Measurements of Frost Thickness and Frost Mass on a Flat Plate under Heat Pump Condition

This study measured the frost thickness and frost mass on a flat plate to propose the correlation equations for the local and average frost thickness, frost density, and frost mass. Key parameters were the cooling surface temperature of the flat plate from 258.2 to 268.2 K, absolute humidity of air from 2.98 to 4.16 g/kg_DA, air temperature from 273.5 to 280.2 K, and air velocity from 1.0 to 2.5 m/s. A 50% ethylene glycol aqueous solution was used as a coolant. The sensitivity analysis of the parameters such as air temperature, air humidity, air velocity, and surface temperature on the frost thickness and frost mass were experimentally investigated under the heat pump condition. Correlation equations for the local and average frost thickness and frost mass under the heat pump condition were proposed. The values predicted by the correlation equations under the freezer condition were larger by a maximum of 30–50% than the values predicted by the present correlation equations under the heat pump condition. The proposed correlation equations might be applied to the part of the freezer condition.     

Frost distribution characteristics of laminar airflow on cold surface of mini-channels

This study was performed for simulating frosting characteristics that occurred on the surface of plate fins of the outside heat exchanger. Test section with local cooling modules at the central part was made as the rectangular cross sectional passage to imitate the outside heat exchanger. Local frost thickness distributions for test conditions having three experimental parameters (plate wall temperature, air humidity and velocity) were presented. Leading edge effect of the plate was clearly confirmed from the measured frost thickness distributions. The central part of the plate had the highest frost thickness because cooling devices were installed at the center of the plate. Due to different heat and mass transfer characteristics of upstream flow and downstream flow, the frost thickness of upstream area was much higher than that of downstream. The effects of plate surface temperature, humidity and velocity of inlet flow on frost thickness, and sensible and latent heat fluxes were analyzed.     

Some Observations of the Frost Formation in Fin Arrays

An experimental study concerning the frost formation and the airside performance of a fin array is reported. Visual observation indicates that the frost thickness at the fin base is thicker than that at the tip. During the period of frost formation along the fin array, one can see an apparent boundary separating a region of very thin frost thickness (the region does not show appreciable frost formation) and a region with appreciable frost thickness. Furthermore, the frost-separating boundary is not horizontal but inclined toward the airflow direction. In the entrance region, the frost formation is apparently less pronounced than that at the rear region. If part of the fin surface is above the freezing point temperature but is still below the dew point temperature, the moist air condenses on the upper part of the fin while frost is formed nearby the fin base. The water condensate on the upper part of the fin array may fall off to wash away the porous structure to become a dot-like pattern. With a fixed frontal velocity, the heat transfer coefficient for a fin spacing of 3 mm is slightly increased with the elapse of time and is higher than that of 8 mm fin spacing. The frost thickness increases with time but decreases with the frontal velocity.     

Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger

In the paper, numerical and experimental analyses of heat and mass transfer during frost formation on a fin-and-tube heat exchanger have been presented. Modelling of the frost formation on cold surfaces placed in a humid air stream, requires a complex mathematical approach. A transient two-dimensional mathematical model of frost formation has been developed. The applied mathematical model has been defined using governing equations for the boundary layer that include air and frost sub-domains as well as a boundary condition on the air–frost interface. The mathematical model with initial and boundary conditions has been discretised according to the finite volume method and solved numerically using the SIMPLER algorithm for the velocity–pressure coupling. Results have shown that the frost layer formation significantly influences the heat transfer between air and fins. As a result of numerical calculations, time-wise frost thickness variations for different air humidities, temperatures and velocities have been presented. Using the developed mathematical model, the algorithm and the computer code, which have been experimentally validated, it is possible to predict a decrease of exchanged heat flux in the heat exchanger under frost growth conditions.     

Analysis of heat transfer and frost layer formation on a cryogenic tank wall exposed to the humid atmospheric air

In this paper heat transfer characteristics and frost layer formation are investigated numerically on the surface of a cryogenic oxidizer tank for a liquid propulsion rocket, where a frost layer could be a significant factor in maintaining oxidizer temperature within a required range. Frost formation is modeled by considering mass diffusion of water vapor in the air into the frost layer and various heat transfer modes such as natural and forced convection, latent heat, solar radiation of short wavelength, and ambient radiation of long wavelength. Computational results are first compared with the available measurements and show favorable agreement on thickness and effective thermal conductivity of the frost layer. In the case of the cryogenic tank, a series of parametric studies is presented in order to examine the effects of important parameters such as temperature and wind speed of ambient air, air humidity, and tank wall temperature on the frost layer formation and the amount of heat transfer into the tank. It is found that the heat transfer by solar radiation is significant and also that heat transfer strongly depends on air humidity, ambient air temperature, and wind speed but not tank wall temperature.     

