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The Solution of Backward Heat Conduction Problem with Piecewise Linear Heat Transfer Coefficient

Author

Listed:
  • Yang Yu

    (School of Automation, Shenyang Aerospace University, Shenyang 110136, China)

  • Xiaochuan Luo

    (College of Information Science and Engineering, Northeastern University, Shenyang 110819, China)

  • Huaxi (Yulin) Zhang

    (LTI Lab., University of Picardie Jules Verne, Saint-Quentin 02100, France)

  • Qingxin Zhang

    (School of Automation, Shenyang Aerospace University, Shenyang 110136, China)

Abstract

In the fields of continuous casting and the roll stepped cooling, the heat transfer coefficient is piecewise linear. However, few papers discuss the solution of the backward heat conduction problem in this situation. Therefore, the aim of this paper is to solve the backward heat conduction problem, which has the piecewise linear heat transfer coefficient. Firstly, the ill-posed of this problem is discussed and the truncated regularized optimization scheme is introduced to solve this problem. Secondly, because the regularization parameter is the key factor for the regularization method, this paper presents an improved method for choosing the regularization parameter to reduce the iterative number and proves the fourth-order convergence of this method. Furthermore, the numerical simulation experiments show that, compared with other methods, the improved method of fourth-order convergence effectively reduces the iterative number. Finally, the truncated regularized optimization scheme is used to estimate the initial temperature, and the results of numerical simulation experiments illustrate that the inverse values match the exact values very well.

Suggested Citation

  • Yang Yu & Xiaochuan Luo & Huaxi (Yulin) Zhang & Qingxin Zhang, 2019. "The Solution of Backward Heat Conduction Problem with Piecewise Linear Heat Transfer Coefficient," Mathematics, MDPI, vol. 7(5), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:388-:d:226741
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    References listed on IDEAS

    as
    1. Su, LingDe, 2019. "A radial basis function (RBF)-finite difference (FD) method for the backward heat conduction problem," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 232-247.
    2. Liu, Xuan & Qian, Zhongmin, 2018. "Backward problems for stochastic differential equations on the Sierpinski gasket," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3387-3418.
    3. Reddy, G.D., 2019. "A class of parameter choice rules for stationary iterated weighted Tikhonov regularization scheme," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 464-476.
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    Cited by:

    1. Minghao Hu & Lihua Wang & Fan Yang & Yueting Zhou, 2023. "Weighted Radial Basis Collocation Method for the Nonlinear Inverse Helmholtz Problems," Mathematics, MDPI, vol. 11(3), pages 1-29, January.
    2. Joseph M. Cabeza-Lainez & Francisco Salguero-Andújar & Inmaculada Rodríguez-Cunill, 2022. "Prevention of Hazards Induced by a Radiation Fireball through Computational Geometry and Parametric Design," Mathematics, MDPI, vol. 10(3), pages 1-20, January.

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