A Green’s function approach is adopted to solve the two-dimensional transient thermoelastic deformation of a thin hollow circular disk. Initially, the disk is kept at temperature For times  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  and fluid temperature  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, displacement and thermal stresses have been computed numerically and illustrated graphically.

Green’s function, hollow circular disk, axisymmetric heat source, thermal stresses.

Received: December 31, 2020; Accepted: February 10, 2021; Published: April 12, 2021

How to cite this article: Kishor R. Gaikwad and Yogesh 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. DOI: 10.17654/HM022020245

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] 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.
[2] B. A. Boley and J. H. Weiner, Theory of Thermal Stresses, John Wiley and Sons, New York, 1960.
[3] S. K. Roy Choudhary, A note of quasi-static stress in a thin circular plate due to transient temperature applied along the circumference of a circle over the upper face, Bull. Acad. Polon. Sci. Ser. Sci. Math. (1972), 20-21.
[4] K. R. Gaikwad and K. P. Ghadle, An inverse quasi-static thermal stresses in a thick annular disc, Int. J. Appl. Math. Stat. 19(D10) (2010), 50-62.
[5] K. S. Parihar and S. S. Patil, Transient heat conduction and analysis of thermal stresses in thin circular plate, J. Thermal Stresses 34(4) (2011), 335-351.
[6] 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(2) (2012), 34-48.
[7] 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, J. Thermal Stresses 35(6) (2012), 485-498.
[8] K. R. Gaikwad, Analysis of thermoelastic deformation of a thin hollow circular disk due to partially distributed heat supply, J. Thermal Stresses 36(3) (2013), 207-224.
[9] K. R. Gaikwad, Two-dimensional steady-state temperature distribution of a thin circular plate due to uniform internal energy generation, Cogent Math. 3 (2016), Art. ID 1135720, 10 pp.
[10] K. R. Gaikwad, Axi-symmetric thermoelastic stress analysis of a thin circular plate due to heat generation, Int. J. Dynam. Syst. Diff. Eqs. 9 (2019), 187-202.
[11] 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, J. Thermal Stresses 44(1) (2021), 75-85.
[12] K. R. Gaikwad and Y. U. Naner, Transient thermoelastic stress analysis of a thin circular plate due to uniform internal heat generation, J. Korean Soc. Ind. Appl. Math. 24(3) (2020), 293-303.
[13] K. R. Gaikwad and 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.
[14] N. Noda, R. B. Hetnarski and Y. Tanigawa, Thermal Stresses, Second Edition, Taylor and Francis, New York, 2003, pp. 376-387.
[15] N. M. Ozisik, Boundary Value Problem of Heat Conduction, International Textbook Company, Scranton, Pennsylvania, 1968, pp. 84-101.
[16] L. Thomas, Fundamentals of Heat Transfer, Prentice-Hall, Englewood Cliffs, 1980.