A simplified finite volume method for effective thermal conductivity in discrete particles

A simplified finite volume method (SFVM) was developed for effective thermal conductivity in discrete particles. The solid granular was simplified as equivalent porous medium in control volumes, and local effective thermal conductivities were calculated to establish thermal resistance network. Finally, the overall effective thermal conductivity was obtained by the Kirchhoff's law. In SFVM, the heavy mesh work can be avoided, and particles are easily divided by regular grids, of which mesh size should go down to 1/11 of particle diameter. The local thermal resistance can be built based on the existing equivalent models, which are determined by the solid-to-gas ratio of thermal conductivity (k_s/k_g). As k_s/k_g < 157.69, the perpendicular model is approprariate. Otherwise, the Maxwell model is more proper. To improve the accuracy, The modification of particle shrinking is neccesary for these equivalent models. The work proves that the partial simplification is allowed for solid granualr in heat conduction problems.