Fate of Thermally Polluted Surface Water in Rivers

By means of the time- and space-averaging processes, the general longitudinal thermal energy equation for nonuniform flow is derived from the three-dimensional instantaneous equations of continuity and of thermal energy for flow of incompressible Newtonian fluid. The equation so formulated includes the longitudinal heat dispersion term and can be used to describe mathematically the average temperature distribution in a natural stream at every instant and at all points of the stream after the injection of thermal pollutant. Analytical solution is sought for a typical thermal pollution problem in a natural stream. An accurate evaluation of the longitudinal heat dispersion coefficient that depends on bulk flow parameters and environmental factors is proposed.