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An Explicit Fourth-Order Compact Numerical Scheme for Heat Transfer of Boundary Layer Flow

Author

Listed:
  • Yasir Nawaz

    (Department of Mathematics, Air University Islamabad, PAF Complex E-9, Islamabad Capital Territory 44000, Pakistan)

  • Muhammad Shoaib Arif

    (Department of Mathematics, Air University Islamabad, PAF Complex E-9, Islamabad Capital Territory 44000, Pakistan)

  • Wasfi Shatanawi

    (Department of Mathematics and General Sciences, Prince Sultan University Riyadh, Riyadh 12435, Saudi Arabia
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics, Hashemite University, Zarqa 13115, Jordan)

  • Amna Nazeer

    (Department of Mathematics, Comsats University, Islamabad Capital Territory 45550, Pakistan)

Abstract

The main contribution of this article is to propose a compact explicit scheme for solving time-dependent partial differential equations (PDEs). The proposed explicit scheme has an advantage over the corresponding implicit compact scheme to find solutions of nonlinear and linear convection–diffusion type equations because the implicit existing compact scheme fails to obtain the solution. In addition, the present scheme provides fourth-order accuracy in space and second-order accuracy in time, and is constructed on three grid points and three time levels. It is a compact multistep scheme and conditionally stable, while the existing multistep scheme developed on three time levels is unconditionally unstable for parabolic and considered a type of equations. The mathematical model of the heat transfer in a mixed convective radiative fluid flow over a flat plate is also given. The convergence conditions of dimensionless forms of these equations are given, and also the proposed scheme solves equations, and results are compared with two existing schemes. It is hoped that the results in the current report are a helpful source for future fluid-flow studies in an industrial environment in an enclosure area.

Suggested Citation

  • Yasir Nawaz & Muhammad Shoaib Arif & Wasfi Shatanawi & Amna Nazeer, 2021. "An Explicit Fourth-Order Compact Numerical Scheme for Heat Transfer of Boundary Layer Flow," Energies, MDPI, vol. 14(12), pages 1-17, June.
  • Handle: RePEc:gam:jeners:v:14:y:2021:i:12:p:3396-:d:571571
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    References listed on IDEAS

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    Cited by:

    1. Yasir Nawaz & Muhammad Shoaib Arif & Kamaleldin Abodayeh & Mairaj Bibi, 2022. "Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer," Energies, MDPI, vol. 15(13), pages 1-22, June.
    2. Magdalena Piasecka & Krzysztof Dutkowski, 2022. "Novel Numerical Methods in Heat and Mass Transfer," Energies, MDPI, vol. 15(7), pages 1-3, April.
    3. Yasir Nawaz & Muhammad Shoaib Arif & Wasfi Shatanawi & Mairaj Bibi, 2022. "A New Explicit Numerical Schemes for Time-Dependent PDEs with Application to Pressure Driven Fluid Flow in a Rectangular Duct," Energies, MDPI, vol. 15(14), pages 1-22, July.

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