Asymptotic behavior of the solution to a convection-diffusion problem with bulk chemical reaction in the wake of a particle
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 5, pp. 834-847 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of steady convective mass transfer between a particle and a continuum with a nonlinear bulk chemical reaction is considered for the case when the Peclet number $\operatorname{Pe}$ and the rate constant $k_\nu$ of the reaction tend to infinity. An asymptotic solution with respect to a small parameter $\varepsilon= \operatorname{Pe}^{-1/3}$ is obtained in the wake of the particle.
@article{ZVMMF_2006_46_5_a5,
     author = {R. G. Akhmetov},
     title = {Asymptotic behavior of the solution to a~convection-diffusion problem with bulk chemical reaction in the wake of a~particle},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {834--847},
     year = {2006},
     volume = {46},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_5_a5/}
}
TY  - JOUR
AU  - R. G. Akhmetov
TI  - Asymptotic behavior of the solution to a convection-diffusion problem with bulk chemical reaction in the wake of a particle
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 834
EP  - 847
VL  - 46
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_5_a5/
LA  - ru
ID  - ZVMMF_2006_46_5_a5
ER  - 
%0 Journal Article
%A R. G. Akhmetov
%T Asymptotic behavior of the solution to a convection-diffusion problem with bulk chemical reaction in the wake of a particle
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 834-847
%V 46
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_5_a5/
%G ru
%F ZVMMF_2006_46_5_a5
R. G. Akhmetov. Asymptotic behavior of the solution to a convection-diffusion problem with bulk chemical reaction in the wake of a particle. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 5, pp. 834-847. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_5_a5/

[1] Levin V. G., Fiziko-khimicheskaya gidrodinamika, Fizmatgiz, M., 1959

[2] Astarita Dzh., Massoperedacha s khimicheskoi reaktsiei, Khimiya, L., 1971

[3] Dankverts P. V., Gazozhidkostnye reaktsii, Khimiya, M., 1973

[4] Frank-Kamenetskii D. A., Diffuziya i teploperedacha v khimicheskoi kinetike, Nauka, M., 1967

[5] Acrivos A., Taylor T. D., “Heat and mass transfer from single spheres in Stokes flow”, Phys. Fluids, 5:4 (1962), 378–394 | DOI | MR

[6] Sih P. H., Newman J., “Mass transfer to the rear of a sphere in Stokes flow”, Internat. J. Heat Mass Transfer., 10:12 (1967), 1749–1756 | DOI

[7] Krylov B. C., “Diffuzionnyi pogranichnyi sloi na poverkhnosti dvizhuscheisya kapli pri nalichii ob'emnoi khimicheskoi reaktsii”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1967, no. 1, 146–149

[8] Zhivotyagin A. F., “Vliyanie gomogennoi khimicheskoi reaktsii na raspredelenie kontsentratsii v diffuzionnom slede kapli”, Vestn. MGU. Ser. 1. Matem. i mekhan., 1980, no. 6, 73–78 | MR

[9] Gupalo Yu. P., Polyanin A. D., Ryazantsev Yu. S., Massoteploobmen reagiruyuschikh chastits s potokom, Nauka, M., 1985

[10] Akhmetov R. G., “Metod soglasovaniya v zadache o diffuzii k chastitse”, Matem. zametki, 47:5 (1990), 144–146 | MR | Zbl

[11] Akhmetov R. T., “Asimptotika resheniya singulyarno vozmuschennoi zadachi dlya uravneniya diffuzii v okrestnosti sedlovoi tochki u predelnogo operatora”, Dokl. RAN, 362:6 (1998), 727–728 | MR | Zbl

[12] Akhmetov R. G., “Asimptotika resheniya zadachi konvektivnoi diffuzii okolo sfery”, Zh. vychisl. matem. i matem. fiz., 38:5 (1998), 801–806 | MR | Zbl

[13] Van-Daik M., Metody vozmuschenii v mekhanike zhidkosti, Mir, M., 1967

[14] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[15] Khappel Dzh., Brenner G., Gidrodinamika pri malykh chislakh Reinoldca, Mir, M., 1976

[16] Akhmetov R. G., “Asimptotika resheniya zadachi o konvektivnoi diffuzii s ob'emnoi khimicheskoi reaktsiei”, Zh. vychisl. matem. i matem. fiz., 42:10 (2002), 1600–1608 | MR | Zbl

[17] Smirnova G. N., “Lineinye parabolicheskie uravneniya, vyrozhdayuschiesya na granitse oblasti”, Sibirskii matem. zhurnal, 4:2 (1963), 343–358 | MR | Zbl

[18] Akhmetov R. G., “Asimptotika resheniya odnoi zadachi konvektivnoi diffuzii s dvumya parametrami”, Differents. ur-niya, Tr. mezhdunar. konf. “Kompleksnyi analiz, differents. ur-niya i smezhnye voprosy”. II, In-t matem. s vychisl. tsentrom RAN, Ufa, 2000, 10–15

[19] Akhmetov R. G., “Asimptotika resheniya kraevoi zadachi dlya odnogo uravneniya s malym parametrom”, Differents. ur-niya s malym parametrom, In-t matem. i mekhan. UrNTs AN SSSR, Sverdlovsk, 1984, 3–17

[20] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1976 | MR

[21] Sutton W. G. L., “On the equation of diffusion in a turbulent medium”, Proc. Roy. Soc. Ser. A, 182:988 (1943), 48–75 | DOI | MR | Zbl

[22] Ilin A. M., “Asimptotika resheniya kraevoi zadachi dlya uravneniya Puassona vne tsilindra i vne polutsilindra”, Matem. sb., 118:2 (1982), 184–202 | MR

[23] Akhmetov R. G., “Asimptotika resheniya kraevoi zadachi dlya odnogo uravneniya diffuzii v poluploskosti”, Differents. ur-niya, 19:2 (1983), 287–194 | MR

[24] Akhmetov R. G., Asimptotika resheniya kraevoi zadachi dlya ellipticheskogo uravneniya v poluploskosti, Dep. V VINITI 16.06.86,4416-V 86, 19 pp.

[25] Rakitskii Yu. V., Ustinov S. M., Chernorutskii I. G., Chislennye metody resheniya zhestkikh sistem, Nauka, M., 1979 | MR

[26] Babenko K. I., Osnovy chislennogo analiza, NITs “Regulyarnaya i khaotich. dinamika”, M., Izhevsk, 2002

[27] Akhmetov V. R., Akhmetov R. G., Zagidullina A. B., “Suschestvovanie i asimptotiki reshenii odnogo klassa kvazilineinykh obyknovennykh differentsialnykh uravnenii vtorogo poryadka”, Differents. ur-niya, 41(46) (2005), 723–729 | MR | Zbl