Generalized Thermoelastic Problem of a Thick Circular Plate with Axisymmetric Heat Supply Due to Internal Heat Generation

Document Type: Research Paper


1 Department of mathematics, Dr. Ambedkar College, Deekshabhoomi, Nagpur -440010, Maharashtra, India

2 Department of mathematics, R.T.M. Nagpur University, Nagpur-440033 Maharashtra, India


A two dimensional generalized thermoelastic problem of a thick circular plate of finite thickness and infinite extent subjected to continuous axisymmetric heat supply and an internal heat generation is studied within the context of generalized thermoelasticity. Unified system of equations for classical coupled thermoelasticity, Lord-Shulman and Green-Lindsay theory is considered. An exact solution of the problem is obtained in the transform domain. Inversion of Laplace transforms is done by employing numerical scheme. Mathematical model is prepared for Copper material plate and the numerical results are discussed and represented graphically.


[1] Biot M. A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240-253.
[2] Nowacki W., 1966, Couple stresses in the theory of thermoelasticity , Bulletin L'Academie Polonaise des Science, Serie des Sciences Technology 14: 129-138.
[3] Lord H., Shulman Y., 1967, A generalized dynamical theory of thermo-elasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.
[4] Green A. E., Lindsay K. A, 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
[5] Nowacki W., 1975, Dynamic Problems of Thermoelasticity, Noordhoff International Publishing, Leyden, The Netherlands.
[6] Hetnarski R. B., Eslami M. R., 2009, Thermal Stresses-Advanced Theory and Applications, Springer.
[7] Chandrasekariah D. S., 1986, Thermoelasticity with second sound: a review, Applied Mechanics Review 39: 355-376.
[8] Hetnarski R. B., Ignaczak J., 1999, Generalized thermoelasticity, Journal of Thermal Stresses 22: 451-476.
[9] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2014, Dynamic problem of generalized thermoelasticity for a semi-infinite cylinder with heat sources, Journal of Thermoelasticity 2(1): 01-08.
[10] Maghraby N. M., Abdel Halim A. A., 2010, A generalized thermoelastic problem for a half space with heat sources under axisymmetric distribution, Australian Journal of Basic and Applied Science 4(8): 3803-3814.
[11] Aouadi M., 2005, Discontinuities in a axisymmetric generalized thermoelastic problem, International Journal of Mathematics and Mathematical Sciences 7: 1015-1029
[12] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2015, Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply, Acta Mechanica 226(7): 2121-2134.
[13] Youssef H. M., 2006, Two-dimensional generalized thermoelasticity problem for a half- space subjected to ramp-type heating, European Journal of Mechanics A/Solids 25: 745-763.
[14] Tripathi J. J., Kedar, G. D., Deshmukh K. C., 2015, Two dimensional generalized thermoelastic diffusion in a half space under axisymmetric distributions, Acta Mechanica 226: 3263-3274.
[15] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2015, Theoretical study of disturbances due to mechanical source in a generalized thermoelastic diffusive half space, Proceeding of the Third International Conference on Advances in Applied Science and Environmental Engineering - ASEE 2015: 57-61.
[16] Gaver D. P., 1966, Observing stochastic processes and approximate transform inversion, Operations Research 14: 444-459.
[17] Stehfast H., 1970, Algorithm 368: Numerical inversion of Laplace transforms, Communications of the ACM 13: 47-49.
[18] Stehfast H., 1970, Remark on algorithm 368, Numerical inversion of Laplace transforms, Communications of the ACM 13: 624.
[19] Press W. H., Flannery B. P., Teukolsky S. A., Vetterling W. T., 1986, Numerical Recipes, Cambridge University Press, Cambridge, The Art of Scientific Computing.