Frost Thermal Conductivity Research Articles

Modelling of chemical processes using artificial neural network

ABSTRACT In this paper, a methodical strategy is put forth for the development of models for chemical processes by using an Artificial Neural Network (ANN). To show the effectiveness of the proposed methodology, three industrial chemical processes were considered. The intended work is to introduce the guideline for designing any ANN model by identifying the optimum number of neurons and hidden layers and coming up with the most suitable architecture for the neural network. The effect of viable parameters on predicting the specified parameter was evaluated using an ANN model. A systematic procedure adopted, ANN networks were designed to predict the boiler efficiency, frost thermal conductivity, and gas holdup under different operating conditions. At last, a comparative study on the experimental output and ANN approximated output for the three chemical processes was done. For developing the ANN model for boiler and frost conductivity, it was found that employing two layers provided a superior fit. The R² values for these fits were found to be 0.98877 and 0.9891, respectively. On the other hand, when configuring the column flotation model, a single layer with nine nodes was identified as the optimal ANN structure, yielding an excellent R² fit value of 0.99337.

An Eulerian multiphase frost model based on heat transfer measurements

In this paper, a laminar numerical model is developed to predict frost formation over a horizontal cold flat surface. An Eulerian-Eulerian multiphase approach is followed to model humid air and ice phases separately. Frost accumulation on the cold surface is modeled with an empirical mass source term. Model constants were tuned in a systematic way using experimental heat flux and frost thickness data. A velocity dependent model constant is introduced into the mass source term. The heat flux rise observed experimentally at the initial stages of the frosting could be captured with the use of the velocity dependent model constant and the addition of this term considerably improved the accuracy of the frost model at the initial stages of frosting. It was also observed that the selected particle diameter for the solid ice phase has a considerable effect on the velocity profile over the frost layer. This requires tuning of the velocity dependent model constant parameters according to the selected ice particle diameter. The developed numerical model was tested with three different frost thermal conductivity models. Using the thermal conductivity of solid ice for the frost thermal conductivity resulted in the most accurate prediction at the early stages of the frost growth process indicating a rather column-wise vertical growth of ice crystals with very low lateral branching. However, the overprediction of the numerical heat flux with the thermal conductivity of solid ice points out a decrease in the thermal conductivity of the newly added frost layers indicating a more pronounced lateral branching of ice crystals within the frost layer. The effect of the diffusion coefficient of the water vapor in humid air on frosting is also investigated. An artificial increase in the diffusion coefficient improved the accuracy of the heat flux prediction of the model at the initial stages of frosting which might indicate an eddy-driven enhanced mixing in the boundary layer which might not be captured in the laminar flow model. Finally, the developed numerical model is also tested on another scenario with the surface temperature held at -30 °C. Detailed analysis of the numerical simulations showed a more porous frost layer with the surface temperature at -30 °C as compared to the frost porosity formed on the surface at -20 °C.

Experimental investigation on thermal conductivity of cryogenic frost under forced convection

An experimental study on the phase change occurring on a cryogenic cooling surface was conducted under forced convection conditions. The mass and surface temperature of frost and the heat flux at the cooling surface were measured in the experiment. The heat and mass transfer analogy was investigated under cryogenic conditions. The mass estimated under various experimental conditions using the modified analogy differed by up to 8% from the experimentally measured mass. The density and thermal conductivity of frost at cryogenic temperatures were lower than those of general-low temperature frost; the dimensionless correlations of density and thermal conductivity of frost were derived via regression analysis. The calculated frost density and thermal conductivities were differed from the measured value by up to 9% and 11%, respectively. Therefore, a model was built to predict the heat and mass transfer and improve the thermal performance on the cooling surfaces of various cryogenic devices using the presented frost density and thermal conductivity correlations.

