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Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain

Author

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  • Farooq Ahmad

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 55425, Saudi Arabia
    School of Mechanical and Aerospace Engineering, NANYANG Technological University, Singapore 639897, Singapore)

  • A. Othman Almatroud

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 55425, Saudi Arabia)

  • Sajjad Hussain

    (School of Mechanical and Aerospace Engineering, NANYANG Technological University, Singapore 639897, Singapore)

  • Shan E. Farooq

    (Mathematics Department, Govt. College University, Lahore 54000, Punjab, Pakistan)

  • Roman Ullah

    (Department of Computing, Muscat College, Muscat 113, Oman)

Abstract

A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary conditions, the isothermal wall and isoflux boundary. On the basis of porosity of medium, similarity functions are utilized to avail a set of ordinary differential equations. The non-linear coupled ODE’s have been solved with a very stable and reliable numerical scheme that involves Simpson’s Rule and Successive over Relaxation method. The accuracy of the results is improved by making iterations on three different grid sizes and higher order accuracy in the results is achieved by Richardson extrapolation. This study provides realistic and differentiated results with due considerations of micropolar fluid theory. The micropolar material parameters demonstrated reduction in the bulk fluid speed, thermal distribution and skin friction coefficient but increase in local heat transfer rate and couple stress. The spin behavior of microstructures is also exhibited through microrotation vector N ( η ) .

Suggested Citation

  • Farooq Ahmad & A. Othman Almatroud & Sajjad Hussain & Shan E. Farooq & Roman Ullah, 2020. "Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain," Mathematics, MDPI, vol. 8(5), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:854-:d:362504
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    References listed on IDEAS

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    1. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    2. M. Dayyan & S. M. Seyyedi & G. G. Domairry & M. Gorji Bandpy, 2013. "Analytical Solution of Flow and Heat Transfer over a Permeable Stretching Wall in a Porous Medium," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-10, September.
    3. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    4. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    5. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 1.
    6. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    7. Kartini Ahmad & Anuar Ishak & Roslinda Nazar, 2013. "Micropolar Fluid Flow and Heat Transfer over a Nonlinearly Stretching Plate with Viscous Dissipation," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-5, June.
    8. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    9. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
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