Quasi-analytical solution to the problem of heat transfer by vortex flow based on self-similarity

Abstract

Highly efficient vortex flow increases fluid flow and simultaneously enhances heat transfer. An accurate vortex flow model is of great importance to analyzing and solving heat transfer problems. The general form of the solution to the vortex flow problem was derived from the self-similarity properties of vortex flow along the radius direction, and its correctness was validated. The temperature distribution function of vortex flow was determined, and the relative thermal conductivity was obtained. A dimensionless number (ρCpvθ′Rk) was defined to characterize the temperature distribution of vortex flow. The rate of heat transfer was also determined. The results indicated that the dimensionless number represents the ratio of convection to thermal conduction, and can be used to accurately describe the temperature distribution of vortex flow. When the temperature at the vortex flow center is close to the average temperature, the difference in temperature phase is significant, and convection plays a dominant role in the heat transfer process. The temperature can be defined by sine function when the radius of vortex is decreased to a certain extent. The results can be applied to the analysis of large-scale vortex flow heat transfer, the optimization design of small-scale vortex flow heat transfer, and the development of vortex flow and temperature sensors.