Frost growth and densification on a flat surface in laminar flow with variable humidity

Experiments are performed concerning frost growth and densification in laminar flow over a flat surface under conditions of constant and variable humidity. The flat plate test specimen is made of aluminum-6031, and has dimensions of 0.3 m × 0.3 m × 6.35 mm. Results for the first variable humidity case are obtained for a plate temperature of 255.4 K, air velocity of 1.77 m/s, air temperature of 295.1 K, and a relative humidity continuously ranging from 81 to 54%. The second variable humidity test case corresponds to plate temperature of 255.4 K, air velocity of 2.44 m/s, air temperature of 291.8 K, and a relative humidity ranging from 66 to 59%. Results for the constant humidity case are obtained for a plate temperature of 263.7 K, air velocity of 1.7 m/s, air temperature of 295 K, and a relative humidity of 71.6%. Comparisons of the data with the author's frost model extended to accommodate variable humidity suggest satisfactory agreement between the theory and the data for both constant and variable humidity.     

Heat Transfer and Pressure Drop Under Dry and Humid Conditions in Flat-Tube Heat Exchangers With Plain Fins

Flat-tube heat exchangers could be an interesting alternative to make indirect cooling of display cabinets more energy-efficient. This application involves low air velocities in combination with condensation of water vapor on the air side, so plain fins could be suitable. Two different heat exchangers having flat tubes and plain fins on the air side were evaluated experimentally. One of the heat exchangers had continuous plate fins, and the other had serpentine fins. The performances during dry and wet test conditions were compared and related to theoretical predictions for different assumptions. The influence of air velocity, air humidity, and inclination angle was investigated. The results show that, in most cases, the heat transfer performance is somewhat reduced under wet conditions in comparison with dry test conditions, and that wet heat transfer surfaces lead to an increased pressure drop. At the lower air velocity range that was investigated, the heat exchanger having continuous plate fins drained better than the one with serpentine fins.     

Experimental investigations of frost release by hydrophilic surfaces

Frost formation occurs when water vapor in the surrounding air comes into contact with cold surfaces through heat and mass transfer. It is usually an undesirable phenomenon in most refrigeration and cryogenic systems. A few studies have shown that changing the surface energy, such as increasing the surface hydrophilicity or hydrophobicity, has significant effects on frost growth. In this paper, a kind of hydrophilic polymer paint is formulated to counteract frost deposition on cold surfaces. The coated surface can retard frost formation up to three hours under low plate temperatures (− 15.3°C) and high air humidity (72%). To test the antifrosting performance of the hydrophilic paint under more practical conditions, it is applied to a fin-and-tube heat exchanger and a domestic refrigerator at a coating thickness of 30 μm. Comparisons of frost deposition, pressure drops, and outlet temperatures are made between uncoated and coated heat exchangers. Under conditions of high air temperature (2.2°C) and relative high air humidity (90%), the paint prolongs the defrosting interval from 80 to 137 min. Experimental observations also show that the coated hydrophilic fins are free of frost deposition during the entire course of the test and that the coating has no significant additional thermal resistance.     

Dimensionless correlations of frost properties on a cold cylinder surface

We propose dimensionless correlations for frost properties on a cold cylinder surface. Frosting experiments were performed while changing various frosting parameters such as the air temperature, cold cylinder surface temperature, air velocity, and absolute humidity. The experimental data showed that a uniform frost layer grew around the circumference of the cylinder at a high air velocity. Dimensionless correlations for the thickness, density, and surface temperature of the frost layer, and for the heat transfer coefficient were obtained as functions of the Reynolds number, Fourier number, absolute humidity, and dimensionless temperature. The applicable ranges of these correlations are Reynolds number of 700–3000 (air velocities of 0.5–2.0 m/s), Fourier number of 56.8–295.7 (operating time of 0–100 min), absolute humidity of 0.00280–0.00568 kg/kg_a, air temperatures of 3–9 °C, and cold cylinder surface temperatures of ?32 to ?20 °C. The proposed correlations agreed with the experimental data within an error of 15%.     

