Application of Special Functions in One Dimensional Advective Diffusion Problem

F.Y.Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V61P519

International Journal of Mathematics Trends and Technology

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Volume 61 | Number 2 | Year 2018 | Article Id. IJMTT-V61P519 | DOI : https://doi.org/10.14445/22315373/IJMTT-V61P519

Application of Special Functions in One Dimensional Advective Diffusion Problem

F.Y.Ayant

Abstract

In the present paper, we construct an one dimensional advective diffusion model problem to evaluate the substance concentration distribution along x-axis between x=-1 and x=1. Here, the diffusivity of the substance and the velocity of the solvent flow are both considered as a variable. Kumar and Satyarth [6] use the product of the class of multivariable polynomials and the multivariable H-function defined here to obtain the analytic solution. Then, we employ the product of the generalized hypergeometric function, class of multivariable polynomials and the multivariable Gimel-function to obtain an analytic formula of our problem. Finally, some particular cases will be given.

Keywords

Multivariable Aleph-function, , classes of multivariable polynomials, generalized hypergeometric function, advective-diffusion model problem, expansion formula, multivariable Gimel-function.

References

[1] Ayant F.Y. An integral associated with the Aleph-functions of several variables. International Journal of Mathematics Trends and Technology (IJMTT). 2016 Vol 31 (3), page 142-154.
[2] F.Y .Ayant, Some transformations and idendities form multivariable Gimel-function, International Journal of Matematics and Technology (IJMTT), 59(4) (2018), 248-255
[3] B.L.J. Braaksma, Asymptotics expansions and analytic continuations for a class of Barnes-integrals, Compositio Math. 15 (1962-1964), 239-341
[4] S.R. Hanna et .al. Review of atmospheric diffusion models for regulatory applications, WMO Tech. Note no. 1777, WMO, Geneva, 1982, 37.
[5] R.M. Harisson R.M. Perry R.Handbook of air pollution analysis, 2nd edn. Chapman and Hall and Methuen, New York, 1986
[6] H. Kumar and P.S.Y. Satyarth. Application of Generalized Polynomials of Several Variables and Multivariable HFunction in one Dimensional Advective Diffusion Problem. Bull. Pure. Appl. Math. Vol 4, no 2, 2010, page 353-362.
[7] T.J.Lyons and W.D. Scott, Principles of Air Pollution Meteorology, CBS. Publisher and Distributers (P) LTD, New Delhi, 1992.
[8] Y.N. Prasad, Multivariable I-function , Vijnana Parisha Anusandhan Patrika 29 (1986), 231-237.
[9] J. Prathima, V. Nambisan and S.K. Kurumujji, A Study of I-function of Several Complex Variables, International Journal of Engineering Mathematics Vol (2014), 1-12.
[10] E.D. Rainville, Specials functions. Mac Millan Co. New York 1960; Reprinted Chelsea Publ. Co Bronx. New York, 1971.
[11] Srivastava H.M. A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177(1985), page 183-191.
[12] Srivastava H.M. and Panda R. Some expansion theorems and generating relations for the H-function of several complex variables. Comment. Math. Univ. St. Paul. 24(1975), page.119-137.
[13] Srivastava H.M. and Panda R. Some expansion theorems and generating relations for the H-function of several complex variables II. Comment. Math. Univ. St. Paul. 25(1976), page.167-197.
[14] H.M. Srivastava and N.P. Singh, The integration of certains products of the multivariable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo. 32(2)(1983), 157-187.

Citation :

F.Y.Ayant, "Application of Special Functions in One Dimensional Advective Diffusion Problem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 61, no. 2, pp. 133-141, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V61P519