Radiative melting of ice layer adhering to a vertical surface

This paper is concerned with melting of a vertical ice layer adhering to the substrate by using radiating heat source of halogen lamps having a large fraction of short wave beam or nichrome heater having a comparatively large fraction of long wave one. From the present experimental results, it can be seen that the heating of short wave radiation produces a peculiar melting behavior of strongly rough melting-surface due to the internal melting at the grain boundary of ice-surface. On the other hand, for the case of long wave radiation the melting-surface becomes very smooth. The melting rate of clear ice layer by short wave radiation obtained from halogen lamps is smaller than that of cloudy ice layer due to the good penetration of short wave fraction through the clear ice layer. Moreover, the raising of temperature of ice-substrate interface could offer a feasibility of removing ice layer from the structure subject to atmospheric icing. Concludingly, it is clarified that the melting rate of ice layer could be predicted numerically by using the band model of extinction coefficient or absorption coefficient presented in this study.

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Schmelzen einer Eisschicht an einer senkrechten Wand durch Strahlung

Zusammenfassung Diese Arbeit behandelt das Schmelzen einer senkrechten Eisschicht auf einer Unterlage mit Hilfe von Halogen-Lampen mit einem hohen Anteil an kurzen Wellen und Nichromheizern mit einem hohen Anteil an langen Wellen. Aus diesen Versuchen läßt sich ableiten, daß die Heizung durch kurzwellige Strahlung ein eigentümliches Schmelzverhalten mit sehr rauher Oberfläche hervorruft, verursacht durch Schmelzen an den Korngrenzen der Eisoberfläche. Bei langwelliger Heizung wird die Oberfläche sehr glatt. Die Abschmelzrate einer Klareisschicht bei kurzwelliger Heizung durch Halogen-Lampen ist geringer als die einer Opaleisschicht wegen des besseren Eindringens der kurzen Wellen in das klare Eis. Der Temperaturanstieg an der Grenze Eis — Unterlage bietet die Möglichkeit der Enteisung von Bauteilen, die der atmosphärischen Vereisung ausgesetzt sind. Es folgt, daß die Abschmelzrate einer Eisschicht, numerisch vorausberechnet werden kann, indem man das Bandmodell des Extinktions- und des Absorptionskoeffizienten dieser Arbeit verwendet.

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Nomenclature A transmission, defined in equation (4) - a monochromatic absorption coefficient of clear ice - C constant - E_b monochromatic emissive power - h_i thickness of ice layer - h_in initial thickness of ice layer - h_m thickness of substrate - k₀ extinction coefficient for h₀ 0 - k_s modified extinction coefficient - k monochromatic extinction coefficient - L_i latent heat of melting - n index number, defined in equation (2) - heat flux absorbed at surface of substrate - q_r0 radiant heat flux impinged onto ices-urface - q_ri{y} radiant heat flux in ice layer - S distance from initial ice-surface to transient melting-surface - T_b temperature of radiating heat source - T_i temperature in ice layer - T_m temperature in substrate - T environmental temperature - T₁ temperature of surface of ice layer - T₂ temperature of substrate-surface - T₃ temperature of back side surface of substrate - t time - y distance from initial ice-surface - Z ratio of backward radiative heat flux to forward one for cloudy ice Greek Symbols heat transfer coefficient - _i thermal diffusivity of ice - _m thermal diffusivity of substrate - _i thermal conductivity of ice - _m thermal conductivity of substrate - wavelength - _c critical wavelength - _i density of ice - Stefan-Boltzmann constant     

The pressure melting of ice around a horizontal elliptical cylinder

The pressure melting processes of a block of ice around a moving, horizontal, elliptical cylinder are investigated. The film thickness of liquid and the relation between the force exerted on the elliptical cylinder and the melting velocity are obtained analytically. The results include those of pressure melting around a horizontal cylinder, and are discussed and compared with that of ΔT-driven melting around an elliptical cylinder. The basic differences between Δp-driven and ΔT-driven melting are obtained. Some important conclusions are drawn.     

