Temperature Distribution in a Turbulent Flow in the Heat Pollution Phenomena

Abstract

Abstract The thermal pollution, with major effects on the water quality degradation by any process involving the temperature transfer, represents nowadays a major concern for the entire scientific world. The turbulent heat and the mass transfer have an essential role in the processes of thermal pollution, mainly in problems associated with the transport of hot fluids in long heating pipes, thermal flows associated with big thermo-electric power plants, etc. In the last decades, the problems of the turbulent heat and mass transfer were analyzed for different dedicated applications. The present paper, in the first part, estimates the universal law of the velocity distribution near a solid wall, with a specific interpretation of the fluid viscosity, valid for all types of flows. Most of the scientific researches associate nowadays both the turbulent heat and the mass transfer with the Prandtl number. In the turbulent fluid flow near a solid and rigid surface, there are three flowing domains, laminar, transient, and fully turbulent, each one with its characteristics. In this paper, it is assumed that the friction effort at the wall remains valid at any distance from the wall, but with different forms associated with the dynamic viscosity. By using the superposition of the molecular and turbulent viscosity and by creating the interdependence between the molecular and turbulent transfer coefficients is estimated the mathematical model of the velocity profile for the fluid flow and temperature distribution. Three supplementary hypotheses have been assumed to estimate the dependence between the laminar and thermal sub-layer and the hydrodynamic sub-layer. The theoretical obtained distribution was compared with some experimental results from the literature and it was observed there is a good agreement between them; the differences are smaller than 3%. In the second part of the paper is determined the temperature field for a fluid flowing also in presence of the solid surfaces with different temperatures, associated not only with the Prandtl number but also with the fluid viscosity and its dependence with the temperature, correlated with the Grashoff number. In the next paragraph is used the concept of the laminar substrate with different thicknesses for the hydrodynamic flows with thermal transfer to the solid walls, and also the inverse transfer from the solid walls affecting the fluid flow and the mass transfer. The obtained mathematical model is correlated with the semi-empirical data from the literature. By numerical modeling, the obtained results were compared with the experimental measurements and it was determined the dependence between the Stanton number and the Prandtl number. The numerical results demonstrate a good agreement with the experimental results in a wide range of the Prandtl numbers from 0.5 to 3000. Finally, are mentioned some conclusions and references.