A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method

Twinkle  Singh; Kunjan  Shah

doi:10.4236/gep.2015.34004

GEP Vol.3 No.4 , June 2015

A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method

Author(s) Kunjan Shah^*, Twinkle Singh

Affiliation(s)
Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Surat, India.

Abstract
The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.

Keywords
Longitudinal Dispersion Phenomenon, Porous Media, New Integral Transform, Homotopy Perturbation Method

Cite this paper
Shah, K. and Singh, T. (2015) A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method. Journal of Geoscience and Environment Protection, 3, 24-30. doi: 10.4236/gep.2015.34004.

References

[1] Bear, J. (1972) Dynamics of Fluids in Porous Media. Dover Publications, New York.

[2] Bernard, R.A. and Wilhelm, R.H. (1950) Turbulent Diffusion in Fixed Beds of Packed Solids. Chemical Engineering Progress, 46, 233-244.

[3] Kovo, A.S. (2008) Mathematical Modelling and Simulation of Dispersion in a Nonideal Plug Flow Reactor. Journal of Dispersion Science and Technology, 29, 1129-1134.
http://dx.doi.org/10.1080/01932690701817859

[4] Ebach, E. and White, R. (1958) Mixing of Fluids Flowing through Beds of Packed Solids. AIChE, 4, 161-169.
http://dx.doi.org/10.1002/aic.690040209

[5] Hunt, B. (1978) Dispersion Calculations in Nonuniform Seepage. Journal of Hydrology, 36, 261-277.
http://dx.doi.org/10.1016/0022-1694(78)90148-8

[6] Patel, T. and Mehta, M.N. (2005) A Solution of Burger’s Equation for Longitudinal Dispersion of Miscible Fluid Flow through Porous Media. Indian Journal of Petroleum Geology, 14, 49-54.

[7] Meher, R.K. and Mehta, M.N. (2010) Adomian Decomposition Method for Dispersion Phenomenon Arising in Longitudinal Dispersion of Miscible Fluid Flow through Porous Media. Advances in Theoretical and Applied Mechanics, 3, 211-220.

[8] Kashuri, A. and Fundo, A. (2013) A New Integral Transform. Advances in Theoretical and Applied Mathematics, 8, 27-43.
http://www.i-scholar.in/index.php/atam/article/view/39052

[9] Pelageia Iakovlevna Polubarinova-Koch (1962) Theory of Ground Water Movement. Princeton University Press, Princeton.

[10] Mehta, M.N. and Patel, T. (2006) A Solution of Burger’s Equation Type One Dimensional Ground Water Recharge by Spreading in Porous Media. Journal of the Indian Academy of Mathematics, 28, 25-32.