ANALYSIS OF FLOW AND HEAT TRANSFER IN THE BOUNDARY LAYER OF FLUID WITH ESSENTIAL DEPENDENCE OF VISCOSITY FROM TEMPERATURE

Abstract

The introduction of new environmentally safe, durable and fire-resistant thermal insulation based on basalt fiber requires the improvement of technological processes for the production of basalt filaments in order to increase their energy efficiency. The quality of basalt fiber significantly depends on the properties of the basalt melt in the process. The process is considered to be more perfect than the more homogeneous and isotropic final properties of the melt. The conditions of flow and heat transfer in the bath and feeder of the melting furnace have a significant impact on the final properties of the melt. The paper presents the results of studies of heat transfer in the boundary layer on a flat plate with the flow of a liquid, the viscosity of which depends significantly on temperature. The system of differential equations, which describes the steady-state flow regime, is solved using symmetry analysis (analysis of Lie groups). On the basis of the developed mathematical model, new results were obtained which characterize the regularities of the flow and heat exchange of a highly viscous fluid in the range of temperature variations from 900 to 1450 ° C. The conditions for the formation of a low-mobility layer of liquid near a solid surface are determined. The influence of the value of a low-mobility fluid layer on the temperature distribution in the boundary layer of basalt melt is established. The results obtained allow us to adjust the temperature regimes in the melting furnace and improve the process of manufacturing ultrathin basalt threads.