Frost formation from general-low to ultra-low temperatures: A review

• Frosting mechanisms from general-low to ultra-low temperatures were investigated. • Frost morphology and properties were identified in terms of frosting factors. • Unique phenomena occurring at ultra-low temperatures were discussed. The frosting at ultra-low temperatures can cause significant degradation of the thermal performance of heat exchangers, which also leads to a decrease in the energy efficiency of air-source heat pumps. In this paper, the temperature terminologies for frosting were classified, and the frosting mechanism and frost properties were investigated from general-low to ultra-low temperatures. The dominant phase change mechanisms at general-low and ultra-low temperatures were condensation-freezing and desublimation, respectively. The frost layer growth mechanism at ultra-low temperatures can be classified into the formation of ice nuclei, growth of ice particles, and deposition of a frost layer in the initial stage of frosting. The frost morphology at ultra-low temperatures showed wisteria or shrub-shaped frost, which was not observed at general-low temperatures. Frost properties are determined depending on frosting factors such as cooling surface temperature, air temperature, absolute humidity, and air velocity, while the thermal conductivity of frost was determined by frost porosity. At ultra-low temperatures, some unusual phenomena were observed that were not observed at general-low temperatures. When the cooling surface temperature was at ultra-low temperatures, the fog was formed near the cooling surface along with the frost, and this fog was dominantly influenced by the frost surface temperature. In addition, unique phenomena such as thread-shaped frost and leading-edge frost concentrations were observed at ultra-low temperatures, and there was a clear difference in the frosting mechanism based on the temperature range.

Frosting mechanism and behaviors on surfaces with simple geometries: A state-of-the-art literature review

• Correlations of frosting characteristic parameters are summarized and analysed. • Effects of frosting conditions on average frost layer characteristics are reviewed. • Frosting distribution characteristic for different cold surfaces are reviewed. • Eight research gaps relating to frosting mechanism and behaviors are identified. Frosting causes negative impacts in many technical and engineering fields, such as refrigeration, air source heat pump, aircraft, wind power generation, and power grids. To alleviate the negative impacts of frosting, studies on frosting characteristics, avoiding and delaying frosting, and defrosting mechanisms and methods have been carried out for decades. Among these studies, frosting characteristics, which are the fundamental basis for defrosting, avoiding, and delaying frosting are consistently the hot research spots. Considering that complex structures can be usually regarded as the combination of simple geometries, in this paper, a comprehensive review of the literature related to the frosting mechanism and behaviors on surfaces with simple geometries is presented. The former covers frost formation process and morphology, frost layer structure model, and frosting characteristic parameters, such as frost thickness and effective frost thermal conductivity. The latter is further divided into six parts based on the configurations of cold surfaces, including flat plates with a fixed surface temperature, flat plates with a fixed base temperature, cylinders, parallel plates, set of fins and semipermeable membranes. Based on the review, the research gaps in the related study fields are identified, and recommendations for further research are offered. The literature review presented in this paper can provide a comprehensive and systematic reference for the people who are working in the study fields where frosting is commonly encountered.

An insight into the estimation of frost thermal conductivity on parallel surface channels using kernel based GPR strategy

In heat exchange applications, frost formation on the cold surface causes a decrease in the rate of heat transfer and growth in the pressure drop. Thus, the study on the frost thermal conductivity has a significant and vital place for the engineers and researchers dealing with the heat exchangers. In the literature, there is a lack of accurate and applicable methods for determination of frost thermal conductivity. Additionally, the high cost and difficulties of experimental works clarify the importance of computational and mathematical methods. The errors in the determination of frost thermal conductivity on parallel surface channels can cause inaccuracy in estimations of frost density and thickness. The main aim of present work is suggesting Gaussian Process Regression (GPR) models based on four different kernel functions for the estimation of frost thermal conductivity in terms of time, air velocity, relative humidity, air temperature, wall temperature, and frost porosity. To achieve this purpose, a total number of 57 frost thermal conductivity values has been collected. Comparing the suggested GPR models and other available computational methods express the quality of the developed models. The best predictive tool has been selected as a GPR model, including Matern kernel function with R2 values of 0.997 and 0.994 in training and testing phases, respectively. In addition, the effectiveness of discussing variables on frost thermal conductivity has been investigated by sensitivity analysis and showed that air temperature is the most effective parameter. The present work gives engineers an insight into frost thermal conductivity and the effective parameters in its determination.The significant advantage of present work is the accurate prediction of thermal conductivity by a brief knownledge in artificial intelligence.

