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Thermal Property Prediction and Measurement of Organic Phase Change Materials in the Liquid Phase Near the Melting Point Q ⇑ William E

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Thermal Property Prediction and Measurement of Organic Phase Change Materials in the Liquid Phase Near the Melting Point Q ⇑ William E Applied Energy 132 (2014) 496–506 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Thermal property prediction and measurement of organic phase change materials in the liquid phase near the melting point q ⇑ William E. O’Connor, Ronald Warzoha, Rebecca Weigand, Amy S. Fleischer, Aaron P. Wemhoff Department of Mechanical Engineering, Villanova University, 800 Lancaster Ave., Villanova, PA 19085, USA highlights Liquid-phase thermal properties for five phase change materials were estimated. Various liquid phase and phase transition thermal properties were measured. The thermal diffusivity was found using a best path to prediction approach. The thermal diffusivity predictive method shows 15% agreement for organic PCMs. article info abstract Article history: Organic phase change materials (PCMs) are a popular choice for many thermal energy storage applica- Received 20 February 2014 tions including solar energy, building envelope thermal barriers, and passive cooling of portable electron- Received in revised form 18 June 2014 ics. Since the extent of phase change during a heating or cooling process is dependent upon rapid thermal Accepted 11 July 2014 penetration into the PCM, accurate knowledge of the thermal diffusivity of the PCM in both solid and liquid phases is crucial. This study addresses the existing gaps in information for liquid-phase PCM properties by examining an approach that determines the best path to prediction (BPP) for the thermal Keywords: diffusivity of both alkanes and unsaturated acids. Knowledge of the BPP will enable researchers to explore Phase change material the influence of PCM molecular structure on bulk thermophysical properties, thereby allowing the Statistical thermodynamics Thermophysical properties fabrication of optimized PCMs. Differential scanning calorimetry The BPP method determines which of the tens of thousands of combinations of 22 different available Transient plane source theoretical techniques provides best agreement with thermal diffusivity values based on reported or Thermal diffusivity measured density, heat capacity, and thermal conductivity for each of five PCMs (heneicosane, tricosane, tetracosane, oleic acid, and linoleic acid) in the liquid phase near the melting point. Separate BPPs were calibrated for alkanes based on heneicosane and tetracosane, and for the unsaturated acids. The alkane and unsaturated acid BPPs were then tested on a variety of similar materials, showing agreement with reported/measured thermal diffusivity within 15% for all materials. The alkane BPP was then applied to find that increasing the length of alkane chains decreases the PCM thermal diffusivity, showing how the determination of the BPP can be used to aid in the prediction of how the molecular structure of organic PCMs influences PCM performance in energy storage applications. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction electronics [17–19]. Since the extent of phase change during a heating or cooling process is dependent upon the amount of ther- Organic phase change materials (PCMs) have been proposed as mal penetration into the PCM, the thermal diffusivity of the PCM is a viable energy storage mechanism through solid–liquid phase an important thermophysical property for the viability of the change at the melting point temperature. This energy storage could material in an energy storage application. have significant applications in solar energy [1–7], building The thermal diffusivity, ath, is defined as envelope thermal barriers [8–16], and passive cooling of portable k ath ¼ ð1Þ qcp q Submitted for consideration for publication in Applied Energy. ⇑ Corresponding author. Fax: +1 610 519 7312. where k is thermal conductivity, q is mass density, and cP is the E-mail address: [email protected] (A.P. Wemhoff). mass-based heat capacity. Data regarding some of the solid and http://dx.doi.org/10.1016/j.apenergy.2014.07.045 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved. W.E. O’Connor et al. / Applied Energy 132 (2014) 496–506 497 Nomenclature ai, di group contribution parameters, dimensionless tck critical temperature group contribution parameter, aP Peng–Robinson fluid model intermolecular potential dimensionless parameter, J m3 tfp1k first-order melting temperature group contribution aR Redlich–Kwong fluid model intermolecular potential parameter, dimensionless parameter, J m3 K0.5 tfp2j second-order melting temperature group contribution aS Soave–Redlich–Kwong fluid model intermolecular parameter, dimensionless potential parameter, J m3 P pressure, Pa aV Van der Waals fluid model intermolecular