The basis of the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out. It is shown that the mathematical representation of the enthalpy model is equivalent to the conventional conservation equations in the solid and liquid regions and at the solid-liquid interface. The model is employed in conjunction with a fully implicit finite-difference scheme to solve for solidification in a convectively cooled square container. The implicit scheme was selected because of its ability to accommodate a wide range of the Stefan number Ste. After its accuracy had been established, the solution method was used to obtain results for the local and surface-integrated heat transfer rates, boundary temperatures, solidified fraction, and interface position, all as functions of time. The results are presented with SteFo (Fo = Fourier number) as a correlating parameter, thereby facilitating their use for all Ste values in the range investigated. At low values of the Biot number, the surface-integrated heat transfer rate was relatively constant during the entire solidification period, which is a desirable characteristic for phase change thermal energy storage.

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An analysis of transient multidimensional solidification in the presence of a growing shrinkage cavity has been performed. The enthalpy model, which had previously been applied only for cases with no density change, has been extended to accommodate substances which undergo a change of density upon phase change. The extended enthalpy model was implemented by an efficient, implicit finite difference scheme. A solidification model was adopted in which the shrinkage cavity is at the top of the container within which the phase change is taking place. Solutions were carried out for solidification of a liquid in a long, horizontal rectangular container with convectively cooled walls. Results are presented for the time variations of various heat transfer quantities and for the evolution of the shrinkage cavity and the solid-liquid interface, for parametric values of the Biot number, liquid-solid density ratio, and Stefan number. The influence of the density ratio and the Stefan number on the heat transfer results was most marked at times near the completion of solidification, whereas the Biot number had a major effect at all times.

A thermodynamic efficiency based on the second law of thermodynamics is defined for heat exchange devices. The efficiency can be simply written in terms of the mean absolute temperatures of the two fluids exchanging heat, and the appropriate environment temperature. It is also shown that for a given ratio of hot to cold inlet temperatures, the efficiency and effectiveness for particular heat exchange configurations are related. This efficiency is compared to second-law efficiencies proposed by other authors, and is shown to be superior in its ability to predict the effect of heat exchanger parameter changes upon the efficiency of energy use. The concept is applied to typical heat exchange cases to demonstrate its usefulness and sensitivity.