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ORIGINAL PAPER
Thermoelastic Behavior of a Hollow Cylinder Using Space-time Fractional Heat Conduction: A Quasi-static Approach
1
Department of Applied Mathematics, Laxminarayan Innovation Technological University, Nagpur, Laxminarayan Innovation Technological University, India
2
Research Scholar, Department of Mathematics, R. T. M. Nagpur University, Nagpur, India
These authors had equal contribution to this work
Submission date: 2025-01-12
Final revision date: 2025-06-12
Acceptance date: 2025-09-10
Online publication date: 2025-12-05
Publication date: 2025-12-05
Corresponding author
Shrikant Warbhe
Department of Applied Mathematics, Laxminarayan Innovation Technological University, Nagpur, Laxminarayan Innovation Technological University, 440033, Nagpur, India
Department of Applied Mathematics, Laxminarayan Innovation Technological University, Nagpur, Laxminarayan Innovation Technological University, 440033, Nagpur, India
International Journal of Applied Mechanics and Engineering 2025;30(4):153-164
KEYWORDS
Thermal stressesQuasi-staticMittag-Leffler functionIntegral transformFractional derivatives and integrals
TOPICS
ABSTRACT
The present study examines thermoelastic behaviour of a hollow cylinder governed by the space-time fractional heat conduction equation, employing a quasi-static approach. The analysis utilizes the Caputo time fractional derivative and finite Riesz space fractional derivative. An arbitrary temperature is applied to the upper surface of the cylinder while, the other boundaries are maintained at zero temperature. The heat conduction equation is solved using the integral transform technique. A mathematical model is developed specifically for pure copper material. The effects of varying the fractional orders of space and time on thermoelasticity, influenced by changes in thermal conductivity, are investigated and the results are depicted graphically.
REFERENCES (27)
1.
Podlubny I. (2002): Geometric and physical interpretation of fractional integration and fractionaldifferentiation.– Fractional Calculus and Applied Analysis, vol.5, pp.367-386, https://arxiv.org/abs/math/011....
2.
Sherief H., El-Sayed A. and Abd El-Latief A.M. (2010): Fractional order theory of thermoelasticity.– International Journal of Solids and Structures, vol.47, pp.269-275, https://doi.org/10.1016/j.ijso....
3.
Povstenko Y. (2005): Fractional heat conduction equation and associated thermal stresses.– Journal of Thermal Stresses, vol.28, pp.83-102, https://doi.org/10.1080/014957....
4.
Povstenko Y. (2009): Thermoelasticity which uses fractional heat conduction equation.– Journal of Mathematical Sciences, vol.162, pp.296-305, https://doi.org/10.1007/s10958....
5.
Povstenko Y. (2010): Signalling problem for time-fractional diffusion-wave equation in a half-plane in the case of angular symmetry.– Nonlinear Dynamics, vol.59, pp.593-605, https://doi.org/10.1007/s11071....
6.
Povstenko Y. (2010): Fractional Cattaneo-type equations and generalized thermoelasticity.– Journal of Thermal Stresses, vol.34, pp.97-114, https://doi.org/10.1080/014957....
7.
Povstenko Y. (2012): Theories of thermal stresses based on space-time fractional telegraph equations.– Computers and Mathematics with Applications, vol.64, pp.3321-3328, https://doi.org/10.1016/j.camw....
8.
Raslan W.E. (2015): Application of fractional order theory of thermoelasticity in a thick plate under axisymmetric temperature distribution.– J. of Thermal Stresses, vol.38, pp.733-743, https://doi.org/10.1080/014957....
9.
Warbhe S.D., Tripathi J.J., Deshmukh K.C. and Verma J. (2017): Fractional heat conduction in a thin circular plate with constant temperature distribution and associated thermal stresses.– Journal of heat Transfer, vol.139, pp.044502-1 to 044502-4, https://doi.org/10.1115/1.4035....
10.
Warbhe S.D., Tripathi J.J., Deshmukh K.C. and Verma J. (2018): Fractional heat conduction in a thin hollow circular disk and associated thermal deflection.– Journal of Thermal Stresses, vol.41, pp.262-270, https://doi.org/10.1080/014957....
