Numerical investigation of a vertical finned-tube and shell energy storage system using coupled boundary condition

•A PCM vertical finned-tube and shell energy storage system is studied numerically.•Significance of applying conjugate B.C (CBC) for HTF laminar flow is shown.•Using CBC, the effects of fins geometric parameters are studied comprehensively.•N = 16 is obtained as optimum number of fins. An energy storage system (ESS) containing phase change materials (PCMs) is one of the methods used for energy control and management. In this paper, it is numerically shown that in a vertically oriented three-dimensional finned-tube and shell ESS under a charging process when laminar HTF flows in the tube, applying coupled boundary condition (CBC) is essential and using constant wall temperature boundary condition (CWTBC), used in many previous studies, leads to high errors compared to applying CBC. Then, using CBC, the effects of fins on the charging time, tc, and different stored energy, Q, are studied comprehensively. The three-dimensional governing equations are solved using the finite volume method (FVM) and the enthalpy-porosity technique. The results showed that the minimum and maximum relative increase of the charging time resulted from applying CBC compared to that of obtained from applying CWTBC are 61.98% and 123.63%, respectively. Increasing the number of fins decreases tc, the stored energy in PCM, QPCM, and the total stored energy, Qtot (the total stored energy is the sum of energy stored in fins, QFins, and PCM, QPCM) about 73.76%, 11.21%, and 2.15%, respectively. Additionally, lowering the number of fins changes tc slightly for N > 16, hence, applying N > 16 is not recommended. With increasing the fins height, tc, QPCM, and Qtot are declined about 76.96%, 9.33%, and 5.3%, respectively. With increasing the fins thickness, tc, QPCM, and Qtot are reduced approximately 23.77%, 9.4%, and 1.56%, respectively.