Investigation of Effective Thermal Conductivity of Spherical Packed Beds Using In-Line Contacting Three-Dimensional Cubic Unit Cell Model

Abstract

This paper estimates the effective stagnant thermal conductivity of a spherical packed bed using an experimentally validated modified collocated unit cell model. The study focused on the effect of primary and secondary parameters on effective thermal conductivity. The effects of concentration of the spherical packed bed, thermal conductivity ratio, contact conductance resulting from particle-to-particle contact, and moderate temperature are studied in detail. Analytical expressions are derived for the in-line contacting three-dimensional solid cubic arrays by adopting the unit-cell-based thermal resistance method for determining the effective stagnant thermal conductivity. The effective thermal conductivity of different heterogeneous packed beds with solid-fluid materials possessing conductivity ratio in the range of 1–1000 and concentrations in the range of 0–1 are predicted for various temperatures at constant pressure regimes using the developed model. Furthermore, the developed model is used to estimate the effective stagnant thermal conductivities of packed beds filled with glass and ceramic bead materials, which are compared with values measured using the steady-state square guarded hot plate apparatus over the moderate temperature range of 323–673 K. The values for both uniform-sized glass and ceramic beads are found to be within ±11.26% and ±13.35% of each other.