Self-freezing in an initially wet porous medium

Freeze-drying has received renewed interest in connection with biotechnology, food preservation and chemical industries. Freeze-drying under reduced pressure causes sublimation to occur. Simultaneous freezing of the moisture phase couples the two processes of freezing and sublimation and creates a self-driven process without need for any additional application of external energy other than that required to lower the surface temperature and pressure initially. A mathematical model consisting of coupled diffusion equations describing thermal and mass equilibrium in the solid-liquid and solid-vapour regions is solved analytically. The liquid-solid region is included with unknown freezing interfacial conditions. The effects of various parameters, such as conductivity ratio, latent heats, initial concentration, surface pressure and surface temperature, are examined with respect to the freezing and sublimation rates. The freezing rate is faster than the sublimation rate, though slower than the corresponding rate for constant freezing temperature. The freezing temperature is higher than the sublimation temperature for a constant composition ice pack.     

An analytical study of the effect of convection heat transfer on the sublimation of a frozen semi-infinite porous medium

Analytical solutions are developed for the effect of convection heat transfer on the temperature, moisture concentration, pressure and sublimation front location in a sublimating frozen semi-infinite moist porous medium. The mass transfer in the dried region is modeled by the application of Darcy's and Fick's laws coupled with an additional model for the pressure in this region. Results are presented which show the influence of convective heat transfer on the sublimation front position to be significant only for those combinations of boundary conditions, initial conditions and thermal-physical properties that yield high rates of sublimation for the no convection heat transfer case.     

Food freezing with simultaneous surface dehydration: approximate prediction of freezing time

Freezing of unpackaged foods induces mass transfer in the form of surface ice sublimation, which in turn modifies heat transfer conditions. At present there are no simplified methods for predicting freezing times when surface dehydration occurs. This paper uses a previously developed model for the simulation of simultaneous heat and mass transfer during food freezing and storage to generate a complete set of predicted freezing times when dehydration occurs. Based on these data a simplified analytical method for the prediction of freezing time during freezing of unpackaged frozen foods was developed. The method accounts for product characteristics (shape, size and composition) and operating conditions (initial and refrigerant temperature, heat transfer coefficient, relative humidity). The prediction equation is very simple and results of its use—simulating usual freezing conditions for different products—shows very good accuracy when tested against the previously cited numerical model and all the available experimental data.     

Food freezing with simultaneous surface dehydration: approximate prediction of weight loss during freezing and storage

Weight loss of unpackaged foods during freezing and later storage is an important quality and economic issue. It is originated on surface ice sublimation due to differences in water activity between food surface and the refrigerating air. Weight loss rate is determined by refrigerating conditions and product characteristics. The modelling of this phenomenon has merited very little attention; at present there are no simplified methods to predict weight losses during the freezing and the storage of unpackaged foods. In previous studies we developed a detailed model for the simultaneous heat and mass transfer during food freezing and storage with ice sublimation. Based on the information of this numerical model, simplified analytical methods for the prediction of weight loss during the freezing and the storage of unpackaged frozen foods were developed. The methods account for product characteristics and storage conditions. The prediction equations are very simple and results of their use—simulating usual freezing and storage conditions for different products—give very good accuracy when tested against the previously cited numerical model and experimental data.     

Numerical models for the simulation of the simultaneous heat and mass transfer during food freezing and storage

A numerical model was developed for the prediction of simultaneous heat and mass transfer during food freezing and storage. The resultant system of coupled partial differential equations, with time-varying coefficients was solved by two explicit finite-differences methods, one with constant mesh size and the other with equal volume elements. The prediction method was applied to the calculation of profiles of temperature and water content, and to the calculation of freezing times and weight losses under industrial freezing conditions, for spherical products such as meat balls and others.     

Simulation experiments on the effect of freezing of carbon substrate catalyst

By adiabatic expansion due to the introduction of an evacuation process, the water drop of about 2 mm diameter were cooled to 243 K by forming ice drops at the triple point of water. The sublimation temperature of ice rapidly decreased 243 K within 60 s and remained constant for 80 s. Subsequently, it became room temperature in about 60 s and the water drop disappeared owing to sublimation. By repeating this process, carbon and catalyst were markedly altered. Transmission electron microscopy (TEM) based on in situ observation elucidated the freezing problem in polymer electrolyte fuel cell (PEFC). Structural alterations of carbon due to freezing were observed and discussed as the oxidation phenomenon of carbon.     