potential Pc critical pressure, Pa 3 parameter, J m Po atmospheric pressure, Pa bP Peng–Robinson fluid model equivalent molecular Pr reduced pressure, dimensionless 3 volume, m Prb reduced boiling point pressure, dimensionless bR Redlich–Kwong fluid model equivalent molecular Q canonical partition function, dimensionless volume, m3 R ideal gas constant, J/(kmol K) bS Soave–Redlich–Kwong fluid model equivalent molecu- T temperature, K 3 lar volume, m Tb boiling point temperature, K bV Van der Waals fluid model equivalent molecular Tc critical temperature, K 3 volume, m Tm melting point temperature, K cp mass-based heat capacity, J/(kg K) Trb reduced boiling point temperature, dimensionless Cpl molar heat capacity, J/(mol K) U system internal energy, J 3 cp,st mass-based heat capacity of sapphire sample, J/(kg K) Vs saturated liquid molar volume, cm /mol Ds difference in heat flow between empty reference pan W weight for second-order groups (= 0 for 1st order, = 1 for and sample of interest, mW 2nd order), dimensionless Dst difference in heat flow between empty reference pan Ws weight of sample of interest, mg and sapphire sample, mW Wst weight of sapphire sample, mg E reference calorimetric sensitivity, dimensionless Z critical compressibility factor, dimensionless 2 f,a fluid model-dependent parameters, dimensionless ath thermal diffusivity, m /s g temperature ramp rate, °C/min DHf latent heat of fusion, J/kg H system enthalpy, J DHm total enthalpy of melting, J/mol h Planck’s constant, J s DSm total entropy of melting, J/(mol K) kB Boltzmann’s constant, J/K e molecular eccentricity, dimensionless M molecular mass, kg/kmol hrot,m rotational temperature, K mi melting enthalpy group contribution parameter, dimen- k thermal conductivity, W/(m K) à sionless kf reduced thermal conductivity correction term, dimen- Mj occurrence of group j in a molecule, dimensionless sionless à N number of molecules in a system, dimensionless km reduced thermal conductivity of a monatomic liquid, Natoms number of atoms, dimensionless dimensionless À1 NA Avogadro’s number, kmol n number of molecular degrees of freedom, dimensionless 3 ni occurrence of group i in a molecule, dimensionless q mass density, kg/m Nk occurrence of group k in a molecule, dimensionless r molecular symmetry, dimensionless pck critical pressure group contribution parameter, dimen- s molecular flexibility, dimensionless sionless x acentric factor, dimensionless liquid phase properties of organic PCMs on the right-hand side of equivalent in numerical investigations [10,12,22]. Therefore, this Eq. (1) are readily available [20,21], but gaps exist in available data. study aims at determining accurate predictive techniques of liquid Furthermore, the gaps in liquid-phase properties cannot be filled by phase thermophysical properties for two principal classes of equivalent solid phase properties since the shifted molecular organic PCMs: alkanes and unsaturated (fatty) acids. arrangement between solid and liquid phases could have a dramatic This study is intended to supplement the large body of work on influence on the thermophysical properties in the following ways PCM enhancement using nanoscale inclusions. Several studies through a loss of a molecular lattice structure: [23–27] investigated the impact of adding highly-conducting The lattice configuration contains a strong influence on the scat- nanoscale inclusions into a base organic PCM. In general, research- tering mechanisms in phonon behavior in thermal conduction. ers have found that these composites contain significant conduc- Losing the lattice structure adjusts the available effective tivity enhancement (in general >100% enhancement for >1 wt% degrees of freedom of the molecules, thereby altering the spe- filler) but with a sacrifice in the latent enthalpy of fusion (7– cific heat. 15% reduction for typical loading values). Fan et al. [26] compared A loss in lattice structure affects the molecular packing arrange- different fillers and found that graphene nanoplatelets and short ment, influencing the material density. cylindrical inclusions (e.g., carbon nanotubes) provide better con- ductivity enhancement than long inclusions. The limiting factor Furthermore, a PCM ideally exists in its liquid phase during one in PCM nano-composite performance is the combination of ther- half of a heating/cooling cycle, and therefore an accurate model of mal properties associated with the base PCM, and therefore the thermal response of the PCM should apply the liquid phase improving the thermal properties of the base PCM – the focus of thermal properties, especially during a freezing process. However, this effort – will lead to more effective PCM nano-composites. many investigators have either ignored thermal gradients within A number of theoretical techniques exist to determine various the PCM [9] or assumed that the solid and liquid properties are properties
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