A new practical approach to design a Phase Change Material-Water longitudinally finned tube heat exchanger

Phase change materials have demonstrated interesting advantages in solar energy storage systems to produce domestic hot water although more efficient heat exchangers are required. Among the different exchanger typologies, longitudinally finned exchangers are widespread. However, according to scientific literature, there is a lack of analytical models able to estimate the thermal power transferred by this kind of exchangers easily. This paper shows a practical and easy to apply analytical model that has been built for that type of exchangers. Thus, based on a change of the solution given by Heisler and Gröber for an infinitely long cylinder, this new analytical approach characterises the thermal energy discharged in terms of dimensionless numbers. The adjustment of the analytical model was achieved from the results provided by a CFD numerical model which was previously validated from experimental data. 544 numerical simulations of the system were carried out varying the Biot number and a surface factor number from 1 to 100 and 3 to 15, respectively. An analytical equation that estimates the energy discharged is provided as a function of Fourier, Biot, and Stefan numbers and the surface factor number, related to the exchanger geometry. An average value of the root mean square error smaller than 4% indicates that the proposed model is sufficiently accurate and might be used in the design stages of this kind of devices. A further validation of the analytical model against experimental observations will be carried out in a future stage of model development.