher than that of the used liquid.