General correlation for frost thermal conductivity on parallel surface channels

Growth of frost layer on cold fins of tube-fin heat exchangers leads to an increase in the pressure drop and a decrease in the frost thermal conductivity and thereby the heat transfer rate. There is a lack of a general model in the literature for estimating the frost thermal conductivity on parallel plate channels, including almost all parameters affecting this factor. In this study, for the first time, the general explicit semi-empirical correlations consist of dimensionless parameters are developed, which apply to parallel surface channels. The dimensionless input parameters include the wall temperature, air temperature, air velocity, frost porosity, relative humidity, specific heat of moist air, latent heat of sublimation, and operating time. The comparative results indicate that the best correlation predicts data points with an coefficient of determination, average absolute relative error, and relative root mean square error equal 0.9921, 2.755%, and 3.713%, respectively. Other available published correlations present higher deviations using the same dataset. Furthermore, to provide a good insight into this study, a sensitivity analysis is carried out employing the validated model. It is shown that the effective thermal conductivity of the frost layer is not only a function of frost density but also depends on a group of dimensionless parameters. It is observed that the thermal conductivity of the frost layer increases with the increase in the Reynolds number, Fourier number, air humidity, and it decreases with the increase in the dimensionless temperature, modified Jakob number, and porosity.

Modeling of frost thermal conductivity on parallel surface channels

Frost buildup on cold plates in heat exchange applications causes an increase in the pressure drop and a decrease in the heat transfer rate. There is a lack of practical and accurate models for evaluation of frost thermal conductivity in the literature. Inaccuracy in estimating the thermal conductivity of frost on parallel surface channels will increase the error in predictions of frost thickness and density. In the present study, a mathematical method known as Least Squares Support Vector Machine (LSSVM) is utilized in order to develop a robust model for predicting the thermal conductivity of frost formation on parallel surface channels. Six key factors affecting the thermal conductivity of frost, namely, frost porosity, wall temperature, air temperature, relative humidity, air velocity, and time duration, are considered as the inputs to the model. Genetic Algorithm (GA) is used to determine the optimized hyper parameters (γ and σ2) of the LSSVM model. The reliability of the GA-LSSVM model is evaluated by comparing the model results with those of existing empirical correlations. The obtained mean square error, root mean square error, and relative root mean square error for the GA-LSSVM model are found to be 1.10e−05, RMSE = 3.3e−03, and RRMSE = 2.42%, respectively. The results show that the GA-LSSVM is a practical and easy-to-use model for estimating the thermal conductivity of frost on parallel surface channels under different conditions.

Modeling and Analysis of Frost Growth in Pilot-Scale Ambient Air Vaporizer

During the operation of an ambient air vaporizer (AAV) designed for vaporizing liquefied natural gas (LNG), the condensation of water vapor results in frost accumulation on the surface of the vaporizer tubes. The frost deposited on the surface lowers the heat transfer rate because the thermal conductivity of frost is less than 1/40 times the thermal conductivity of aluminum, which was used as the material for the tube and fin. It is essential to understand the behavior of frost accumulation because the actual challenge in this field is to predict frost growth in cryogenic conditions and the dynamic heat transfer performance of the AAV owing to frost. In this study, the formation of a frost layer on the surface of an LNG vaporizer and the reduction in heat performance are evaluated using a dynamic numerical model that combines heat transfer and mass transfer. The trend of frost growth and the temperature profile of LNG with position and time were studied by modeling and simulation. The numerical results pr...

