Thermal conductivity of porous sintered metal powder and the Langmuir shape factor

The objective of this study is to re-examine the classical parallel and classical series models of the effective thermal conductivity of porous media and review the underlying assumptions used to develop these asymptotic models. The Langmuir shape factor concept is introduced to gain insight into these classical models and add extra degrees of freedom to formulate semi-empirical correlations for the effective thermal conductivity based on the parallel, series, and combination of parallel and series heat flow configurations. The analytical models reveal the average areas of the heat flow as potential targets for curve fitting equations with fitting parameters. Experimental data for sintered porous copper were used to calibrate the theoretical models. Correlations for the effective thermal conductivity, Langmuir shape factors, average heat conduction areas, and the average lengths of the heat transfer pathway of the two phases as functions of porosity were obtained and compared graphically.