Document: NRC Regulatory Guide
Document ID: f4c5fb1d-efb9-4168-9804-5ad3f6f64d06
Document Type: regulatory_guide
Title: Reporting Procedure for Mathematical Models Selected To Predict Heated Effluent Dispersion in Natural Water Bodies
Source: NRC Regulatory Guide Division 4
Source URL: https://www.nrc.gov/docs/ML0037/ML003739535.pdf
Revision Date: 2023-06
Chapter: 
Section ID: RG-4.4
CFR Part: 
CFR Title: 

Content:
l Report No. 75, 1972. 4.4-9 APPENDIX 8 MATHEMATICAL FORMULATION OF THERMAL DISPERSION 1. FWmxmlont SIul-iNo where AU thermal dispersin pbelso as govewed by the basic laws, of moss, moamtum, and eerly conservation and an equation of taMe. Individu models differ in formulation to the extent thdt approximations and usplyfYi aumptos are applied to the et of "equation ezprMS those el If one condden a fluid having velocity components uj 0 a 1, 2, 3) with density p a function of position xj (-1,2, 3), the bade hydrodynamic and thermodynamic equations governing thermal diuu-oW may be written in Cartesion tensor notation as folow6: 1 Caemertion of me at+ ax (B-1) Cemuyatl of mo2entoak a + PUj a8is - 2cokpuJGk L p p + a r,.+2ss where ;A - coefficient of viscosity Eljk- permutation (cyclic) tensor the component of the earth's rotation v.c tor in the k direction p - Pressure - the i component ofamy external fore CAmWatiu of eat mery ( sby) p i (cT) + p9i ± (c,T) axj (kE - pl + 0-) 'S. CNdrs*klbr, "Hydrodymmic and Hydroosuagtic Stablity." Oxford Unlwrdty, Oxford at the Clbendon pr.m, 1961. Tm k @ = specif heat at constant volume coefficient of thermal conductivity VIToUm energy dissipation function The term p(Buj/8xj) represents the increase in internal enerwy due to compression of the fluid. quadon of date If one ipnores the effects on density of dssolved 9"d and restricts attention to temperatures above that of maximum density, an approximate equation of state may be written as P = pO l1 - a(T - TO)N (114) where To = reference temperature at which p = Po a - coefficient of thermal expansion. 2. Conuei agl Equaons with he Boeinaq The derivation of the above equations was quite PM alin that the coefficients x, c, a, k, and the denalty p wer not assuned to be constant. In any pMGacUW situation, however, these quantities are only very sightly tempemture dependent and, with one exception, may be treated a- constants. The one exception is the external force term, pXi, in the