Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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ANALYSIS OF NON-INTEGER ORDER THERMOELASTIC TEMPERATURE DISTRIBUTION AND THERMAL DEFLECTION OF THIN HOLLOW CIRCULAR DISK UNDER THE AXI-SYMMETRIC HEAT SUPPLY

  • KHAVALE, SATISH G. (PG DEPARTMENT OF MATHEMATICS, NES, SCIENCE COLLEGE) ;
  • GAIKWAD, KISHOR R. (PG DEPARTMENT OF MATHEMATICS, NES, SCIENCE COLLEGE)
  • Received : 2021.10.12
  • Accepted : 2022.03.04
  • Published : 2022.03.25
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Abstract

Analysis of non-integer order thermoelastic temperature distribution and it's thermal deflection of thin hollow circular disk under the axi-symmetric heat supply is investigated. Initially, the disk is kept at zero temperature. For t > 0 the parametric surfaces are thermally insulated and axi-symmetric heat supply on the thickness of the disk. The governing heat conduction equation has been solved by integral transform technique, including Mittag-Leffler function. The results have been computed numerically and illustrated graphically with the help of PTC-Mathcad.

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Acknowledgement

The authors are grateful thanks to Chhatrapati Shahu Maharaj Research, Training and Human Development Institute (SARTHI) for awarding the Chief Minister Special Research Fellowiship - 2019 (CMSRF - 2019). ORCID ID: 0000-0003-3551-301X

References

  1. M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys, 27 (1956), 240-253. https://doi.org/10.1063/1.1722351
  2. H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15 (1967), 299-307. https://doi.org/10.1016/0022-5096(67)90024-5
  3. M. Ishihara, Y. Tanigawa, R. Kawamura, N. Noda, Theoretical analysis of thermoelastoplastic deformation of a circular plate due to a partially distributed heat supply, Journal of Thermal stresses, 20 (1997), 203-225. https://doi.org/10.1080/01495739708956099
  4. A. Kar and M. Kanoria, Generalized thermoelasticity problem of a hollow sphere under thermal shock, European Journal of Pure and Applied Mathematics, 2 (2009), 125-146.
  5. K. R. Gaikwad and K. P. Ghadle, On the steady-state thermoelastic problem for a finite length hollow cylinder, International Journal of Mathematics, 1 (2009), 31-38.
  6. K. R. Gaikwad and K. P. Ghadle, Quasi-static thermoelastic problem of an infinitely long circular cylinder, Journal of the Korean Society for Industrial and Applied Mathematics, 14 (2010), 141-149. https://doi.org/10.12941/jksiam.2010.14.3.141
  7. K. R. Gaikwad, An inverse heat conduction problem in a thick annular disc, Int. J. of Appl. Math. and Mech., 7 (2011), 27-41.
  8. K. R. Gaikwad and K. P. Ghadle, An inverse quasi-static thermoelastic problem in a thick circular plate, Southern Journal of Pure and Applied Mathematics, 5 (2011), 13-25.
  9. K. R. Gaikwad and K. P. Ghadle, On a certain thermoelastic problem of temperature and thermal stresses in a thick circular plate, Australian Journal of Basic and Applied Sciences, 6 (2012), 34-48.
  10. K. R. Gaikwad and K. P. Ghadle, Nonhomogeneous heat conduction problem and its thermal deflection due to internal heat generation in a thin hollow circular disk, Journal of Thermal stresses, 35 (2012), 485-498. https://doi.org/10.1080/01495739.2012.671744
  11. K. R.Gaikwad, Analysis of thermoelastic deformation of a thin hollow circular disk due to partially distributed heat supply, Journal of Thermal stresses, 36 (2013), 207-224. https://doi.org/10.1080/01495739.2013.765168
  12. K. R. Gaikwad, Mathematical modelling and its simulation of a quasi-static thermoelastic problem in a semi-infinite hollow circular disk due to internal heat generation, Journal of Korean Society for Industrial and Applied Mathematics, 19 (2015), 69-81. https://doi.org/10.12941/jksiam.2015.19.069
  13. K. R. Gaikwad, Axi-symmetric thermoelastic stress analysis of a thin circular plate due to heat generation, International Journal of Dynamical Systems and Differential Equations, 9 (2019), 187-202. https://doi.org/10.1504/ijdsde.2019.100571
  14. K. R. Gaikwad and S. G. Khavale, Time Fractional Heat Conduction Problem in a Thin Hollow Circular Disk and It's Thermal Deflection, Easy Chair, 1672 (2019), 1-10.
  15. K. R. Gaikwad and Y. U. Naner, Analysis Of Transient Thermoelastic Temperture Distribution Of A Thin Circular Plate And Its Thermal Deflection Under Uniform Heat Generation, journal of thermal stress, 44(1) (1982), 75-85.
  16. K. R. Gaikwad and Y. U. Naner, Transient Thermoelastic Stress Analysis of A Thin Circular Plate Due to Uniform Internal Heat Generation, Journal of the Korean Society for Industrial and Apllied Mathematics, 24 (2020), 293-303.
  17. S. G. Khavale and K. R. Gaikwad, Generalized theory of magneto-thermo-viscoelastic Spherical cavity problem under Fractional order derivative: State Space Approach, Advances in Mathematics:Scientific Journal, 9 (2020), 9769-9780. https://doi.org/10.37418/amsj.9.11.86
  18. K. R. Gaikwad and Y. U. Naner, Green's Function Approach To Thermal Deflection Of A Thin Hollow Circular Disk Under Axisymmetric Heat Source, Journal of the Korean Society for Industrial and Apllied Mathematics, 25(1) (2021), 1-15.
  19. K. R. Gaikwad, Y. U. Naner, S. G. Khavale, Time fraectional thermoelastic stress anlysis of a thin rectangular plate, NOVYI MIR Researech Journal, 6(1) (2021), 42-56.
  20. K. R. Gaikwad and Y. U. Naner, Green's Function Approach To Transient Thermoelastic Deformation Of A Thin Hollow Circular Disk Under Axisymmetric Heat Source, JP Journal of Heat and Mass Transfer, 22(2) (2021), 245-257. https://doi.org/10.17654/HM022020245
  21. K. R. Gaikwad and V. G. Bhandwalkar, Fractional Order Thermoelastic Problem For Finite Piezoelectric Rod Subjected To Different Types Of Thermal Loading - Direct Approach, Journal of the Korean Society for Industrial and Apllied Mathematics, 25(3) (2021), 117-131.
  22. H. H. Sherief, A. El-Said, A. Abd El-Latief, Fractional order theory of thermoelasticity, International Journal of Solids and Structures, 47 (2010), 269-275. https://doi.org/10.1016/j.ijsolstr.2009.09.034
  23. I. Podlubny, Fractional differential Equation, Academic Press, San Diego, 1999.
  24. N. M. Ozisik, Boundary Value Problem of Heat Conduction, International Textbook Company, Pennsylvania, 1968.