Estimation of effective thermal conductivity of packed beds incorporating effects of primary and secondary parameters

Abstract

This paper presents a detailed description and experimental validation of a modified collocated unit cell model for the estimation of effective thermal conductivity of packed beds. The effect of primary and secondary parameters influencing the effective thermal conductivity viz. conductivity ratio (α) and concentration (ν) of the spherical particles (fraction of total volume occupied by the particles) of the packed bed, inter-particle gap, thermal contact conductance between the surfaces in contact, temperature, pressure and Knudsen number respectively are investigated in detail. Analytical expressions for effective thermal conductivity are derived for spatially periodic 2D square cylinder and in-line touching geometries based on the unit cell based thermal resistance approach. Using the developed model, the effective thermal conductivity of various packed materials in the conductivity ratio (ks/kf) range between 1–1000 and concentration (ν) 0 to 1 are predicted for varied temperature and pressure regimes. Predictions obtained from the developed model are compared against existing models available in literature in the pressure range 10−2 to 103 kPa at constant temperature. Furthermore, effective thermal conductivities of packed beds comprising of glass and ceramic beads are predicted using the developed model and compared with measured values obtained using the standard square guarded hot plate (SGHP) apparatus in the temperature range of 323–673 K. Both values are found to agree within ±12.24% and ±14.54% for glass and ceramic beads respectively.