A fractional model of fluid flow through porous media with mean capillary pressure

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• 作者：Anupama Choudhary^a ; ^{choudhary.anupama9@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Devendra Kumar^b ; ^{devendra.maths@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Jagdev Singh^c ; ^{jagdevsinghrathore@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fluid flow through porous media ; Capillary pressure ; Generalized fractional derivative ; Sumudu transform ; Fourier sine transform ; Mittag-Leffler function
• 刊名：Journal of the Association of Arab Universities for Basic and Applied Sciences
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：21
• 期：Complete
• 页码：59-63
• 全文大小：393 K

文摘

In this paper, we discuss a fractional model arising in flow of two incompatible liquids through homogenous porous media with mean capillary pressure. The solution is derived by the application of the Sumudu transform and the Fourier sine transform. The results are received in compact and graceful forms in terms of the generalized Mittag-Leffler function, which are suitable for numerical computation. The mathematical formulation leads to generalized fractional derivative which has been solved by using a numerical technique by employing the iterative process with the help of appropriate boundary conditions. This problem has great importance in petroleum technology.