IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v14y2021i17p5512-d628691.html
   My bibliography  Save this article

Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach

Author

Listed:
  • Slawomir Blasiak

    (Department of Manufacturing Engineering and Metrology, Faculty of Mechatronics and Mechanical Engineering, Kielce University of Technology, Aleja Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland)

Abstract

This article presents a variable-order derivative (VOD) time fractional model for describing heat transfer in the rotor or stator in non-contacting mechanical face seals. Most theoretical studies so far have been based on the classical equation of heat transfer. Recently, constant-order derivative (COD) time fractional models have also been used. The VOD time fractional model considered here is able to provide adequate information on the heat transfer phenomena occurring in non-contacting face seals, especially during the startup. The model was solved analytically, but the characteristic features of the model were determined through numerical simulations. The equation of heat transfer in this model was analyzed as a function of time. The phenomena observed in the seal include the conduction of heat from the fluid film in the gap to the rotor and the stator, followed by convection to the fluid surrounding them. In the calculations, it is assumed that the working medium is water. The major objective of the study was to compare the results of the classical equation of heat transfer with the results of the equations involving the use of the fractional-order derivative. The order of the derivative was assumed to be a function of time. The mathematical analysis based on the fractional differential equation is suitable to develop more detailed mathematical models describing physical phenomena.

Suggested Citation

  • Slawomir Blasiak, 2021. "Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach," Energies, MDPI, vol. 14(17), pages 1-13, September.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:17:p:5512-:d:628691
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/14/17/5512/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/14/17/5512/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Songshu Liu & Lixin Feng, 2020. "An Inverse Problem for a Two-Dimensional Time-Fractional Sideways Heat Equation," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, March.
    2. Y. Z. Povstenko, 2014. "Fundamental Solutions to Time-Fractional Advection Diffusion Equation in a Case of Two Space Variables," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, March.
    3. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
    4. Jiang, Xiaoyun & Xu, Mingyu, 2010. "The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3368-3374.
    5. Koca, Ilknur, 2019. "Modeling the heat flow equation with fractional-fractal differentiation," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 83-91.
    6. Y. Z. Povstenko, 2012. "Axisymmetric Solutions to Time-Fractional Heat Conduction Equation in a Half-Space under Robin Boundary Conditions," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-13, August.
    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. Andrei Zoltan Farkas & Veronica Argeșanu & Beniamin Boșcai & Denisa Abrudan, 2022. "Maintenance Cycle Reduction Time and Energy Savings of Mechanical Face Seals Using Thermodynamic FEM Analysis," Energies, MDPI, vol. 15(24), pages 1-22, December.
    2. Li, Nan & Wang, Xiaoping & Xu, Huanying & Qi, Haitao, 2024. "Numerical study on radiative MHD flow of viscoelastic fluids with distributed-order and variable-order space fractional operators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 291-305.
    3. Artur S. Bartosik, 2022. "Numerical Heat Transfer and Fluid Flow: A Review of Contributions to the Special Issue," Energies, MDPI, vol. 15(8), pages 1-8, April.

    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. Richard L. Magin & Ervin K. Lenzi, 2021. "Slices of the Anomalous Phase Cube Depict Regions of Sub- and Super-Diffusion in the Fractional Diffusion Equation," Mathematics, MDPI, vol. 9(13), pages 1-29, June.
    2. Virginia Kiryakova & Jordanka Paneva-Konovska, 2024. "Going Next after “A Guide to Special Functions in Fractional Calculus”: A Discussion Survey," Mathematics, MDPI, vol. 12(2), pages 1-39, January.
    3. Edgardo Alvarez & Carlos Lizama, 2020. "The Super-Diffusive Singular Perturbation Problem," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    4. Sweilam, N.H. & El-Sakout, D.M. & Muttardi, M.M., 2020. "Numerical study for time fractional stochastic semi linear advection diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Ravi Agarwal & Snezhana Hristova & Donal O’Regan & Peter Kopanov, 2020. "p -Moment Mittag–Leffler Stability of Riemann–Liouville Fractional Differential Equations with Random Impulses," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    6. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    7. Praveendra Singh & Madhu Jain, 2024. "Inventory policy for degrading items under advanced payment with price and memory sensitive demand using metaheuristic techniques," Operational Research, Springer, vol. 24(3), pages 1-34, September.
    8. Rakesh K. Parmar, 2015. "A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus," Mathematics, MDPI, vol. 3(4), pages 1-14, November.
    9. Nikolai Leonenko & Ely Merzbach, 2015. "Fractional Poisson Fields," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 155-168, March.
    10. Angstmann, C.N. & Henry, B.I. & Jacobs, B.A. & McGann, A.V., 2017. "A time-fractional generalised advection equation from a stochastic process," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 175-183.
    11. Xiong, Xiangtuan & Xue, Xuemin, 2019. "A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 292-303.
    12. Soma Dhar & Lipi B. Mahanta & Kishore Kumar Das, 2019. "Formulation Of The Simple Markovian Model Using Fractional Calculus Approach And Its Application To Analysis Of Queue Behaviour Of Severe Patients," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 117-129, March.
    13. Saif Eddin Jabari & Nikolaos M. Freris & Deepthi Mary Dilip, 2020. "Sparse Travel Time Estimation from Streaming Data," Transportation Science, INFORMS, vol. 54(1), pages 1-20, January.
    14. Katarzyna Górska & Andrzej Horzela, 2021. "Non-Debye Relaxations: Two Types of Memories and Their Stieltjes Character," Mathematics, MDPI, vol. 9(5), pages 1-13, February.
    15. Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
    16. Goswami, Koushik, 2021. "Work fluctuations in a generalized Gaussian active bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    17. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2021. "Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model," Mathematics, MDPI, vol. 9(7), pages 1-34, March.
    18. Virginia Kiryakova, 2021. "A Guide to Special Functions in Fractional Calculus," Mathematics, MDPI, vol. 9(1), pages 1-40, January.
    19. Murat A. Sultanov & Durdimurod K. Durdiev & Askar A. Rahmonov, 2021. "Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential Equation," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    20. Kassim, Mohammed D. & Tatar, Nasser-eddine, 2021. "Nonlinear fractional distributed Halanay inequality and application to neural network systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

    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:17:p:5512-:d:628691. 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.