Free convection frost growth in a narrow vertical channel

Processes involving heat transfer from a humid air stream to a cold plate, with simultaneous deposition of frost, are of great importance in a variety of refrigeration equipment. In this work, frost growth on a vertical plate in free convection has been experimentally investigated. The cold plate (0.095 m high, 0.282 m wide) was placed in a narrow (2.395 m high, 0.01 m deep) vertical channel open at the top and bottom in order to permit the natural circulation of ambient air. The cold plate temperature and the air relative humidity were varied in the −40 to −4 °C and 31–85% range, respectively, with the air temperature held fixed at 27 °C (±1 °C). The main quantities (thickness, temperature and mass of frost, heat flux at the cold plate), measured during the time evolution of the process, are presented as functions of the input parameters (relative humidity and cold plate temperature); in particular, the role exerted by the plate confinement on the frost growth is discussed. Data are recast in order to identify compact parameters able to correlate with good accuracy frost thickness, mass and density data.     

Frost deposition in a parallel plate channel under laminar flow conditions

The subject of this paper is a theoretical and experimental study of frost formation on cooled parallel plates in laminar forced convection. In the experiments time variation of the frost layer thickness was measured at several locations downstream along the test section which was positioned in an open-loop wind tunnel. The parameters varied were air velocity (Reynolds number), air temperature, air humidity ratio, and plate temperature. The process was simulated numerically using a two-dimensional transient model based on the conservation equations of mass, momentum, energy, and species. The physical domain of interest was divided into two subdomains, one for the moist air stream between the plates (gaseous phase), and one for the frost layer (solid phase). The two sets of governing equations were coupled by boundary conditions at the moving interface which required an iterative solution strategy. With this approach, the local distribution of temperature and porosity in the frost layer, which is nearly impossible to obtain in the experiments, could be predicted at any time. The results of the total heat and mass transfer rates as well as the development of the local and average frost thicknesses were compared with the experimental findings.     

Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls

Numerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 10⁵ to 10⁸ with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed except for the density where Boussinesq’s approximation has been considered. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh number with corrugation amplitude and frequency.     

Experimental investigation on the performance of air cooler under frosting conditions

Evaluation of heat transfer performance of the air cooler under frosting conditions is of great importance for the refrigeration industry. In this paper, effects of frost growth on the performance of the air cooler have been studied with an experimental air cooler of industrial size with different fin spacings, i.e., 6, 8 and 10 mm. Results showed that factors affecting the heat transfer performance of the air cooler include the evaporation temperature, the frost height, the fin spacing and the air velocity. The overall heat transfer coefficients based on a logarithmic mean temperature difference (LMTD) and the energy transfer coefficients based on a logarithmic mean enthalpy difference (LMED) were calculated. As the frost accumulated on the air cooler, the overall heat transfer coefficient and energy transfer coefficient will drop gradually.     

Frosting of heat pump with heat recovery facility

This paper aims to prolong the heat pump frost time and reduce its growth with heat recovery facility, which should mix the exhausted indoor and outdoor air before entering the evaporator. An ideal mathematic model is developed for heat transfer, frost generation and airside pressure drop. The properties of the mixture would be obtained by solving the mass and energy conservation equations. A parametric analysis is performed to investigate the effects of air inlet temperature, relative humidity and air mass flow rate on total heat transfer coefficient, frost thickness and airside pressure drop, respectively. The results show that rationalizing the ratio of indoor and outdoor air could prolong frosting time and reduce the frost thickness greatly. The total heat transfer coefficient, frost thickness and airside pressure drop increase monotonically with time going, but are not proportional. Decreasing the mixture inlet air temperature and relative humidity could essentially reduce frost growth on the tube surfaces. This can also be observed when increasing the air mass flow rate.     

Predictions of frost growth on a cold plate in atmospheric air

A theoretical model for frost formation on a cold plate placed in atmospheric air has been developed in this study. Effects of plate surface temperature (T_w) and air conditions, such as air velocity (V), temperature (T_a), and humidity ratio (ω_a), on the frost growth rate can be evaluated by using this model. Results show that the predictions of frost growth rate by the developed model agree closely with the existing experimental data during the forst layer growth period for most of the cases considered. Predictions by this model have also been compared with those obtained by the existing theoretical models.     