Analysis of Thermal Conductivity of Frost on Cryogenic Finned-tube Vaporizer Using Fractal Method

Thermal conductivity of frost is not only related to density, but also affected by its microstructure and environmental conditions, and it will continuously change with the formation and growth of frost. Images of frost formation and growth on the cryogenic surface in various shapes at different stages were obtained by experimental measurements, and a numerical simulation of frost formation and growth was carried out based on Diffusion Limited Aggregation (DLA) model of fractal theory in this paper. Based on the frost structure obtained by experiment, the fractal dimension of pore area distribution and porosity of frost layer on the cryogenic finned-tube vaporizer were calculated by using fractal method, and combined with heat conduction model of frost layer obtained by thermal resistance method, the thermal conductivity of frost on the cryogenic surface was calculated. The result shows that the thermal conductivity calculated by the fractal model coincides with the range of the experimental data. Additionally, comparison with other heat conduction models indicated that it is feasible to introduce the fractal dimension of pore area distribution into heat conduction model to deduce the thermal conductivity of frost.

Frost Growth Simulation in Cryogenic Vertical Pipe Flow

This study reports a numerical CFD study concerning the effect of frost thickness on the heat transfer performance of a vertical pipe. Simulation are made under various variables affecting the frost growth such as outer flowing air conditions (temperature, flow velocity, humidity) and inner flow conditions of cryogenic fluid. The frost growth is mainly associated with the outer conditions. The frost thermal conductivity could play an important role in the froth growth. There is no great. The simulation for frost formation carried out with coupling to a commercial CFD code(CFX). The CFD simulation offers the possibility to predict frost formation within vertical geometries. The frost formation is based on the Lewis analogy of heat and mass transfer and it is embedded with CFX. The vertical surface temperature of the freezing body is determined by fluid structure interactive error method.

Numerical Model on Frost Height of Round Plate Fin Used for Outdoor Heat Exchanger of Mobile Electric Heat Pumps

The objective of this study is to provide the numerical model for prediction of the frost growth of the round plate fin for the purpose of using it as a round plate fin-tube heat exchanger (evaporator) under frosting conditions. In this study, numerical model was considering the frost density change with time, and it showed better agreement with experimental data of Sahin (1994) than that of the Kim model (2004) and the Jonse and Parker model (1975). This is because the prediction on the frost height with time was improved by using the frost thermal conductivity reflecting the void fraction and density of ice crystal with frost growth. Therefore, the developed numerical model could be used for frosting performance prediction of the round plate fin-tube heat exchanger.

An Experimental Study on Engineering Properties of Rubber Particles-Improved Fly Ash Soil

In this paper, by studying the engineering properties of rubber particles-improved fly ash soil, the authors provide technical parameters for setting up cold-resistance layer in the seasonal frozen zone. In the experiment, rubber particles are mixed into the fly ash soil by mass of 0%, 1%, 2%, 3%, 5% and 7% and unconfined compressive strength testing, frost heave test, insulation test and thermal conductivity test. By analyzing the test results, the authors drew the conclusion that fly ash soil improved by rubber particles has a high compressive strength, a small amount of frost heave, good insulation performance, small thermal conductivity coefficient.Therefore, improved fly ash soil with rubber particles is one of the preferred materials to set up the cold resistance layer in seasonal frost zone.

The effects of frost thickness on the heat transfer of finned tube heat exchanger subject to the combined influence of fan types

This study conducts a numerical study concerning the effect of frost thickness on the heat transfer performance of a four rows plate finned tube heat exchanger. Calculations are made under constant air volume and variable air volume conditions. It is found that the initial surge of heat transfer rate in the frosted finned tube heat exchanger is mainly associated with the critical radius effect rather than the surface roughness. The frost thermal conductivity plays an important role in the surge phenomenon. There is hardly any initial surge when frost thermal conductivity is below 0.1 W m −1 K −1. It is also recommended that a refrigerator should defrost when half of a single flow channel area is blocked by frost. The calculations also reveal that a centrifugal fan is recommended with a small fin-pitch heat exchanger. However, if a long term operation at a thick frost situation is unavoidable, an axial fan should be selected. There is no great difference between selection of an axial fan or centrifugal fan for a larger fin pitch heat exchanger.