Heat transfer during the melting of ice around a horizontal,isothermal cylinder

An experimental investigation of the melting of ice around a horizontal, isothermal cylinder is performed. Emphasis is placed on interpreting the heat transfer mechanisms which control solid-liquid interface position. Flow visualization and interferometric techniques are employed to study the transient flow patterns and corresponding temperature distributions in the melted region. It has been determined that density inversion plays an important role in the melting of water. The location of the maximum density surface in the liquid has a significant effect on natural convection, and hence on the shape and size of the melted region. Local Nusselt numbers at the surface of the cylinder and at the solid-liquid interface are determined and found to be complicated functions of time and imposed thermal conditions. Average Nusselt numbers at the solid-liquid interface and at the surface of the cylinder decrease with time and quasi-steady conditions are not reached.     

Experiments on melting of a vertical ice layer immersed in immiscible liquid

Experiments on the melting of a vertical ice layer immersed in immiscible liquid yielded quantitative results both for the timewise evolution of the melting front and the heat transfer. Vegetable oil, which was contained in a rectangular vessel, was adopted as a testing liquid. A bubble-free ice block stuck on a cooled wall was installed vertically in the vessel. The experiments were carried out for the immiscible liquid temperatures from 7.6 to 30.0 ^°C, while for the cooled wall temperatures from 0 to ?11.5 ^°C. The flow structure of the liquid and the melting front were extensively observed and recorded photographically. It was found that the heat transfer and the rate of melting are significantly affected by a couple of fluid motions of both the water melt induced by melting of ice and the immiscible liquid based on free convection.     

Visual observations of flow structure and melting front morphology in horizontal ice plate melting from above into a mixture

Visual observations reveal a complicated flow in the liquid melt and a melting front configuration resulting from horizontal ice plate melting from above into a 20 wt% calcium chloride aqueous solution. The initial temperature of the ice plate and the mixture are both −5°C. Small scale “mountain and valley” structures (∼1 mm) appear on the flat melting front just after melting begins, which have been called “sharkskin”. Innumerable upward and downward flows appear near the sharkskin and are controlled by its “mountain and valley” structure. These typical flows will considerably promote the melting of the ice plate to be 30% larger as compared to the numerically predicted results assuming a flat melting front (i.e., without the sharkskin), and also by three times larger compared with the results for melting from below.     

Free convection heat transfer around a horizontal ice cylinder formed through melting within an immiscible liquid

An experimental study has been performed to determine the melting heat transfer characteristics of a horizontal ice cylinder immersed in an immiscible liquid. Vegetable oil, which was contained within a horizontal heated copper tube, was adopted as a testing liquid. A bubble-free ice cylinder was situated at the center of the tube. The experiments were carried out for the heated tube temperatures ranging from 8.0 to 30.0 °C, while for the cooled tube temperatures from ч.0 to ⪡.0 °C. The flow pattern of the liquid and the ice-liquid interface shape of the ice cylinder being formed through melting were extensively observed and recorded photographically. The local/average heat transfer coefficient along the ice cylinder at steady state was determined as a function of the heated tube temperature as well as the cooled tube temperature. The measurements show that the ice layer profiles at steady state are quite similar irrespective of the thermal conditions. Zusammenfassung Die Experimentelle Untersuchung hatte zum Ziel, den Wärmeübergangsmechanismus beim Schmelzen eines horizontalen, in eine nichtmischbare Flüssigkeit eingetauchten Eiszylinders aufzuklären. In einem horizontalen, beheizten Kupferrohr befindliches Pflanzenöl diente als Versuchsflüssigkeit. Ein blasenfreier Eiszylinder befand sich in der Mitte des Rohres. Bei den Experimenten variierten die Temperaturen des Heizrohres zwischen 8.0 und 30.0 °C, die des gekühlten Innenrohres zwischen ч.0 und ⪡.0 °C. Das Strömungsmuster der Flüssigkeit und die sich während des Schmelzvorganges ausbildende Form der Eis-Flüssigkeitsgrenze am Eiszylinder wurden genauestens beobachtet und photographisch festgehalten. Der Lokale, den Eiszylinder entlang gemittelte Wärmeübergangskoeffizient wurde für den Stationärfall als Funktion der Heiz- und Kühlrohrtemperaturen bestimmt. Die Messungen zeigen, daß die Eisschichtprofile im Stationärfall - unabhängig von den thermischen Bedingungen - weitgehend ähnlich sind.     

