Effective thermal conductivities in packed beds: Review of correlations and its influence on system performance

This paper reviews the extensive literature about the different experimental correlations for effective thermal conductivity in packed beds. The review covers correlations for stagnant thermal conductivity (with a motionless fluid) k(eff)(0), including thermal radiation heat transfer, k(eff)(0,rad). In addition, correlations for effective conductivity with the fluid in motion for both axial, k(eff)(a), and radial, k(eff)(r), directions are reviewed together with expressions for effective conductivity in packed beds filled with encapsulated phase change materials k(effpcm). High discrepancies of one order of magnitude in the correlations available in the literature for axial effective thermal conductivity, k(eff)(a) are observed. Nevertheless, a sensitivity analysis concludes that the influence of k(eff)(a) on a packed bed performance is negligible for most cases because the conduction characteristic time is usually much larger than that for convection. Only for very low flow rates (as in thermocline tanks) can it influence the charging and discharging times. The review concludes that more research and new correlations are necessary for thermocline tanks and for beds filled with encapsulated PCMs. In addition, new correlations for the axial effective thermal conductivity obtained when the fluid flows in the same direction as the heat flux are necessary. The numerical models available in the literature used correlations that were not obtained for the working conditions of these energy storage systems, which may result in large discrepancies in the results of these models.