Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
권호 표지
DOI QR코드

DOI QR Code

GREEN'S FUNCTION APPROACH TO THERMAL DEFLECTION OF A THIN HOLLOW CIRCULAR DISK UNDER AXISYMMETRIC HEAT SOURCE

  • GAIKWAD, KISHOR R. (PG DEPARTMENT OF MATHEMATICS, NES SCIENCE COLLEGE) ;
  • NANER, YOGESH U. (DEPARTMENT OF MATHEMATICS, SHRI RUKHMINI ART'S, COMMERCE AND SCIENCE COLLEGE)
  • Received : 2020.12.29
  • Accepted : 2021.03.24
  • Published : 2021.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

A Green's function approach is adopted to solve the two-dimensional thermoelastic problem of a thin hollow circular disk. Initially, the disk is kept at temperature T0(r, z). For times t > 0, the inner and outer circular edges are thermally insulated and the upper and lower surfaces of the disk are subjected to convection heat transfer with convection coefficient hc and fluid temperature T∞, while the disk is also subjected to the axisymmetric heat source. As a special case, different metallic disks have been considered. The results for temperature and thermal deflection has been computed numerically and illustrated graphically.

Keywords

References

  1. S. K. Roy Choudhary, A note on quasi-static thermal deflection of a thin clamped circular plate due to ramp-type heating of a concentric circular region of the upper face, Journal of the Franklin Institute, 296(3) (1973), 213-219. https://doi.org/10.1016/0016-0032(73)90059-8
  2. K. Grysa and Z. Kozlowski, One-dimensional problems of temperature and heat flux determination at the surfaces of a thermoelastic slab, Part II:, The Numerical Analysis, Nucl. Eng. Des., 74 (1982), 15-24. https://doi.org/10.1016/0029-5493(83)90136-X.
  3. Y. Ootao, T. Akai, Y. Tanigawa, Three dimentional transient thermal stress analysis of a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction, Journal of Thermal Stresses, 18(5) (1995), 497-512. https://doi.org/10.1080/01495739508946317.
  4. Y. Ootao and Y. Tanigawa, Transient thermoelastic analysis for a functionally graded hollow cylinder, Journal of Thermal Stresses, 29 (2006), 1031-1046. https://doi.org/10.1080/01495730600710356.
  5. Y. Tanigawa, M. Ishihara, H. Morishita, and R. Kawamura, Theoretical Analysis of Two-Dimensional Thermoelastoplastic Bending Deformation of Plate Subject to Partially Distributed Heat Supply, Trans. JSME, 62(595) (1996).
  6. M. Ishihara, Y. Tanigawa, R. Kawamura, N. Noda, Theoretical analysis of ther moelastoplastic 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.
  7. T. K. Chakraborty and T. K. Tar, Defection of a circular plate due to heating of a concentric circular region, J. Appl. Math. Comput., 10(1-2) (2002), 217-226. https://doi.org/10.1007/BF02936219
  8. M. N. Gaikwad and K. C. Deshmukh, Thermal deflection of an inverse thermoelastic problem in a thin isotropic circular plate, Appl. Math. Model., 29(9) (2005), 797-804. https://doi.org/10.1016/j.apm.2004.10.012.
  9. N. L. Khobragade and K. C. Deshmukh, An inverse quasi-static thermal deflection problem for a thin clamped circular plate, Journal of Thermal Stresses, 28 (2005), 353-361. https://doi.org/10.1080/01495730590916605.
  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(6) (2012), 485-498. http://dx.doi.org/10.1080/01495739.2012.671744.
  11. K. R. Gaikwad, 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.
  12. K. R. Gaikwad and Y. U. Naner, Analysis of transient thermoelastic temperature distribution of a thin circular plate and its thermal deflection under uniform heat generation, Journal of Thermal Stresses, 44(1) (2021), 75-85. https://doi.org/10.1080/01495739.2020.1828009.
  13. K. R. Gaikwad, Two-dimensional steady-state temperature distribution of a thin circular plate due to uniform internal energy generation, Cogent Mathematics, Taylor and Francis Group, 3(1) (2016), 1-10. http://dx.doi.org/10.1080/23311835.2015.1135720.
  14. K. R. Gaikwad, Mathematical modelling and its simulation of a quasi-static thermoelastic problem in a semiinfinite hollow circular disk due to internal heat generation, Journal of Korean Society for Industrial and Applied Mathematics, 19(1) (2015), 69--81. DOI: 10.12941/jksiam.2015.19.069
  15. K. R. Gaikwad, Mathematical modelling of thermoelastic problem in a circular sector disk subject to heat generation, Int. J. Adv. Appl. Math. and Mech., 2(3) (2015), 183-195.
  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 Applied Mathematics, 24(3) (2020), 293-303. http://dx.doi.org/10.12941/jksiam.2020.24.293
  17. K. R. Gaikwad, S. G. Khavale, Generalized theory of magneto-thermo-viscoelastic spherical cavity problem under fractional order derivative: state space approach, Advances in Mathematics: Scientific Journal, 9(11) (2020), 9769--9780. https://doi.org/10.37418/amsj.9.11.86
  18. K. S. Parihar and S. S. Patil, Transient heat conduction and analysis of thermal stresses in thin circular plate, Journal of Thermal Stresses, 34(4) (2011), 335--351. https://doi.org/10.1080/01495739.2010.550812.
  19. K. R. Gaikwad, Analysis of thermoelastic deformation of a thin hollow circular disk due to partially distributed heat supply, Journal of Thermal Stresses, vol. 36, no. 3, pp. 207-224, 2013. http://dx.doi.org/10.1080/01495739.2013.765168.
  20. 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), pp. 187-202. https://doi.org/10.1504/IJDSDE.2019.100571.
  21. N. M. Ozisik, Boundary Value Problem of Heat Conduction, International Textbook Company, Scranton, Pennsylvania, (1968), 84-101.
  22. N. Noda, R.B. Hetnarski, Y. Tanigawa, Thermal Stresses, Second Edition, Taylor and Francis, New York, (2003), 376-387.
  23. Thomas, L.: Fundamentals of Heat Transfer. Prentice-Hall, Englewood Cliffs, 1980.