Three-dimensional melting of ice around a liquid-carrying tube

Three-dimensional melting of ice around a liquid-carrying tube placed in an adiabatic rectangular cavity is investigated mainly by means of a numerical analysis. Natural convection in the melt layer enhances melting by about 1.2 times compared with the approximate solution of a conduction mode derived from London and Seban and Hausen. The morphology of the melt layer changes in axial direction. Melting is not sensitive to the cavity height and the tube length, but is very responsive to the liquid inlet temperature.     

Numerical simulation of melting ice around a floating by microwaves

In this paper a new method in using microwaves is provided for melting the ice around a floating equipment in a freezing condition in cold regions. The numerical simulation’s results for validation are compared with the simple model’s experimental data. Using microwave in melting the ice around a floating equipment is caused by lack of the mechanical wear, low energy dissipation factor and acceptable defrosting process speed in small lakes.     

Melting of horizontal ice layer from above by combined effect of temperature and concentration of aqua-solvent

This paper is concerned with the melting of horizontal ice layer from above by aqua-solvent with low solidification point. The solute used in this experiment are Sodium chloride NaCl, Calcium chloride CaCl₂, Magnesium chloride MgCl₂, and Urea CO(NH₂)₂- The upper surface of aqua-solvent melt layer is heated by an infrared lamp, whose temperature is in the range of about 8 ?C to 40 ?C. The ice layer located under the aqua-solvent melt layer melts greatly by a combined effect of both thermal energy and chemical reaction, and the typical temperature distribution in both aqua-solvent and ice layer is examined. The relation between melt amount of ice layer per unit temperature gradient and mean concentration in aqua-solvent melt layer was obtained.     

Turbulent convection in a plane horizontal layer

The problem of convection in an incompressible fluid between two horizontal planes maintained at a constant temperature without friction on the boundaries is considered. The medium is assumed to be turbulent. A theoretical model is constructed using mathematical modeling of the coherent structure in the turbulent flow. This turbulent convection-model has one empirical constant in the relations closing the generalized Reynolds equations. The problem formulated is solved analytically by means of the Stuart-Landau method. The main characteristics of the finite-amplitude ordered convection are obtained and their dependence on the empirical constant is studied.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 49–56, November–December, 1993.     

Natural convection heat transfer from a horizontal ice cylinder

Heat transfer characteristics passing through the maximum density point around a horizontal ice cylinder immersed in water was studied both theoretically and experimentally. For the sake of a precise comparison, the stagnation point Nusselt number was measured and results then compared with those of the numerical computations that were obtained by solving the full Navier-Stokes equations. A fairly good agreement was seen between the theory and the experiment.At about 6°C of water temperature where the stagnation Nusselt number takes its minimum value, the instability of the flow was observed. It was found that two different computer solutions exist, which shows unstable aspects corresponding to the experimental result.     

Thermocapillary convection in a horizontal layer of liquid

An exact solution is found for the equations for free convection in a planar horizontal layer of liquid with a constant temperature gradient at the boundaries. Two cases of boundary conditions for the velocity are considered: 1) the liquid is bounded by two solid planes, 2) the upper surface of the liquid is free, and the surface tension is a function of temperature.     

Radiative and convective heat transfer in a plane layer of absorbent curtain

An examination is made of the thermal state of a plane layer of gray gas injected into a turbulent stream of high temperature gas flowing over a permeable flat plate.Similarity-type formulations of problems are encountered both in examination of flow near a stagnation point, and also in analysis of the lifting of the boundary layer by intense injection through a porous plate [1]. The examination described relates to the following idealized formulation of the problem (Fig. la).In a plane layer of gray absorbing medium, formed by plane-parallel diffusely radiating surfaces (1-porous plate; 2-boundary of high temperature turbulent gas stream), heat transfer is accomplished by radiation and convection of the layer normal to the surfaces and by molecular heat conduction. All the physical and optical properties of the medium and of the boundary surfaces are assumed to be constant, independent of temperature.The temperature of the wetted surface of the specimen and also that of the fictitious surface determining the upper bound of the lift-off region, are given.Also assumed given is the velocity of the injected medium, which is constant throughout the entire lift-off layer. This idealization appreciably facilitates our examination without in principle changing its features.A very simplified examination of this problem was given in [2]. The special case of a medium with low optical thickness was examined in [3,4].The problem was examined in [5] under the assumption that molecular heat conduction in the medium is negligibly small.In the formulation considered the generalized energy equation has the form     

Free convective heat transfer and criterion of onset of free convection in a horizontal melt layer of ice heated by upper rigid surface