Numerical investigations and engineering applications on freezing expansion of soil restrained two-phase closed thermosyphons

A numerical simulation has been carried out to describe the coupled heat transfer of water-saturated soil with a two-phase closed thermosyphon. This problem is characterized by the phase change occurring in the water-saturated soil, moving freezing front and heat transfer of a two-phase closed thermosyphon. According to the governing equations in the porous media and heat transfer characteristics of the two-phase closed thermosyphon, the temperature distributions in the water-saturated soil and the moving freezing front are solved numerically by the finite-difference method. The predictions of the present study are well agreed with the measured data. The mechanism of the freezing expansion restrained by the two-phase closed thermosyphon is exposed, based on which the effective radius can be determined for engineering applications.     

An analytical method to calculate the coupled heat and moisture transfer in building materials

A dynamic model for evaluating the transient thermal and moisture transfer behavior in porous building materials was presented. Both heat and moisture transfer were simultaneously considered and their interactions were modeled. An analytical method has been proposed to calculate the coupled heat and moisture transfer process in building materials. The coupled system was first subjected to Laplace transformation, and then the equations were solved by introducing the Transfer Function Method. The transient temperature and moisture content distribution across the material can thus be easily obtained form the solutions. The results were compared with the experimental data and other analytical solutions available in the literature; a good agreement was obtained.     

Thermophysical properties of heat-of-fusion storage materials for cooling applications

The present work includes the investigation of the thermophysical properties of latent storage materials (melting temperature range 0–20°C) to be used in cooling and air conditioning applications. These are hexadecane, decanol and caprilic acid. Measurements with a differential scanning calorimeter (DSC) to obtain the melting and freezing point, the degree of supercooling, the latent heat of fusion, and the specific heat in solid and liquid phases of the materials were performed and the possibility of their use in heat storage systems was discussed.     

Freezing of Water in a Slab with Boundary Conditions of the Third Kind

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Numerical simulation of conjugate heat and mass transfer during multi-dimensional freeze drying of slab-shaped food products

The freeze drying characteristics of planar and slab-shaped food products were numerically studied using a simulation program that considered the conjugate heat and mass transfer, sublimation of ice, and motion of sublimation interface. The fixed grid method, which was adopted in the numerical simulation, was able to handle the complex sublimation interface during the multi-dimensional freeze drying of slab-shaped products appropriately. The results showed that the lateral permeable surface of the slab-shaped products significantly altered the freeze drying characteristics by reducing the diffusion length for the water vapor transport as well as by increasing the interfacial area for sublimation. These two effects were found to cooperatively enhance the freeze drying rate while decreasing the average sublimation temperature.     

Experimental Studies on Heat Transfer in the Tip Gap of a Sectorial Turbine Cascade

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Study of the ice sublimation processEtude du processus de sublimation de la glaceUntersuchung des EissublimationsprozessesИccлeдoвaниe пpoцecca cyблимaции льдa

The basic transfer equations for evaporation of a solid body into vacuum are considered. Experimental results on ice sublimation with thermoradiative and conductive heat supply as well as on sublimation in drying processes and continuous sublimation process from a permeable plate are presented. These studies explain the peculiarities of the sublimation mechanism for different energy supplies and under periodic and continuous conditions of the process. With ice sublimation from a porous permeable plate near a surface, a stepwise change in temperature is observed at a distance of several lengths of the mean free path of vapour molecules.     

DESUBLIMATION: A MOVING BOUNDARY PROBLEM AND NUMERICAL SOLUTION

A numerical model for the recovery of sublimation products is presented. The necessary differential equations describing the process are solved. The effects of velocity and composition of the gas mixture, physical properties of the materials involved, flow rate and properties of the cooling liquid, and geometry of the system are considered. The controlling mechanisms of heat and mass transfer are discussed.     

