Design Method

Fig. 4 and 6 present effectiveness curves in which the capacity of the TSU is constant. These figures can be readily used as design curves which characterise the performance of the TSU subject to a single parameter, phase change fraction. In any design, using Eqn. (2), the minimum effectiveness can be determined which will define the outlet temperature from the TSU which will remain within specifications. For a given set of parameters this effectiveness is now directly related to the capacity of the TSU.

Consequently the proportion of phase change can be found which will ensure that the outlet temperature during the charging/discharging process will meet design requirements. This proportion defines the redundant PCM which occurs due to the 2nd law losses described in [3]. Consequently, the size of the TSU can be determined for a given set of parameters which will reliably meet thermal performance criteria. For example, in the solar heating application the minimum outlet temperature during the freezing process is 30 oC. This equates to a minimum effectiveness of 0.43. If the TSU is defined by H=50 mm and a flow rate of 0.35 kg/s, then, referring to Fig. 6, the useful proportion of the TSU is 67%. Therefore, to achieve the required, capacity the TSU should have 50% more PCM.

3. Conclusions

Using the knowledge of the solid/liquid phase change profile, it is possible to develop a one dimensional equation of the effectiveness of a TSU for design purposes, applying the s-NTU approach. The effectiveness was defined in terms of the phase change fraction and is able to reflect two dimensional and one dimensional phase change within a PCM slab. The use of the phase change fraction enables the characterisation of the TSU into a single effectiveness chart. From a design perspective this presents a useful method for determining the size of the TSU, which is the principle unknown variable in the design of the thermal storage unit. This analysis process also provides a method for optimisation of a design by enabling direct comparison of the impact of different parameters.


[1] E. Halawa, F. Bruno and W. Saman, Energy Conversion and Management, 46 (2005) 2592-2604.

[2] D. Morrison and S. Abdel — Khalik, Solar Energy, 20 (1978) 57-67.

[3] H. El-Dessouky and F. Al-Juwayhel, Energy Conversion and Management, 38 (1997) 601-617.

[4] K. Ismail and M. Goncalves, Energy Conversion and Management, 40 (1999) 115-138.

[5] E. Halawa (2006) Thermal Performance Analysis of a Roof Integrated Solar Heating System Incorporating Phase Change Thermal Storage, PhD Thesis, University of South Australia.

[6] A. Sari and K. Kaygusuz, Energy Conversion and Management, 43 (2002) 863-876.

[7] J. P. Holman (1992) Heat Transfer, 7th edn, Mc Graw Hill, London.


A, m2

Heat transfer area


Reynolds Number

Cp, kJ/kgK

Specific heat of fluid


Total thermal resistance

h, W/m2K

Convection heat transfer coefficient T1, oC

Inlet fluid temperature

H, m

Half slab thickness




Outlet fluid temperature

k, W/mK

Thermal conductivity

T, oC

PCM melting point

L, m

Length of slab

U, W/m2K

Overall heat transfer coefficient

m, kg/s

Fluid mass flow rate

W, m

PCM slab width


Number of transfer units

x, m

Direction in flow path


Nusselt Number

y, m

Direction perpendicular to flow path


Prandtl Number


Heat exchange effectiveness


Phase change fraction