Analytical formulation of effective heat transfer coefficient and extension of lumped capacitance method to simplify the analysis of packed bed storage systems

Abstract

Analysis of the transient temperature evolution during charging or discharging of the packed bed thermal storage systems is immensely simplified with the formulation of an effective heat transfer coefficient between the solid storage materials and the heat transfer fluid. It can cut significant computational cost which is otherwise required for a complete numerical simulation. The lumped capacitance method, the simplest of the available options, is restricted only to the low Biot number scenarios and hence is seldom applicable to any real system. The formulation of the effective heat transfer coefficient allows the extension of the lumped capacitance method for moderate Biot numbers. The present work develops such a formulation to simplify the analysis of packed bed storage systems through analytical route. Earlier attempts in this direction were made through weighted average time method which is inherently restricted to the simple one-dimensional heat conduction problems. On the other hand, we find out the effective heat transfer coefficient starting from a general three dimensional analytical solution of the transient heat conduction and proceed with the well-known one term approximation which acts as the basis of the Heisler charts. The method is not dimensionally restricted and hence we can include realistic three dimensional shapes such as cuboid, short cylinder etc. in the formulation. We validate our method by comparing the resulting temperature profiles for the one-dimensional geometries which have been attempted earlier by the weighted average time method. We also provide the accuracy estimation (as a function of increasing Biot number) against the full numerical simulation for the geometries where the weighted average time is not applicable. Therefore, the current study provides the tool for an inexpensive theoretical estimation for the transient heat transfer behaviour in the thermal storage tanks which has long term design implications particularly for the large scale concentrated solar thermal power plants.