Analytical Solutions for Open-Channel Temperature Response to Unsteady Thermal Discharge and Boundary Heating

Analytical solutions are derived for a one-dimensional model of the bulk temperature response of open-channel flow with unsteady and nonuniform heating at the upstream end, the water surface, and the riverbed. The solutions are explicit formulas comprised of transient terms, which play dominant roles in the upstream region, and equilibrium terms, which determine the temperature far downstream. The applicability of the solutions to practical problems is illustrated for two cases: (1) a stream bounded at its upstream end by a dam and with a midreach inflow; and (2) Boulder Creek, Colo., which is impacted by effluent released from a wastewater treatment plant. The model prediction is in reasonable agreement with gauged data.