Experimental study of the heat transfer enhancement of an outer tube with an inner-tube insertion

This experimental study aims to investigate the heat transfer phenomena of an outer tube with an inner-tube insertion. The naphthalene sublimation method is adopted which measures the sublimation depth of naphthalene necessary to reduce the local heat transfer through the analogue relation between heat and mass transfer. The working fluid is air and the data runs are performed for Reynolds numbers of 1058, 1360 and 1965. The comparison between experimental and numerical results shows good agreement. It is also found that, with an inner-tube insertion, the heat transfer rate of the outer tube increases as the Reynolds number of the tube flow and the size of inner tube increase, as long as the inner tube is not larger than a given size.     

采集凝固热热泵技术凝固及换热性能的理论分析

介绍了一种新型的采集凝固热热泵技术,建立了凝固热采集装置中层流流动水在常壁温条件下的管内凝固问题的数学模型。采用准稳态近似方法进行了凝固特性的分析,使用当量平均表面换热系数和潜热显热比两个参数讨论了冰层对换热性能的影响。计算结果与所得结论对凝固热采集装置的设计和热泵系统性能的改善有一定指导作用。     

A numerical analysis of buoyancy-driven melting and freezing

A numerical investigation of transient natural convective heat transfer with coupled phase change is presented. The numerical model attempts to capture the solid-fluid interface using a fixed-grid solution and is applied to two pure substance cases found in published literature, one considering the melting of 95% pure Lauric acid and the other involving the freezing of water. The governing equations are solved in a manner such that if the temperature falls below the freezing isotherm then the convection terms in the equations of motion are effectively disengaged. Variations in the specific heat of the material are incorporated in order to account for the phase change. A non-Boussinesq approach is considered which accounts for any density extrema in the flow, particularly for the density inversion found in water. In both of the cases considered the phase change occurs between fixed temperature boundaries and Rayleigh numbers rest well within the laminar flow regime. From the results obtained it is demonstrated that a relatively simple numerical technique can be applied to capture the physics of buoyancy-driven melting and freezing and that the results are in reasonable concurrence with experimental data.     

Numerical Modeling of the Freezing of a Porous Humid Food inside a Cavity due to Natural Convection

The conjugate heat transfer problem of food freezing inside a cavity was numerically investigated. A vegetable sponge has been considered as a food block freezing inside a square freezing chamber due to natural convection. The need for specifying the block surface convective heat transfer coefficients was eliminated by solving the surrounding cooling fluid and, therefore, a comprehensive understanding on heat transfer and airflow during freezing can be achieved. The 2-D unsteady Navier-Stokes and energy equations were solved using a finite volume method with the semi-implicit SIMPLE algorithm. Thermophysical properties of food block components were considered to be dependent on temperature, as well as moisture and ice content, which has been rarely considered in food freezing studies. The specific heat capacity method was employed to model the freezing process. The Krischer model was adopted for predicting the thermal conductivity of the food, which indicates that the model works with reasonable accuracy for humid porous foods. The mechanism of natural convection in the cavity was carefully studied and the effects of different parameters on the freezing time were examined. The food freezing curves were investigated for various Rayleigh numbers in the range of 10⁴ ≤ Ra ≤ 10⁶, with different area ratios of A = 1/16, 1/9, and 1/4, and food initial water contents of X _tw  = 0.48, 0.58, and 0.68. It was concluded that increasing the Rayleigh number reduces the freezing time. On the other hand, area ratio and initial water content of the food were proved to extend the freezing time.     

组合相变材料储热系统的储热速率研究

建立了组合式柱内封装相变材料熔化－固化循环相变储热系统的物理模型,用有限差分法进行了数值模拟求解。结果表明,与采用单一相变材料的传统储热系统相比,在给定相变材料组合方式和传热流体进口温度条件下,传热流体流量存在最佳值;选用三种石蜡作用相变材料和水作传热流体的模拟计算结果表明,相变速率可提高１５％￣２５％左右。     

Low temperature latent heat thermal energy storage: Heat storage materials

Heat-of-fusion storage materials for low temperature latent heat storage in the temperature range 0–120°C are reviewed. Organic and inorganic heat storage materials classified as paraffins, fatty acids, inorganic salt hydrates and eutectic compounds are considered. The melting and freezing behaviour of the various substances is investigated using the techniques of Thermal Analysis and Differential Scanning Calorimetry. The importance of thermal cycling tests for establishing the long-term stability of the storage materials is discussed. Finally, some data pertaining to the corrosion compatibility of heat-of-fusion substances with conventional materials of construction is presented.