Coupled Heat and Mass Transfer during Crystallization of MgSO4 ...

Crystallization of MgSO 4 · 7H 2 O on a Cooled Surface Crystal Growth & Design, Vol. xxx, No. xx, XXXX ITable 3. List of Captionslist of symbolsunita activityC concentration mol m -3Cp specific heat kJ kg -1 K -1D AB diffusion coefficient m 2 s -1∆H cryst. heat of crystallization J mol -1h convection heat transfer coefficient W m -2 K -1J mass flux mol m -2 s -1J′ q heat flux J m -2 s -1kenthalpy fraction transferred to thecoolant sideN A ′ convective mass flux mol s -1 m -2R ideal gas constant J K -1 mol -1i,sR qq heat transfer resistivity of the surface m 2 s 1 J -1 K -1to the salt sidei,sR µµ mass transfer resistivity of the surface JK -1 mol -2 m -2 s -1to the salt sideR i,sqµ ) R qµ coupling film resistivities of the m 2 s 1 mol -1 K -1surface to the salt sidei,sR qq heat transfer resistivity of the surface m 2 s 1 J -1 K -1to the liquid sidei,sR µµ mass transfer resistivity of the surface JK -1 mol -2 m -2 s -1to the liquid sideR i,sqµ ) R qµ coupling film resistivities of the m 2 s 1 mol -1 K -1surface to the liquid sideq′′ convective heat flux W m -2q* i,s heat of transfer coefficient ratio to the J mol -1salt side of the surfaceq* i,l heat of transfer coefficient ratio to the J mol -1liquid side of the surfaceT temperature °Cz distance from the salt surface mGreek symbolsUnitδ thickness µm, mmλ thermal conductivity W m -1 K -1µ chemical potential J K -1V measured velocity, salt growth rate m s -1F density at the given condition kmol m -3σ entropy production W m -2 K -1cilsTLCsub-superscriptscoolantinterfaceliquidsaltthermo liquid crystalReferences(1) Kjelstrup, S.; Bedeaux, D. Non-equilibrium thermodynamic of heterogeneoussystems; Series on Advances in Statistical Mechanics, Vol.16; World Scientific: Singapore, 2008.(2) Bedeaux, D.; Albano, A. M.; Mazur, P. Physica A 1976, 82, 438–462.(3) Bedeaux, D. AdV. Chem. Phys. 1986, 64, 47–109.(4) Albano, A. M.; Bedeaux, D. Physica A 1987, 147, 407–435.(5) Ratje, S. K.; Flesland, O. J. Food Eng. 1995, 25, 553–567.(6) Chen, X. C.; Chen, P.; Free, K. W. J. Food Eng. 1997, 31, 395–402.(7) Badam, V. K.; Kumar, V.; Durst, F.; Danov, K. Experimental andtheoretical investigations on interfacial temperature jumps duringevaporation. Exp. Therm. Fluid Sci., 2007, 32(1), 276–292.(8) Kjelstrup Ratkje, S.; Bedeaux, D. J. Electrochem. Soc. 1996, 143 (3),779–789.(9) Gibbs, J. W. The Scientific Papers of J.W. Gibbs; Dover: New York,1961.(10) Bedeaux, D.; Kjelstrup, S. Int. J. Thermodyn. 2005, 8 (1), 25–41.(11) Pronk, P. Fluidized bed heat exchangers to prevent fouling in ice slurrysystems and industrial crystallizers. PhD Dissertation, Delft Universityof Technology, The Netherlands, 2006.(12) Mersmann, A. Crystallization Technology Handbook, 2nd ed.; MarcelDekker Inc.: New York, 2001.(13) Xu, J.; Kjelstrup, S.; Bedeaux, D.; Røsjorde, A.; Rekvig, L. J. ColloidInterface Sci. 2006, 299, 455–463.(14) Delfos, R.; Lagerwaard, R.; Roos, M. Bottom temperature structurein low-conductivity Rayleigh-Benard convection, EUROTHERM-71 Visualization, Imaging and Data Analysis in ConVectiVe Heat andMass Transfer, October 28-30, 2002, Reims, France.(15) Pillay, V.; Gaertner, R. S.; Himawan, C.; Seckler, M. M.; Lewis,A. E.; Witkamp, G. J. J. Chem. Eng. Data 2005, 50 (2), 551–555.(16) Incropera, F. P.; De Witt, D. P. Fundamentals of Heat and MassTransfer, 3rd ed.; John Wiley & Sons: New York, 1990.(17) Gmelins Handbuch der Anorganschen Chemie, 8th ed.; DeutscheChemische Gesellschaft, Verlag Chemie: Weinheim, 1952.(18) Lobo, V. M. M. Handbook of Electrolyte Solutions.; Elsevier:Amsterdam, 1989.(19) Melinder, Å. Thermophysical Properties of Liquid Secondary Refrigerants.Charts and Tables.; International Institute of Refrigeration: Paris,1997.(20) Thermtest. Thermal conductiVity database of materials; http://www.thermtest.com, 2007.CG800377X