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Caputo Time Fractional Model Based On Generalized Fourier’S And Fick’S Laws For Brinkman-Type Fluid: Exact Solution Via Integral Transform

Author

Listed:
  • SAQIB MURTAZA

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand)

  • ZUBAIR AHMAD

    (��Department of Mathematics and Physics, University of Campania “Luigi Vanvitelli†, Caserta 81100, Italy‡Novel Global Community Educational Foundation, Australia)

  • M. DAHER ALBALWI

    (�Yanbu Industrial College, The Royal Commission for Jubail and Yanbu, Riyadh 30436, Saudi Arabia)

  • Z. AKHTAR

    (�Division of Science and Technology, University of Education, Township, Lahore 54590, Pakistan)

  • MUHAMMAD ASAD KHAN

    (��Department of Mathematics and Physics, University of Campania “Luigi Vanvitelli†, Caserta 81100, Italy)

  • HIJAZ AHMAD

    (��Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia**Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia 99138, Turkey††Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon)

  • DUMITRU BALEANU

    (��†Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon‡‡Institute of Space Sciences, R76900 Magurele-Bucharest, Romania§§Department of Medical Research, China Medical University, Taichung 40402, Taiwan)

Abstract

This paper proposes a new method for the development of the Caputo time fractional model. The method relies on generalized Fourier’s and Fick’ laws to describe the flow behavior of Brinkman-type fluids. An analysis of the free convection flow through a channel is carried out using a new transformation method. This transformation affects fluid energy and concentration equations. The specific governing equations are solved using a Laplace transform and Fourier sine transform. We obtain the solutions of the governing partial differential equations (PDEs) in terms of the Mittag–Leffler function. Mathematical software has been used for both graphical and numerical computation in order to examine the effects of embedded parameters. From graphical and tabular analysis, fractional-order solution provides more than one layer for fluid behavior, thermal, and concentration distribution in the channel. Experimentalists and engineers can choose from many best-fitted layers to compare their data and results. A deviation in the velocity profile’s behavior is also seen for larger values of the Brinkman parameter.

Suggested Citation

  • Saqib Murtaza & Zubair Ahmad & M. Daher Albalwi & Z. Akhtar & Muhammad Asad Khan & Hijaz Ahmad & Dumitru Baleanu, 2023. "Caputo Time Fractional Model Based On Generalized Fourier’S And Fick’S Laws For Brinkman-Type Fluid: Exact Solution Via Integral Transform," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-16.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:10:n:s0218348x23401631
    DOI: 10.1142/S0218348X23401631
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