IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v14y2021i12p3396-d571571.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/14/12/3396/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1996-1073/14/12/3396/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Wang, Kun & Wang, Hongyue, 2018. "Stability and error estimates of a new high-order compact ADI method for the unsteady 3D convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 140-159.
    3. Noor Saeed Khan & Taza Gul & Poom Kumam & Zahir Shah & Saeed Islam & Waris Khan & Samina Zuhra & Arif Sohail, 2019. "Influence of Inclined Magnetic Field on Carreau Nanoliquid Thin Film Flow and Heat Transfer with Graphene Nanoparticles," Energies, MDPI, vol. 12(8), pages 1-20, April.
    4. Matthias Ehrhardt & Ronald E. Mickens, 2008. "A Fast, Stable And Accurate Numerical Method For The Black–Scholes Equation Of American Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 471-501.
    5. Das, Abhishek & Natesan, Srinivasan, 2015. "Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 168-186.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Anuar Jamaludin & Roslinda Nazar & Ioan Pop, 2019. "Mixed Convection Stagnation-Point Flow of a Nanofluid Past a Permeable Stretching/Shrinking Sheet in the Presence of Thermal Radiation and Heat Source/Sink," Energies, MDPI, vol. 12(5), pages 1-20, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kau, James B. & Keenan, Donald C., 1999. "Patterns of rational default," Regional Science and Urban Economics, Elsevier, vol. 29(6), pages 765-785, November.
    2. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    3. Jun, Doobae & Ku, Hyejin, 2015. "Static hedging of chained-type barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 317-327.
    4. Vorst, A. C. F., 1988. "Option Pricing And Stochastic Processes," Econometric Institute Archives 272366, Erasmus University Rotterdam.
    5. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    6. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    7. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    8. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2003. "Are convertible bonds underpriced? An analysis of the French market," Journal of Banking & Finance, Elsevier, vol. 27(4), pages 635-653, April.
    9. Sergio Zúñiga, 1999. "Modelos de Tasas de Interés en Chile: Una Revisión," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 36(108), pages 875-893.
    10. Zhijian (James) Huang & Yuchen Luo, 2016. "Revisiting Structural Modeling of Credit Risk—Evidence from the Credit Default Swap (CDS) Market," JRFM, MDPI, vol. 9(2), pages 1-20, May.
    11. José Martins & Rui Cunha Marques & Carlos Oliveira Cruz & Álvaro Fonseca, 2017. "Flexibility in planning and development of a container terminal: an application of an American-style call option," Transportation Planning and Technology, Taylor & Francis Journals, vol. 40(7), pages 828-840, October.
    12. Marcelo F. Perillo, 2021. "Valuación de Títulos de Deuda Indexados al Comportamiento de un Índice Accionario: Un Modelo sin Riesgo de Crédito," CEMA Working Papers: Serie Documentos de Trabajo. 784, Universidad del CEMA.
    13. Kartono, Agus & Solekha, Siti & Sumaryada, Tony & Irmansyah,, 2021. "Foreign currency exchange rate prediction using non-linear Schrödinger equations with economic fundamental parameters," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    14. Jochen Bigus, 2002. "Investitionsanreize, Koalitionsverhalten und Gläubigerkonflikte," Schmalenbach Journal of Business Research, Springer, vol. 54(4), pages 317-342, June.
    15. Kim, Amy M. & Li, Huanan, 2020. "Incorporating the impacts of climate change in transportation infrastructure decision models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 134(C), pages 271-287.
    16. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    17. Wang, Jun & Liang, Jin-Rong & Lv, Long-Jin & Qiu, Wei-Yuan & Ren, Fu-Yao, 2012. "Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 750-759.
    18. George W. Kutner & James A. Seifert, 1989. "The Valuation of Mortgage Loan Commitments Using Option Pricing Estimates," Journal of Real Estate Research, American Real Estate Society, vol. 4(2), pages 13-20.
    19. Hilscher, Jens & Raviv, Alon, 2014. "Bank stability and market discipline: The effect of contingent capital on risk taking and default probability," Journal of Corporate Finance, Elsevier, vol. 29(C), pages 542-560.
    20. Andres, Christian & Cumming, Douglas & Karabiber, Timur & Schweizer, Denis, 2014. "Do markets anticipate capital structure decisions? — Feedback effects in equity liquidity," Journal of Corporate Finance, Elsevier, vol. 27(C), pages 133-156.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:14:y:2021:i:12:p:3396-:d:571571. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.