Estimation of vapor velocity,vapor density and vapor temperature in a snow pack and its application in avalanche forecasting

In the proposed study, fluid flow and heat transfer of water vapor in a snow pack are studied. Variation of flow parameters such as velocity, density, dynamic pressure and temperature of vapor have been observed for various snow densities and vapor viscosities in the snow pack. The results have been compared with available empirical results that are for the growth of grain size at various heights in snow pack. The advantage of the present model in using for avalanche predictions has been highlighted.     

On the Rayleigh–Taylor instability for confined liquid films with injection through the bounding surfaces

An experimental and numerical investigation has been conducted to evaluate the hydrodynamic characteristics of a thin liquid film bounded by a downward-facing flat wall through which the liquid is continually injected. Both horizontal and inclined surfaces have been examined. The effect of different parameters, namely, the film thickness, liquid injection velocity, inclination angle and liquid properties on liquid film behavior have been examined. Non-intrusive optical techniques have been used to follow the transient evolution of the film free surface. Specifically, the frequency of droplet detachment, the size of the detached droplets, and the penetration depth prior to droplet detachment have been measured. These data have been compared against predictions of a mechanistic numerical model based on the level contour reconstruction front tracking method. The numerical model predictions are in good agreement with the experimental data.     

Numerical and Experimental Modelling of Gas Flow and Heat Transfer in the Air Gap of an Electric Machine. Part Ⅱ： Grooved Surfaces

The study deals with the cooling of a high-speed electric machine through an air gap with numerical and experimental methods. The rotation speed of the test machine is between 5000-40000 r/min and the machine is cooled by a forced gas flow through the air gap. In the previous part of the research the friction coefficient was measured for smooth and grooved stator cases with a smooth rotor. The heat transfer coefficient was recently calculated by a numerical method and measured for a smooth stator-rotor combination. In this report the cases with axial groove slots at the stator and/or rotor surfaces are studied. Numerical flow simulations and measurements have been done for the test machine dimensions at a large velocity range. At constant mass flow rate the heat transfer coefficients by the numerical method attain bigger values with groove slots on the stator or rotor surfaces. The results by the numerical method have been confirmed with measurements. The RdF-sensor was glued to the stator and rotor surfaces to measure the heat flux through the surface, as well as the temperature.     

Prediction of the frost formation on a cold flat surface

A mathematical model is presented to predict the behavior of frost formation by simultaneously considering the air flow and the frost layer. The present model is validated by comparing with several other analytical models and our experiments. It is found that most of the previous models cause considerable errors depending on the working conditions or the correlations used in predicting the frost thickness growth, whereas the model in this work estimates the thickness, density, and surface temperature of the frost layer more accurately within an error of 10% except the early stage of frosting in comparison with the experimental data. Numerical results are presented for the variations of heat and mass transfer during the frost formation and for the behavior of frost layer growth along the direction of air flow. Also, a correlation between the convective heat and mass transfer is obtained as Le⁽¹⁻ⁿ⁾=0.905±0.005 in this work.     

CFD analysis of the thermal losses on the upper part of a flat solar collector

To investigate the reduction of heat losses on the upper part of a flat solar collector, a two‐dimensional study was carried out by CFD analysis using Fluent. For this purpose, the heat transfer behavior in the air gap over a wide range of thicknesses of the latter (1‐20 mm) and the addition of a second glass cover fixed at midheight of the air gap spacing have been investigated. For small thicknesses of the air gap (1‐8 mm), the heat transfer is essentially conductive. An increase in the thickness leads to the intensification of the natural convection which induces high thermal losses. The simulation results have shown that the addition of a second cover glazing leads to the weakening of the natural convection and thus to an average enhancement of the solar collector temperature over the range of thicknesses studied of approximately 17%. The overall thermal losses coefficient is then reduced by an average of 26% compared with the single‐glazed solar collector. They have also shown that the thickness of the air gaps resulting in the minimum overall heat losses is 8 mm and that the thickness of the second glass cover has no significant effect on these results. In addition, this study has highlighted the importance of taking into account the radiation heat transfer in establishing the thermal balance of a flat solar collector. Indeed, this consideration leads to an average decrease of the absorber temperature of about 30%.