Simulation and experiment of the unsteady heat transport in the onset time of nucleation and crystallization of ice from the subcooled solution FrankG.F.Qin a, * ,JianChaoZhao a ,AndrewB.Russell a,1 ,XiaoDongChen a , John J. Chen a , Lindsay Robertson b a Department of Chemical and Materials Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand b Fonterra Research Centre, Palmerston North, New Zealand Received 30 August 2002; received in revised form 31 January 2003 Abstract Heattransferisanunsteadyprocessintheinitialperiodoficenucleationorphasetransitionfromaqueoussolution. Duringthisperiodthelatentheatoffreezingincreasesthetemperatureinbulksolutionmonotonouslyuntilthesystem reaches equilibrium. Meanwhile heat can transfer from the solution to the environment or vise versa. The analysis of this unsteady heat transfer process leads to the establishment of a mathematical model, which is represented by two simultaneous differential equations. Using the Laplace transform and inverse transform, and incorporating the initial condition of ice nucleation, we obtained an analytical solution of this model. Further discussion of the modelÕs fitness bycomparingtotheexperimentaldataleadstoarecognitionthaticefouling(oriceadhesion)onthecoolerwallshould behighlightedinestimatingtheheattransferresistanceattheverybeginningoftheiceformation.Themodelfitstothe experimental data satisfactorily. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Unsteady heat transfer; Nucleation; Ice formation; Freeze concentration; Laplace transform 1. Introduction Phenomena of the onset of ice nucleation and crys- tallization from the subcooled solution have been stud- ied by many researchers. One of the basic motives, in early years, was the requirement of freeze concentration (or freeze desalination), in which the solution was con- centrated as the result of ice crystallization (and the ice itself was desalinated). A general problem is the ten- dency of forming very fine ice crystals so that the sep- aration of the final concentrate from the ice slurry becomes difficult. Incomplete separation of ice and liq- uid leads to the loss of valuable solute. The phenomena of ice formation and nucleation aroused new interest in recent years because of the consideration of using ice–aqueous-solutions as heat (or cold) storage system. For this purpose, Intemann and Kazmierczak did experimental researches on the heat transfer and ice formations deposited upon subcooled tube banks immersed in flowing water [1,2]. In their paper, the increasing heat transfer resistance of the ice scales was recognized and emphasized during the phase change process. To prevent the ice adhesion on the cooling surface, Tsuchida et al. used stainless steel with PFA (tetra-fluro-ethylene-perfluoro-alkylvinyl-ether-co- polymer) resin coating and PTFE (poly-tera-fluoro- ethylene) as the cooling surface, and employed an emulsion, which was a mixture of silanol–aqueous so- lution and silicone oil, as the heat storage material [3]. * Corresponding author. E-mail address: fqin001@ec.auckland.ac.nz (F.G.F. Qin). 1 Current address: Unilever R&D Coluworth, Sharnbrook Bedford, UK. 0017-9310/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0017-9310(03)00097-8 International Journal of Heat and Mass Transfer 46 (2003) 3221–3231 www.elsevier.com/locate/ijhmt