Review Article: A Critical Review of Properties and Models for Frost Formation Analysis

There has been a continuing effort to advance the understanding and modeling of frost formation on refrigerated surfaces during the last two decades for better design of air-to-refrigerant heat transfer equipment and effective and energy-saving control of defrosting processes. A review and comparative analysis of the available literature concerning frost properties, correlations, and mathematical models are presented in this study to provide an overview of the analytical tools for researchers, product developers, and designers. The frost research can be divided into two general groups—experimental correlations and mathematical models. In general, the properties correlated are the frost thermal conductivity, the frost average density, and air-frost heat transfer coefficient (Nusselt number). A limited operational range of these relations is observed. The mathematical models include both differential and integral approaches, which are, in general, solved numerically. These models are classified based on the geometrical configuration of cold surface. A comprehensive comparison of the models is given to assist the reader in making their decisions for design analysis. The existing gaps in the frost research are identified and recommendations are made.

New model for frost growth rate

Many models have been published to predict frost growth. These may be divided into empirical and theoretical models. All prior theoretical models assume the water vapor is saturated at the interface between the air stream and frost layer. This paper provides a new theoretically based numerical model of frost deposition and growth. The present model: (1) uses supersaturated water vapor at the frost surface, which is fundamentally correct; (2) improved correlations for frost thermal conductivity; (3) uses a rationally based tortuosity factor; and (4) calculates the local frost density variation. For numerical simulation of the frost growth rate, the measured thermal conductivity was used. Frost growth rate on a cold surface was measured, and the experimental data were compared to the numerical model and agreed within 15%. The proposed supersaturation model was also compared to previous investigators’ experimental data, and it was found that the supersaturation model is superior to analytical or numerical models that assume the water vapor at the frost surface to be saturated.

Modeling of frost growth and frost properties with airflow over a flat plate

A physical model of frost layer growth and frost properties with airflow over a flat plate at subfreezing temperature was developed. Frost roughness was measured, and an empirical correlation for the average frost roughness was suggested. Heat and mass transfer coefficients were calculated using the modified Prandtl mixing-length scheme containing the effects of both frost roughness and turbulent boundary layer thickness. Frost thermal conductivity was theoretically analyzed by solving the combined equations of air equivalent conductivity and thermal conductivity of the frost inner layer. Based on the present model, heat and mass transfer coefficient, frost thermal conductivity, frost thickness, frost mass concentration and frost density with time and space were estimated. The model showed good agreement with the basic trends of the test data taken from other literature. Spatial and temporal changes of heat flux and frost surface temperature were also investigated.

Correlations of Frost Properties Considering the Environmental Parameters over a Cold Flat Plate

This study has been performed experimentally to measure the frost properties over a cold flat plate in order to obtain the correlations of the frost properties with various environmental parameters. Correlations of the frost surface temperature, thickness, density, and thermal conductivity are presented along with the experimental results as a function of environmental parameters, distance from the leading edge of test plate, and time. These correlations can be used to predict the frost properties with a maximum error of 8% in the following ranges : air temperature 15∼25, relative humidity 60∼80%, air velocity 1∼3m/s and cooling plate temperature -15∼-25.

Effective thermal conductivity of frost during the crystal growth period

An effective frost thermal conductivity for the crystal growth period of frost formation was developed based on a simple model consisting of cylindrical frost columns surrounded by moist air. Being closely related to the frost layer density, the thermal conductivity of frost layer is found to be affected by the vapor diffusion inside the frost layer as well. The density of frost columns, on the other hand, depends on the sublimation temperature of ice crystals and the humidity ratio of air, therefore, the whole process of frost formation and the thermal conductivity of frost layer, in particular, is shown to depend on the controlling temperatures, i.e. plate temperature, air temperature, and air humidity ratio.

A semi-empirical transient method for modelling frost formation on a flat plate

This paper models the frost formation process employing a semi-empirical transient model for a flat plate under forced convection conditions. This continuous differential model employs the Euler's method to solve for the temperature and thickness of the frost layer using existing correlations for the convective heat transfer coefficient and the Lewis analogy to compute both a mass transfer coefficient and an enthalpy transfer coefficient. The model is also based on empirical correlations for predicting the frost thermal conductivity and density. Model results are compared with existing experimental data and with numerical data of other investigators and are found to agree very well in the applicable temperature and humidity range of the frost density and conductivity correlations.