DOI QR코드

DOI QR Code

MATHEMATICAL MODELLING AND ITS SIMULATION OF A QUASI-STATIC THERMOELASTIC PROBLEM IN A SEMI-INFINITE HOLLOW CIRCULAR DISK DUE TO INTERNAL HEAT GENERATION

  • Gaikwad, Kishor R. (Post Graduate Department of Mathematics, NES, Science College)
  • Received : 2015.01.03
  • Accepted : 2015.02.12
  • Published : 2015.03.25

Abstract

The present paper deals with the determination of temperature, displacement and thermal stresses in a semi-infinite hollow circular disk due to internal heat generation within it. Initially the disk is kept at arbitrary temperature F(r, z). For times t > 0 heat is generated within the circular disk at a rate of g(r, z, t) $Btu/hr.ft^3$. The heat flux is applied on the inner circular boundary (r = a) and the outer circular boundary (r = b). Also, the lower surface (z = 0) is kept at temperature $Q_3(r,t)$ and the upper surface ($Z={\infty}$) is kept at zero temperature. Hollow circular disk extends in the z-direction from z = 0 to infinity. The governing heat conduction equation has been solved by using finite Hankel transform and the generalized finite Fourier transform. As a special case mathematical model is constructed for different metallic disk have been considered. The results are obtained in series form in terms of Bessel's functions. These have been computed numerically and illustrated graphically.

References

  1. J. L. Nowinski, Theory of thermoelasticity with application, 407, Sijthof Noordhoff, Alphen Aan Den Rijn, The Netherlands, 1978.
  2. W. Nowacki, The state of stresses in a thick circular plate due to temperature field, Bull. Acad. Polon. Sci., Ser. Scl. Tech., 5 (1957), 227.
  3. Y. Obata and N. Noda, Steady Thermal Stresses in a Hollow Circular Cylinder and a Hollow Sphere of a Functionally Gradient Material, Journal of Thermal Stresses, 17 (3) (1994), 471-487. https://doi.org/10.1080/01495739408946273
  4. Y. Ootao, T. Akai and 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
  5. M. Ishihara, Y. Tanigawa, R. Kawamura and 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
  6. Eduardo, Divo. and Alain, J. Kassab, Generalized boundary integral equation for heat conduction in nonhomogeneous media, recent developments on the sifting property, Engineering Analysis with Boundary Elements, 22 (3) (1998), 221-234. https://doi.org/10.1016/S0955-7997(98)00037-X
  7. Bao-Lin Wang and Yiu-Wing Mai, Transient one-dimensional heat conduction problems solved by finite element, International Journal of Mechanical Sciences, 47 (2) (2005), 301-317.
  8. Cheng-Hung Huang and Hsin-HsienWu, An inverse hyperbolic heat conduction problem in estimating surface heat flux by the conjugate gradient method, Journal of Physics D: Applied Physics, 39 (18) (2006).
  9. Zhengzhu Dong, Weihong Peng, Jun Li, Fashan Li, Thermal Bending of Circular Plates for Non- Axisymmetrical Problems, World Journal of Mechanics, 1 (2011), 44-49. https://doi.org/10.4236/wjm.2011.12006
  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. 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 (3) (2013), 207-224. https://doi.org/10.1080/01495739.2013.765168
  12. Ozisik, N. M.: Boundary Value Problem of Heat Conduction, 84-101 International Textbook Company, Scranton, Pennsylvania, 1968.