Abstract:

The results of designing the mathematical model of non-stationary thermal conductivity of the bubble’s oscillating wall, with account of the changes in the aggregate state and the thermal and physical characteristics of the substance, are presented. It is shown that when applying the finite elements method, it is a system of nonlinear differential equations of the 1st order. Consideration of these features in the mathematical model allows obtaining the temperature values of liquid and solid phases at any time when changing the bubble’s size and the heat flow direction at its boundary. Based on the suggested mathematical model, a series of assessment calculations was performed. Applying mathematical modeling, the temperature fields’ distribution in the liquid under the conditions of the phase transition processes and changes in the bubble size is obtained. The performed studies show that for an immobile bubble under the boundary condition of the 2nd kind, the icing and ice melting velocities are almost equal, but the temperature on the interphase gas-water surface is approximately four times exceeding the temperature on the gas-ice surface, which corresponds to the water and ice thermal conductivity ratio. The temperature in the phase liquid-ice transition zone is practically constant. With the expansion of the bubble, liquid freezing and ice melting are going more than 1.6 times faster than in the immobile bubble. When compressing the bubble, the thickness of the ice formed or melted is approximately 1.7 times smaller than that of the immobile wall bubble. The analysis of the results obtained has shown that they are predictable and fully correspond to the physicists’ ideas of the heat transfer and phase transition processes flow in the liquid.The suggested calculation method can be used to determine the thermal characteristics of the liquid and steam in various technological processes associated with gases dissolution in the liquid, foam hardening and gas hydrates formation. The mathematical model designed can be applied as a component for calculation of more complicated physical processes. The study results can be applied to optimize various technological processes associated with materials swelling, gases adsorption, liquids boiling and gas hydrates formation Author Biographies Anatoliy Pavlenko, Kielce University of Technology Tysiacholittia panstva Polskoho str., 7, Kielce, Poland, 25-314 Doctor of Technical Sciences, professor Department of Building Physics and Renewable Energy

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