Analytical Solutions of the Advection–Diffusion Equation with Variable Vertical Eddy Diffusivity and Wind Speed Using Hankel Transform

Essa, Khaled S. M.; Shalaby, Aly; E., Ibrahim, Mahmoud A.; Mosallem, A. M.

doi:10.1007/s00024-020-02496-y

Cited by 9 publications

(10 citation statements)

References 21 publications

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“…( 12), one obtains: Equation (13) becomes: where Equation ( 14) becomes: where F 0 is a constant. Then, the solution in the neutral case was obtained as follows: (11) Taking where x dn is the decay distance of pollutant in neutral condition. Equation (17) becomes: Now, F 0 can be determined by using the formula:…”

Section: For Neutral Conditionsmentioning

confidence: 99%

“…Heines and Peters [16], and Bennett [3] investigated the physical effect of model for the dry deposition of pollutants to a rough surface. Recently, Essa et al [11,12] estimated the solution of the advection-diffusion equation in two dimensions with variable vertical eddy diffusivity and wind speed using Hankel transform. Also, Essa et al [11,12] found the solution of advection-diffusion equation in three dimensions using Hankel transform.…”

Section: Introductionmentioning

confidence: 99%

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Different solutions of the diffusion equation and its applications

Essa

Etman

El-Otaify

et al. 2021

Beni-Suef Univ J Basic Appl Sci

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In this report, we solved the advection–diffusion equation under pollutants deposition on the ground surface, taking wind speed and vertical diffusion depend on the vertical height. Also, we estimated a simple diffusion model from point source in an urban atmosphere and the conservative material with downwind was evaluated. Then, we calculated the extreme ground-level concentration as a function of stack height and plume rise in two cases. Comparison between the proposed models and the emission from the Egyptian Atomic Research Reactor at Inshas had been done. Lastly, we discussed the results in this report.

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Section: For Neutral Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Different solutions of the diffusion equation and its applications

Essa

Etman

El-Otaify

et al. 2021

Beni-Suef Univ J Basic Appl Sci

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“…The horizontal and vertical dispersion parameters, respectively σy and σz that represent the turbulent parameterization key in this approach, once they contain the physical ingredients that describe the dispersion process and, consequently, express the spatial extent of the contaminant plume under the effect of the turbulent motion in the Planetary Boundary Layer (PBL) [7]. The solution was presented by Essa [8] for the advection-diffusion with variable vertical eddy-diffusivity and wind-speed parameters using the Hankel-transform to get the integrated cross-wind concentration. This work introduced the instantaneous and continuous sources as (I) point, (II) line, and (III) area sources.…”

Section: Introductionmentioning

confidence: 99%

Studying the Effect of the Instantaneous and Continuous Pollutants Sources on the Advection-diffusion Equation and Its Applications

Essa,

El Saied,

Wheida

et al. 2024

Iraqi Journal of Science

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This study investigates instantaneous and continuous sources as point, line, and area sources. Gaussian concentration in the case of the puff model with an instantaneous point source inhomogeneous longitudinal diffusion is investigated. The concentration is calculated using different dispersion parameters to get the proposed normalized concentration of the puff model at ground level around the centerline, which is compared with observed data by the Copenhagen experiment and previous work [1]. Also, the continuous point source is used to get the Gaussian plume model in three dimensions using dispersion parameters to compare with the observed concentration data measured by the Egyptian Atomic Energy Authority for Iodine-135 (I135) in an unstable condition.

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“…Advection-diffusion equation in three-dimensional with Steady state was solved using Fourier transform considering vertical turbulent diffusivity was as function of linear downwind distance and constant wind speed to obtain a normalized crosswind integrated concentration [1]. Also, the above problem was obtained by assuming that the vertical turbulent diffusivity was as function of power law of vertical height [2]. Semi-analytical model for coupled multispecies adjective-dispersive transport subject to rate-limited had been studied [3].…”

Section: Introductionmentioning

confidence: 99%

Solving of Advection-Diffusion Equation in Three Dimensions in all stabilities

Essa,

Taha

2023

Egypt. J. Physics

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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 (I 135 ) 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 (I 131 ) 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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Analytical Solutions of the Advection–Diffusion Equation with Variable Vertical Eddy Diffusivity and Wind Speed Using Hankel Transform

Cited by 9 publications

References 21 publications

Different solutions of the diffusion equation and its applications

Different solutions of the diffusion equation and its applications

Studying the Effect of the Instantaneous and Continuous Pollutants Sources on the Advection-diffusion Equation and Its Applications

Solving of Advection-Diffusion Equation in Three Dimensions in all stabilities

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