A Fractional Model for Diffusion Equation Using Generalized Fick??™s Law: Exact Solution with Laplace Transform

Authors

  • Nadeem Ahmad Sheikh Fundamental and Applied Science Department, Universiti Teknologi PETRONAS, Perak 32610, Malaysia
  • Dennis Ling Chuan Ching Fundamental and Applied Science Department, Universiti Teknologi PETRONAS, Perak 32610, Malaysia
  • Ilyas Khan Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia.
  • Afnan Ahmad Civil and Environmental Engineering Department, Universiti Teknologi PETRONAS, Perak 32610, Malaysia
  • Syed Ammad Civil and Environmental Engineering Department, Universiti Teknologi PETRONAS, Perak 32610, Malaysia

DOI:

https://doi.org/10.33959/cuijca.v3i2.28

Abstract

Fractional calculus is the generalization of classical calculus. Many researchers have used different definitions in their studies. The most common definition is Caputo fractional derivatives operator. In this article the concentration equation is converted to fractional form using the generalized Fick??™s law. The fractional partial differential is then transformed with an appropriate transformation. The Laplace and Fourier sine transformations are jointly used to solve the equation. The impact of fractional parameter and Schmidt number is checked on the concentration profile and presented in graphs and tabular form. The results show that diffusion is decreasing with increasing values of Schmidt number.

Author Biography

Nadeem Ahmad Sheikh, Fundamental and Applied Science Department, Universiti Teknologi PETRONAS, Perak 32610, Malaysia

Mr. Nadeem Ahmad Sheikh is Lecturer in Department of Mathematics. His Area of research covers Exact Solutions of fluid flow problems, fractional derivatives, nanofluids, heat and mass transfer, porous media and MHD.

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Published

2020-02-03

How to Cite

Sheikh, N. A., Ching, D. L. C., Khan, I., Ahmad, A., & Ammad, S. (2020). A Fractional Model for Diffusion Equation Using Generalized Fick??™s Law: Exact Solution with Laplace Transform. City University International Journal of Computational Analysis, 3(2), 36–47. https://doi.org/10.33959/cuijca.v3i2.28

Issue

Vol. 3 No. 2: Jul-Dec (2019)

Section

Articles

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Copyright (c) 2020 Nadeem Ahmad Sheikh, Dennis Ling Chuan Ching, Ilyas Khan, Afnan Ahmad, Syed Ammad

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