Developing thermal flow in open-cell foams

Predicting heat transfer is a primary task in the design of open-cell foams. When a Local Thermal Non Equilibrium (LTNE) model is employed, convection heat transfer between the solid and fluid phases is considered, and a volumetric heat transfer coefficient needs to be defined. Some recent studies pointed out that the effects of developing convection heat transfer between the fluid and the solid in a foam are to be taken into account. The developing thermal flow of air through an open-cell foam, with a uniform heat flux solid/fluid boundary condition, is investigated numerically in this paper. The geometry is modeled with reference to Kelvin's tetrakaidecahedron foam model. A correlation among the porosity, the cell diameter and the ratio of heat transfer surface to volume is derived. Three regions are identified along the flow direction: an impingement region, a thermally developing region and a thermally developed region. Dimensional and dimensionless convection heat transfer coefficients have been predicted numerically as a function of the axial coordinate of the foam, for different values of the Reynolds number and the porosity. A correlation is presented among the predicted values of the volumetric Nusselt number, the porosity, and the Reynolds number in the thermally developed region, which is in good agreement with experimental data and numerical predictions by other authors. Finally, the analysis of the convection heat transfer through a single foam cell, at a local pore-scale, is presented.