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

Kunjan Shah^*, Twinkle Singh

Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Surat, India.

DOI: 10.4236/gep.2015.34004                

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

Conflicts of Interest

The authors declare no conflicts of interest.

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