Extending the validity of lumped capacitance method for large Biot number in thermal storage application Ben Xu, Pei-Wen Li ⇑ , Cho Lik Chan Depart. of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA Received 18 January 2012; received in revised form 20 March 2012; accepted 25 March 2012 Available online 14 April 2012 Communicated by: Associate Editor D. Laing Abstract In a typical thermal energy storage system, a heat transfer fluid is usually used to deposit/extract heat when it flows through a packed bed of solid thermal storage material. A one-dimensional model of the heat transfer and energy storage/extraction for a packed-bed ther- mal storage system has been developed previously by the authors. The model treats the transient heat conduction in the thermal storage material by using the lumped capacitance method, which is not valid when the Biot number is large. The current work presents an effec- tive heat transfer coefficient between the solid and fluid for large Biot numbers. With the corrected heat transfer coefficient, the lumped capacitance method can be applied to model the thermal storage in a wide range of Biot numbers. Four typical structures for the solid thermal storage material are considered. Formulas for the effective heat transfer coefficient (and effective Biot number) are presented. To verify the prediction by the lumped capacitance method using the effective heat transfer coefficient, we compare the results to the cor- responding analytical solutions. The results are in very good agreement. The effective heat transfer coefficient extended the validity of the lumped capacitance method to large Biot numbers, which is of significance to the analysis of thermal energy storage systems. Ó 2012 Elsevier Ltd. All rights reserved. Keywords: Thermal energy storage; Lumped capacitance method; Large Biot numbers; Corrected heat transfer coefficient; Validity extending 1. Introduction Harvesting more and more renewable energy is a world- wide-important issue in the coming decades. With the recent development of concentrated solar thermal technol- ogies (Pitz-Paal et al., 2007; Laing et al., 2010), thermal energy storage is becoming more and more important. The stored solar thermal energy can supply the heat needed for building heating and industrial drying, as well as extending the operation of solar thermal power plants at night to meet the needs of peak demands of power (Wyman et al., 1980; Singer et al., 2010). The ability of thermal energy storage to extend the daily operation of power plants beyond sunlight hours can ideally expand power generation at a lower per unit cost. It can also alleviate resource intermittency, increasing energy value and opera- tional flexibility (Montes et al., 2009; Price et al., 2002). Consequently, the cost of electricity from concentrated solar thermal power plants can be reduced (Gil et al., 2010; Renewable Energy, 2007; Herrmann and Kearney, 2002; McMahan et al., 2007; Herrmann et al., 2004; Warerkar et al., 2011). In a solar thermal power plant, heat transfer fluid (HTF) is typically used to collect and deliver heat that is received from concentrated sunlight. Hot HTF from solar collection fields may be directly stored in tanks for thermal storage. This situation can be considered as ideal thermal storage (assuming the tank has no heat loss) since discharged fluid will continuously exit at the same high temperature until the tank is completely emptied. However, due to the high cost of HTF (typically liquid salts or oils), direct storage 0038-092X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2012.03.016 ⇑ Corresponding author. Tel.: +1 520 626 7789. E-mail address: peiwen@email.arizona.edu (P.-W. Li). www.elsevier.com/locate/solener Available online at www.sciencedirect.com Solar Energy 86 (2012) 1709–1724