Heat transmission, Mathematical models, Thermal pollution of rivers lakes
A mathematical model is presented for the problem of determining the two-dimensional temperature distribution resulting from the discharge of a heated effluent into a shallow, quiescent receptacle. The physical model of the problem is the two-dimensional jet augmented by an imposed condition of viscous drag due to bottom friction effects. By virtue of the assumption that the physical properties of the effluent are independent of temperature over the operational temperature range of the plume, the analysis separates the total problem into a flow problem and a temperature problem. Solution of the temperature distribution is accomplished both analytically and numerically. Analytically, the temperature distribution is found through sequential integral solution of the equations defining the mathematical model, under the physical assumptions of a Gaussian flow distribution and the following relationship between the velocity and temperature distributions: [formula] where the subscript (max) denotes conditions along the jet centerline. Numerically, the equations defining the mathematical model are solved by a finite differencing technique implemented with the aid of an I.B.M. 360 digital computer. Comparison of the predictions of the model with the classical two-dimensional momentum jet indicate that the model is a reasonable approximation of the real physical problem. In addition, there is seen to be a critical dependence of the flow in the plume on the depth of the receptacle.
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Master of Science (M.S.)
College of Engineering
Environmental Systems Management
Length of Campus-only Access
Masters Thesis (Open Access)
Heat -- Transmission -- Mathematical models, Thermal pollution of rivers lakes etc
Epstein, Alan H., "A Mathematical Model for Determining the Thermal Distribution Resulting from Discharge of a Heated Effluent" (1972). Retrospective Theses and Dissertations. 11.
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