Solving of Advection-Diffusion Equation in Three Dimensions in All Stabilities

Essa, Khaled S. M.; Taha, H. M.

doi:10.21608/ejphysics.2023.251868.1094

Solving of Advection-Diffusion Equation in Three Dimensions in All Stabilities

Document Type : Original Article

Authors

Department of Mathematics and Theoretical Physics, Nuclear Research Centre, Egyptian Atomic Energy Authority, Cairo, Egypt.

10.21608/ejphysics.2023.251868.1094

Abstract

In this work the Separation and Laplace transform methods are used to propose model solution for the equation of the Advection-diffusion in the three-dimensions in stable, neutral and unstable conditions (in all stabilities). Considering the mixing height is discretizing into N-sub-layers using the form of wind velocity and vertical turbulence in all stabilities. The wind speed, the lateral and the vertical turbulent diffusivities are considered the vertical height dependent. The inverse of Laplace transform is obtained by Gaussian Quadrature Scheme. The proposed concentrations were calculated using the proposed model in all stabilities. For unstable conditions the proposed concentrations were compared with the first 1st experimental data recorded for radioactive Iodine-135 (I135) of the first reactor at Egyptian Atomic Energy Authority test at Inshas. While, for stable and neutral conditions the proposed concentrations were compared with the second 2nd experimental data of Iodine I-131 (I131) released from the second research reactor. Taking into consideration that Comparing between the proposed model, previous work and observed concentrations of Iodine-135 in unstable, and Iodine-131 in neutral and stable conditions. The results show that there is a good perfect agreement between the proposed and observed isotope concentrations. Also, the statistical techniques show that the existence of a factor of two between the model proposed and the concentrations of the observed isotope. All results are represented by figures and tables.

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