Review on thermal energy storage with phase change: materials ...
Review on thermal energy storage with phase change: materials ... Review on thermal energy storage with phase change: materials ...
264 B. Zalba et al. / Applied Thermal Engineering 23 (2003) 251–283Table 8Comparison of organic and inorganic materials for heat storageOrganicsInorganicsAdvantagesAdvantagesNo corrosivesGreater phase change enthalpyLow or none undercoolingChemical and thermal stabilityDisadvantagesLower phase change enthalpyLow thermal conductivityInflammabilityDisadvantagesUndercoolingCorrosionPhase separationPhase segregation, lack of thermal stabilityTable 9Important characteristics of energy storage materialsThermal properties Physical properties Chemical properties Economic propertiesPhase change temperature fittedto applicationLow density variation Stability Cheap and abundantHigh change of enthalpy neartemperature of useHigh thermal conductivity inboth liquid and solid phases(although not always)High densitySmall or no undercoolingNo phase separationCompatibility with containermaterialsNon-toxic, non-flammable,non-polluting3. Heat transfer3.1. Theory and simulationAs regards the thermal gradient, information about the analysis of irreversibilities and theapplication of the second principle of thermodynamics can be found in articles by Strub [65] andBejan [97], and a whole review in Chapter 9 of Dincer and Rosen [4]. Studies of these latterauthors show that the use of exergy is very important in developing a good understanding of thethermodynamic behaviour of TES systems, and for rationally assessing, comparing and improvingtheir efficiencies. In particular, the use of exergy analysis is important because it clearlytakes into account the loss of availability and temperature of heat in storage operations, andhence it more correctly reflects the thermodynamic and economic value of the storage operation.3.1.1. Moving boundary problemsThe analysis of heat transfer problems in melting and solidification processes, called movingboundary problems in scientific literature, is especially complicated due to the fact that the solid–liquid boundary moves depending on the speed at which the latent heat is absorbed or lost at the
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.
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264 B. Zalba et al. / Applied Thermal Engineering 23 (2003) 251–283Table 8Comparis<strong>on</strong> of organic and inorganic <strong>materials</strong> for heat <strong>storage</strong>OrganicsInorganicsAdvantagesAdvantagesNo corrosivesGreater <strong>phase</strong> <strong>change</strong> enthalpyLow or n<strong>on</strong>e undercoolingChemical and <strong>thermal</strong> stabilityDisadvantagesLower <strong>phase</strong> <strong>change</strong> enthalpyLow <strong>thermal</strong> c<strong>on</strong>ductivityInflammabilityDisadvantagesUndercoolingCorrosi<strong>on</strong>Phase separati<strong>on</strong>Phase segregati<strong>on</strong>, lack of <strong>thermal</strong> stabilityTable 9Important characteristics of <strong>energy</strong> <strong>storage</strong> <strong>materials</strong>Thermal properties Physical properties Chemical properties Ec<strong>on</strong>omic propertiesPhase <strong>change</strong> temperature fittedto applicati<strong>on</strong>Low density variati<strong>on</strong> Stability Cheap and abundantHigh <strong>change</strong> of enthalpy neartemperature of useHigh <strong>thermal</strong> c<strong>on</strong>ductivity inboth liquid and solid <strong>phase</strong>s(although not always)High densitySmall or no undercoolingNo <strong>phase</strong> separati<strong>on</strong>Compatibility <strong>with</strong> c<strong>on</strong>tainer<strong>materials</strong>N<strong>on</strong>-toxic, n<strong>on</strong>-flammable,n<strong>on</strong>-polluting3. Heat transfer3.1. Theory and simulati<strong>on</strong>As regards the <strong>thermal</strong> gradient, informati<strong>on</strong> about the analysis of irreversibilities and theapplicati<strong>on</strong> of the sec<strong>on</strong>d principle of thermodynamics can be found in articles by Strub [65] andBejan [97], and a whole review in Chapter 9 of Dincer and Rosen [4]. Studies of these latterauthors show that the use of exergy is very important in developing a good understanding of thethermodynamic behaviour of TES systems, and for rati<strong>on</strong>ally assessing, comparing and improvingtheir efficiencies. In particular, the use of exergy analysis is important because it clearlytakes into account the loss of availability and temperature of heat in <strong>storage</strong> operati<strong>on</strong>s, andhence it more correctly reflects the thermodynamic and ec<strong>on</strong>omic value of the <strong>storage</strong> operati<strong>on</strong>.3.1.1. Moving boundary problemsThe analysis of heat transfer problems in melting and solidificati<strong>on</strong> processes, called movingboundary problems in scientific literature, is especially complicated due to the fact that the solid–liquid boundary moves depending <strong>on</strong> the speed at which the latent heat is absorbed or lost at the
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