Review on thermal energy storage with phase change: materials ...

B. Zalba et al. / Applied Thermal Engineering 23 (2003) 251–283 265boundary, so that the position of the boundary is not known a priori and forms part of thesolution.A review on analytical/numerical and experimental work in the area of phase change, specificallyfreezing and melting processes was carried out by Eckert et al. in 1994 [67]. They divided thereview in melting and freezing of spheres, cylinders and slabs; Stefan problems; ice formation inporous materials; contact melting; and solidification during casting.When the substance that solidifies is pure, the solidification occurs at a single temperature,while in the opposite case (with mixtures, alloys and impure materials) the solidification takesplace over a range of temperatures, and therefore there appears a two-phase zone (a ‘‘mushyregion’’) between the solid and liquid zones. In this latter case, it is appropriate to consider theenergy equation in terms of enthalpy which, if the advective movements in the inner of the liquidare disregarded, is expressed mathematically as:q ohot ¼ ~rðk ~rT ÞThe solution of this equation obviously requires knowledge of the enthalpy–temperature functionaldependency, which for an impure substance is as shown in Fig. 3. Similarly, it is necessaryto know the function relating the thermal conductivity and the temperature.The main advantages of this procedure are:• The equation is directly applicable to the three phases.• The temperature is determined at each point and the value of the thermophysical properties canbe evaluated.• Finally, according to the temperature field, it is possible to ascertain the position of the twoboundaries if so desired, although as indicated above this is not necessary.Fig. 3. Enthalpy variation with temperature.