###### The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc. # Mathematical Modelling and Experimental Investigation of Melting and Solidification in a Finned Phase Change Material Storage

## Piia Lamberg

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Mechanical Engineering, Helsinki University of Technology, for public examination and debate in Auditorium K216 at Helsinki University of Technology (Espoo, Finland) on the 5th of December, 2003, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-6608-3)   [855 KB]
Dissertation is also available in print (ISBN 951-22-6607-5)

### Abstract

In latent heat storage, internal heat transfer enhancement techniques such as fins have to be used because of the low heat conductivity of the phase change material (PCM). During the phase change in a PCM storage system the solid-liquid interface moves away from the heat transfer surface and the surface heat flux decreases due to the increasing thermal resistance of the molten or solidified medium. Internal heat transfer enhancement is essential, especially in a solidification process where the main heat transfer mode is conduction.

The objective of this study was to develop an analytical model which predicts the solid-liquid interface location and temperature distribution of the fin in melting and especially, in solidification processes with a constant end wall temperature in a finned two-dimensional PCM storage. Heat transfer during the melting and solidification processes in a finned PCM storage was also studied numerically and experimentally. The objective of the experimental work was to evaluate different numerical methods in order to find a reliable numerical method for the comparison of several PCM storage structures.

The results of the derived analytical model were compared to numerical results calculated with the FEMLAB multiphysics simulation tool and Digital Fortran 5.0. The simplified analytical equations were solved with FEMLAB in order to find out the accuracy of the analytical solution. The two-dimensional heat transfer problem was also solved numerically by means of the effective heat capacity method and enthalpy method, using FEMLAB and Digital Fortran. The two-dimensional results were compared to simplified one-dimensional results in order to find out the accuracy of the simplified analytical model. The results of the experimental work were compared to the numerical results calculated with FEMLAB, using the effective heat capacity method and enthalpy method, in order to find out the accuracy of different numerical methods.

A simplified analytical model based on a linear, transient, thin-fin equation was introduced which predicts the solid-liquid interface location and temperature distribution of the fin in the melting process with a constant imposed end wall temperature for the melting process in a semi-infinite PCM storage and for the solidification process in a finite PCM storage with internal fins. The results show that the analytical models give a satisfactory estimate of fin temperature and the solid-liquid interface. It was noticed that the assumptions made in simplifying the two-dimensional heat transfer problem into a one-dimensional form affected the accuracy to a greater extent than the assumptions made when solving the one-dimensional equations analytically.

The results showed that the effective heat capacity method with a narrow temperature range, dT = 2 °C, was the most precise numerical method when numerical results were compared to experimental results in a finned paraffin PCM storage. The FEMLAB program was very suitable for solving different kinds of phase change problems in one, two, or three dimensions.

This thesis consists of an overview and of the following 5 publications:

1. Lamberg P., Lehtiniemi R. and Henell A.-M., Numerical and experimental investigation of melting and freezing processes in phase change material storage. International Journal of Thermal Sciences, in press. © 2003 by authors and © 2003 Elsevier Science. By permission.
2. Lehtiniemi R., Lamberg P. and Henell A.-M., 2002. Validating a numerical phase change model by using infrared thermography. Proceedings of the 6th International Conference on Quantitative Infrared Thermography (QIRT 2002). Dubrovnik, Croatia, 24-27 September 2002.
3. Lamberg P. and Sirén K., 2003. Analytical model for melting in a semi-infinite PCM storage with an internal fin. Heat and Mass Transfer 39, No. 2, pages 167-176. © 2003 Springer-Verlag. By permission.
4. Lamberg P. and Sirén K., 2003. Approximate analytical model for solidification in a finite PCM storage with internal fins. Applied Mathematical Modelling 27, No. 7, pages 491-513. © 2003 Elsevier Science. By permission.
5. Lamberg P., 2004. Approximate analytical model for two-phase solidification problem in a finned phase-change material storage. Applied Energy 77, No. 2, pages 131-152. © 2004 Elsevier Science. By permission.

Keywords: phase change material, PCM, heat transfer in PCM storage