Abstract
Waste heat dispersion from power plants and heavy industries is always a major concern. Every industry needs a cheap source for cooling its necessary components, and water serves this purpose. This is due to ease of availability and high specific heat capacity of water. But after industrial use, the heated effluent is again discharged in the same water body from where it is taken. This not only disturbs the aquatic life but also affects the balance of the ecosystem. We sometimes forget that affecting one essential component of ecosystem will completely disturb the environment, since water is a necessary component out of three basic components of life (air, water and soil). This chapter presents the background of the thermal pollution, modelling approach and analysis methods. For primary analysis of thermal pollution, an analytical solution of two-dimensional thermal dispersion is discussed. Dispersion is considered over a surface with velocity in only one direction i.e. in the direction of the wind. A parabolic partial differential equation is solved analytically to predict temperature contours over a surface. Due to lack of adequate boundary condition, this solution is only capable of predicting far-field temperatures. For prediction of near-field temperatures, the same parabolic equation or a full three-dimensional energy and momentum equations can be solved numerically. A numerical problem formulation methodology is discussed for accurate prediction of thermal pollution. Finally, a scaling analysis is shown to develop an experimental model for proper validation of the numerical code and laboratory-scale experimental study.
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Abbreviations
- A :
-
Constant of linearization of heat interaction with the atmosphere in (W)
- B :
-
Constant of linearization of heat interaction with the atmosphere in (W/K)
- C p :
-
Specific heat capacity of fluid (kJ/kgK)
- D x :
-
Thermal diffusivity in X-direction (m2/s)
- D y :
-
Thermal diffusivity in Y-direction (m2/s)
- D i :
-
Diffusion coefficient for heat (m2/s)
- D :
-
Characteristic discharge dimension (m)
- H w :
-
Height from the point of emission of effluent to the free surface (m)
- \(\tilde{k}\) :
-
Turbulent kinetic energy (m2/s2)
- q o :
-
Heat added by effluent (W)
- T :
-
Temperature (K)
- T 0 :
-
Initial temperature of effluent discharge (K)
- U :
-
Velocity of the fluid (m/s)
- \(\rho\) :
-
Density of water (kg/m3)
- \(\rho_{o}\) :
-
Overall density of the top layer of water (kg/m3)
- \(\Delta\) :
-
Variation
- \(\eta\) :
-
Y-axis distance
- \(\sigma\) :
-
X-axis distance
- \(\mu_{t}\) :
-
Eddy viscosity
- \(\epsilon\) :
-
Turbulent dissipation rate (m2/s3)
- \(\nabla\) :
-
Gradient
- w :
-
Fluid as water
- i :
-
Gridcounts in the X-direction
- j :
-
Gridcounts in the Y-direction
- e :
-
Effluent flow property
- a :
-
Ambient flow property
- m :
-
Model
- p :
-
Prototype
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Punetha, M. (2018). Thermal Pollution: Mathematical Modelling and Analysis. In: Gupta, T., Agarwal, A., Agarwal, R., Labhsetwar, N. (eds) Environmental Contaminants. Energy, Environment, and Sustainability. Springer, Singapore. https://doi.org/10.1007/978-981-10-7332-8_18
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