11.
Tripathi J.J.,Warbhe S.D., Deshmukh K.C. and Verma J. (2017): Fractional order thermoelastic deflection in a thin circular plate.– Applications and Applied Mathematics: an International Journal, vol.12, pp.898-909.
12.
Tripathi J.J.,Warbhe S.D., Deshmukh K.C. and Verma J. (2018): Fractional order generalized thermoelastic response in a half space due to a periodically varying heat source.– Multidiscipline Modelling in Materials and Structures, vol.4, pp.2-15, https://doi.org/10.1108/MMMS- 04-2017-0022.
13.
Warbhe S.D. (2020): Fractional heat conduction in a rectangular plate with bending moments.– Journal of Applied Mathematics and Computational Mechanics, vol.19, pp.115-126, https://doi.org/10.17512/jamcm....
14.
Ezzat M.A. and El-Karamany A.S. (2011): On fractional thermoelasticity.– Mathematics and Mechanics of Solids, vol.16, pp.334-346, http://doi.org/10.1177/1081286....
15.
El-Karamany A.S. and Ezzat M.A. (2016): Thermoelastic diffusion with memory-dependent derivative.– Journal of Thermal Stresses, vol.39, pp.1035-1050, https://doi.org/10.1080/014957....
16.
Ezzat M.A., El-Karamany A.S. and El-Bary A.A. (2018): Two-temperature theory in Green-Naghdi thermoelasticity with fractional phase-lag heat transfer.– Microsystem Technologies, vol.24, pp.951-961, DOI:10.1007/s00542-017-3425-6.
17.
Ezzat M.A. and El-Bary A.A. (2016): Magneto-thermoelectric viscoelastic materials with memory-dependent derivative involving two-temperature.– International Journal of Applied Electromagnetics and Mechanics, vol.50, pp.549-567, https://doi.org/10.3233/JAE-15....
18.
Ezzat M.A. and El-Bary A.A. (2016): Effects of variable thermal conductivity and fractional order of heat transfer on a perfect conducting infinitely long hollow cylinder.– Int. J. of Thermal Sciences, vol.108, pp.62-69, https://doi.org/10.1016/j.ijth....
19.
Ezzat M.A., El-Karamany A.S. and El-Bary A.A. (2017): On dual-phase-lag thermoelasticity theory with memory-dependent derivative.– Mechanics of Advanced Materials and Structures, vol.24, pp.908-916, https://doi.org/10.1080/153764....
20.
Fil’Shtinskii L.A., Kirichok T.A. and Kushnir D.V. (2013): One dimensional fractional quasi-static thermoelasticity problem for a half space.– WSEAS Transactions on Heat and Mass Transfer, vol.8,pp.31-36.
21.
Povstenko Y. (2009): Theory of thermoelasticity based on the space-time-fractional heat conduction equation.– Physica Scripta, vol.136, pp.014017-014022, DOI:10.1088/0031-8949/2009/T136/014017.
22.
Sherief H. and Abd El-Latief A.M. (2014): Application of fractional order theory of thermoelasticity to a 2D problem for a half-space.– App. Math. and Computation, vol.248, pp.584-582, https://doi.org/10.1016/j.amc.....
23.
Salama M.M., Kozae A.M., Elsafty M.A. and Abelaziz S.S. (2015): A half-space problem in the theory of fractional order thermoelasticity with diffusion.– Int. Journal of Scientific & Engineering Research, vol.6, pp.358-371.
24.
El-Sayed A.M. and Gaber M. (2006): On the finite Caputo and finite Riesz derivatives.– Electronic Journal of Theoretical Physics, vol.12, pp.81-95.
25.
Saichev A.I. and Zaslavsky G.M. (1997): Fractional kinetic equations: solutions and applications.– Chaos, vol.7, pp.753-764, https://doi.org/10.1063/1.1662....
26.
Ozisik M.N. (1968): Boundary Value Problem of Heat Conduction.– Scranton, PA: International Textbook Co.
27.
Povstenko Y. (2015): Linear Fractional Diffusion-Wave Equation for Scientists and Engineers.– Birkhäser, New York.
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