A geometry factor for natural convection in open cell metal foam

A dimensionless geometry factor, defined as the ratio of the product of the microscopic length scale and the solid fluid interface area to the solid volume in a representative elementary volume (REV), connects the macroscopic and microscopic drag and heat flux between the solid and fluid phases in a porous medium. Unlike the conventional porosity based geometry factor (1-porosity), the geometry factor represents how widely the solid is distributed in the REV. Based on this geometry factor, the microscopic drag coefficients and heat transfer correlations are presented in a uniform form for porous media of arbitrary microscopic geometry, such as spheres, tubes, and metal foams. Also relationships between the microscopic drag coefficients and permeability, Forcheimer coefficient, and Ergun constants are obtained based on the geometry factor. Numerical simulations based on this model agree with previous studies on sphere packed spheres, tube bundle heat exchangers, and natural convection in saturated metal foams including a metal foam with a superposed fluid layer. The effects of Rayleigh number, geometry factor, and ratio of macroscopic to microscopic length scale on overall heat transfer in natural convection in a saturated metal foam are presented. Transient isotherms and streamlines provide a full map of the overall Nusselt number versus Rayleigh number relation and show the relation between the oscillation of Nusselt number and the shedding of the thermal plumes at large Rayleigh number.