An experimental and analytical investigation pertaining to the effect of density inversion of water on the free convective heat transfer and the onset of free convection in a horizontal melt layer of ice heated by upper rigid surface is carried out. Temperatures of the upper surface are varied from 1°C to 15°C, with Rayleigh number ranging from 2 × 10² to 1 × 10⁵. From the present study, it can be demonstrated both experimentally and analytically that the density inversion of water plays an influential role in such a melt layer and the onset of free convection and the free convective heat transfer are considerably affected by the temperature of upper rigid surface T₂, in the case of T₂ ≤ 8° C, unlike the results obtained for common fluids without density inversion.     

Stability of a nonuniformly heated fluid in a porous horizontal layer

We investigate the stability of a nonuniformly heated fluid in the gravitational field in a plane horizontal porous layer through which vertical forced motion is effected. A similar system was studied in [1, 2]. In the present paper, the nonuniformity of the permeability of the porous layer with respect to the depth and the dependence of the viscosity of the saturating fluid on the temperature are taken into account in addition. As a result of the application of the linear stability theory, an eigenvalue problem arises, which is solved numerically. A family of curves representing the dependence of the critical modified Rayleigh number Ra _k ^⋆ on the injection parameter (the Péclet number Pe) for different degrees of inhomogeneity of the permeability and the viscosity is obtained. It is found that although Pe=0 corresponds to Ra _k ^⋆ for uniform permeability and viscosity and the stability increases monotonically as Pe increases, the presence of nonuniformity of the permeability or the viscosity leads to the appearance of a stability minimum in the region Pe≈1, while under the simultaneous influence of these two factors, the minimum is shifted into the region Pe≈2. The results of the paper can be used, for example, in the investigation of heat transfer in the case of forced fluid motion in the fissures of a permeable rock mass, when, in the case of pumping through a horizontal fissure, the fluid penetrates vertically across its permeable walls into the stratum. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–7, November–December, 1986.     

Convection in a horizontal fluid layer with specific-volume inversion

The effect of the position of the inversion point within the layer on the critical values of the Rayleigh number and the amplitudes of the rectangular-cell convective flows is numerically investigated. The monotonic instability of the mechanical equilibrium of the fluid with respect to small perturbations periodic along the layer is studied by the linearization method. The Lyapunov-Schmidt method is used to construct the secondary steady convective flows. The applicability of these methods in incompressible fluid stability problems was demonstrated in [8–10]. The calculations show that, starting from a certain value of the parameter , the branching is subcritical for any cell side ratio and a fixed wave vector modulus. For smaller values of the nature of the branching depends on the cell side ratio. This points to subcritical branching and hysteresis effects in those cases in which the periodicity of the perturbations is determined by external factors (corrugation of the boundary, spatially periodic temperature modulation, etc.). It is noted that the rectangular convection amplitude tends to zero when the cell side ratio tends to 3, the value at which hexagonal cellular convection is possible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 43–49, January–February, 1989.The author wishes to thank V. I. Yudovich for his interest and useful advice and the participants in the Rostov State University Computational Mathematics Department's Scientific Seminar for discussing the results.     

Effect of the melting system sizes on the temperature and concentration combined melting of a vertical ice plate in a rectangular cavity

This paper is concerned with the melting of a vertical ice plate into a calcium chloride aqueous solution inside a rectangular cavity. The initial temperature of the ice plate and the mixture are both −5°C and the initial concentration of the mixture is 20 wt%. The effect of the liquid height H, the width W, the aspect ratio of the liquid region A (=H/W) and the initial ice plate thickness δ _i on the transient melting mass per unit melting front area, M, is mainly considered numerically. M keeps a similar value in spite of H varied for A = 1 at early melting stage, however, becomes considerably influenced by H as melting progresses. The ice plate melts influenced by A for H = 20 mm fixed at early melting stage due to the fast development of the stagnant region and M decreases with increasing A (=1∼ 10). A dimensionless correlation of the transient melting mass, the aspect ratio and the melting time was presented under the restricted condition of H = 20 mm.     

Natural convection of non-Newtonian fluids in a horizontal porous layer

Heat and Mass Transfer - The buoyancy-induced flows of non-Newtonian fluids in a horizontal fluid saturated porous layer is studied analytically and numerically using the power-law model to...