#### Keywords

Heat transmission, Mathematical models, Thermal pollution of rivers lakes

#### Abstract

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.

#### Notes

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#### Graduation Date

Summer 1972

#### Semester

Summer

#### Advisor

Nimmo, Bruce

#### Degree

Master of Science (M.S.)

#### College

College of Engineering

#### Degree Program

Environmental Systems Management

#### Format

#### Pages

84 p.

#### Language

English

#### Rights

Public Domain

#### Length of Campus-only Access

None

#### Access Status

Masters Thesis (Open Access)

#### Identifier

DP0012146

#### Subjects

Heat -- Transmission -- Mathematical models, Thermal pollution of rivers lakes etc

#### STARS Citation

Epstein, Alan H., "A Mathematical Model for Determining the Thermal Distribution Resulting from Discharge of a Heated Effluent" (1972). *Retrospective Theses and Dissertations*. 11.

https://stars.library.ucf.edu/rtd/11

#### Contributor (Linked data)

University of Central Florida. College of Engineering [VIAF]

#### Collection (Linked data)

#### Accessibility Status

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