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

• Published in: Applied thermal engineering Vol. 171; p. 115048
• Main Authors: Díaz-Heras, M., Belmonte, J.F., Almendros-Ibáñez, J.A.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 05.05.2020; Elsevier BV
• Subjects: Computational fluid dynamics; Convection; Correlation; Effective thermal conductivity; Encapsulation; Energy storage; Flow velocity; Fluid dynamics; Fluid flow; Heat conductivity; Heat flux; Heat transfer; Low flow; Numerical models; Packed beds; Phase change materials; Sensitivity analysis; Stagnant effective thermal conductivity; Storage systems; Tanks; Thermal conductivity; Thermal radiation; Packed beds; Effective thermal conductivity; Stagnant effective thermal conductivity; Energy storage
• ISSN: 1359-4311; 1873-5606
• DOI: 10.1016/j.applthermaleng.2020.115048

•Keff correlations for both motionless fluids and in motion are reviewed.•Reviewed correlations for axial flow reported differences of one order of magnitude.•There are no proper correlations for low-velocity fluids in dual thermocline tanks.•No proper correlations for packed beds containing PCMs can be found in literature.•For most cases, conduction characteristic time is much lower than convection one. 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) keff0, including thermal radiation heat transfer, keff0,rad. In addition, correlations for effective conductivity with the fluid in motion for both axial, keffa, and radial, keffr, directions are reviewed together with expressions for effective conductivity in packed beds filled with encapsulated phase change materials keffpcm. High discrepancies of one order of magnitude in the correlations available in the literature for axial effective thermal conductivity, keffa, are observed. Nevertheless, a sensitivity analysis concludes that the influence of keffa 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.