scholarly journals Different solutions of the diffusion equation and its applications

Author(s):  
Khaled S. M. Essa ◽  
Soad M. Etman ◽  
Maha S. El-Otaify ◽  
M. Embaby ◽  
Ahmed M. Mosallem ◽  
...  

AbstractIn 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.

MAUSAM ◽  
2021 ◽  
Vol 64 (4) ◽  
pp. 655-662
Author(s):  
M.ABDEL WAHAB ◽  
KHALED SMESSA ◽  
M. EMBABY ◽  
SAWSAN EMELSAID

bl 'kks/k i= esa fu"izHkkoh vkSj vfLFkj fLFkfr;ksa esa ØkWliou lekdfyr lkanz.k ysus ds fy, nks fn’kkvksa esa vfHkogu folj.k lehdj.k ¼ADE½ dks gy fd;k x;k gSA ykIykl :ikarj.k rduhd dk mi;ksx rFkk m/okZ/kj Å¡pkbZ ij vk/kkfjr iou xfr vkSj Hkaoj folj.k’khyrk dh leh{kk djrs gq, ;g gy fudkyk x;k gSA blds lkFk gh Hkw&Lrj  vkSj vf/kdre lkanz.kksa dk Hkh vkdyu fd;k x;k gSA geus bl ekWMy esa iwokZuqekfur vkSj izsf{kr lkanz.k vk¡dM+ksa ds e/; rqyuk djus ds fy, dksiugsxu ¼MsuekdZ½ ls fy, x, vkuqHkfod vk¡dM+ksa dk mi;ksx fd;k gSA  The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration in neutral and unstable conditions. The solution is solved using Laplace transformation technique and considering the wind speed and eddy diffusivity depending on the vertical height. Also the ground level and maximum concentrations are estimated. We use in this model empirical data from Copenhagen (Denmark) to compare between predicted and observed concentration data.


2016 ◽  
Vol 38 ◽  
pp. 560 ◽  
Author(s):  
Tiziano Tirabassi ◽  
Davidson Martin Moreira

The settling velocity and deposition of particulate matter on the earth's surface has been introduced in an analytical solution of advection-diffusion equation. The influence of particle diameters in ground level concentration distribution was investigated in function of different atmospheric stability condiyions 


2018 ◽  
Vol 40 ◽  
pp. 69
Author(s):  
Tiziano Tirabassi ◽  
Daniela Buske

After setting realistic scenarios of the wind and diffusivity parameterizations the Ground Level Concentration is worked out by an analytical solution of the advection-diffusion equation, then an explicit approximate expression is provided for it allowing a simple expression for the position and value of the maximum.


2019 ◽  
Author(s):  
Fanhao Meng ◽  
Min Qin ◽  
Ke Tang ◽  
Jun Duan ◽  
Wu Fang ◽  
...  

Abstract. The production of HONO on aerosol surfaces and ground surfaces in urban atmosphere is of interests. However, ground surface measurement commonly in our society is not able to distinguish these two parts. Here, for the first time, we reported high-resolution vertical profile measurements of HONO and NO2 in urban Beijing at night using an incoherent broadband cavity enhanced absorption spectrometer (IBBCEAS) amounted on a movable container which attached to a meteorological tower of 325 m high. The mixing ratios of HONO during one haze episode (E1), the clean episode (C2) and another haze episode (E3) were 4.26 ± 2.08, 0.83 ± 0.65, and 3.54 ± 0.91 ppb, respectively. High-resolution vertical profiles revealed that the vertical distribution of HONO is consistent with stratification and layering in the nocturnal urban atmosphere below 250 m. Direct emissions from combustion processes contributed 51.1 % to ambient HONO concentration at night. The HONO production from the heterogeneous conversion of NO2 on the aerosol surfaces cannot explain HONO vertical measurements at night, indicating that the heterogeneous reaction of NO2 on ground surfaces dominated the nocturnal HONO production. The nocturnal HONO in the boundary layer is primarily derived from the heterogeneous conversion of NO2 at ground level and direct emissions; it is then transported throughout the column by vertical convection. ϕNO2 → HONO, the HONO yield from deposited NO2, is used to evaluate HONO production from the heterogeneous conversion of NO2 at night. The derived ϕNO2 → HONO values on 9 (C2), 10 (C2) and 11 December (E3) were 0.10, 0.08, and 0.09, respectively, indicating a significant production of HONO from heterogeneous reaction of NO2 at ground level. The similar ϕNO2 → HONO values measured during clean and haze episodes suggest that the heterogeneous conversion potential of NO2 at ground level is consistent at night. Furthermore, the dry deposition loss of HONO to the ground surface and vertical mixing effects associated with convection reached a near steady state at midnight on 11–12 December, indicating that significant quantities of HONO are deposited to the ground surface at night, and the ground surface is the source and sink of HONO at night.


2007 ◽  
Vol 22 (1) ◽  
pp. 10-20
Author(s):  
Jonas C. Carvalho ◽  
Davidson M. Moreira

In this article an evaluation of two semi-analytical techniques is carried out, considering the quality and accuracy of these techniques in reproducing the ground-level concentration values of passive pollutant released from low and high sources. The first technique is an Eulerian model based on the solution of the advection-diffusion equation by the Laplace transform technique. The second is a Lagrangian model based on solution of the Langevin equation through the Picard Iterative Method. Turbulence parameters are calculated according to a parameterization capable of generating continuous values in all stability conditions and in all heights of the planetary boundary layer. Numerical simulations and comparisons show a good agreement between predicted and observed concentrations values. Comparisons between the two proposed techniques reveal that Lagrangian model generated more accurate results, but Eulerian model demands a lesser computational time.


MAUSAM ◽  
2021 ◽  
Vol 62 (2) ◽  
pp. 239-244
Author(s):  
KHALEDS.M. ESSA ◽  
FAWZIA MUBARAK

A short range model calculating ground-level concentration from elevated sources is estimated, which realized a Fickian-type formula. Taking the source and mixing height are functions of the wind velocity and eddy diffusivity profiles. The model estimated with an exact solution of the advection diffusion equation is compared with experimental ground level concentrations using meteorological data collected near the ground.


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