Transient temperature solution for stream flow from a controlled temperature source

Abstract

An exact solution representing the idealized thermal response of a flowing stream is presented and analyzed. The flowing stream, issuing from a controlled temperature water source such as a large lake or reservoir, is modeled as a one-dimensional region subject to sinusoidal solar heating and convective heat exchange with air, whose temperature also varies sinusoidally. The maximum downstream diurnal temperature fluctuation is found to occur at 12 hours of travel, at the average water flow speed, from the water source. For an isothermal water source the peak daily fluctuation at this location has a magnitude approximately 50% larger than the temperature fluctuation far downstream from the source.