Thermosensitive response of a functionally graded cylinder with fractional order derivative

• Autorzy: Lamba Navneet Kumar

Identyfikatory

DOI

10.2478/ijame-2022-0008

• Języki publikacji: EN

Abstrakty

EN

The present paper deals with thermal behaviour analysis of an axisymmetric functionally graded thermosensitive hollow cylinder. The system of coordinates are expressed in cylindrical-polar form. The heat conduction equation is of time-fractional order02<α≤, subjected to the effect of internal heat generation. Convective boundary conditions are applied to inner and outer curved surfaces whereas heat dissipates following Newton’s law of cooling. The lower surface is subjected to heat flux, whereas the upper surface is thermally insulated. Kirchhoff’s transformation is used to remove the nonlinearity of the heat equation and further it is solved to find temperature and associated stresses by applying integral transformation method. For numerical analysis a ceramic-metal-based functionally graded material is considered and the obtained results of temperature distribution and associated stresses are presented graphically.

Słowa kluczowe

EN

time fractional; thermal stresses; thick hollow cylinder; internal heat generation; FGMs; thermosenstive

PL

termoczułość; naprężenia termiczne; wytwarzanie ciepła

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2022
• Tom: Vol. 27, no. 1
• Strony: 107--124
• Opis fizyczny: Bibliogr. 27 poz., wykr.

Twórcy

autor

Lamba Navneet Kumar

• Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Mandhal, Nagpur, INDIA

Bibliografia

• [1] Povstenko Y.Z. (2005): Fractional heat conduction equation and associated thermal stresses.– Journal of Thermal Stresses, vol.28, pp.83-102.
• [2] Povstenko Y. Z. (2010): Fractional radial heat conduction in an infinite medium with a cylindrical cavity and associated thermal stresses.– Mech. Res. Commun., vol.37, pp.436-440.
• [3] Povstenko Y.Z. (2011): Non-axisymmetric solutions to time-fractional diffusion-wave equation in an infinite cylinder.– Fract. Calc. Appl. Anal., vol.14, No.3, pp.418-435.
• [4] Povstenko Y.Z. (2011): Solutions to time-fractional diffusion-wave equation in cylindrical coordinates.– Advances in Differential Equations, vol.2011, Article ID.930297, p.14, doi:10.1155/2011/930297.
• [5] Povstenko Y.Z. (2011): Non-axisymmetric solutions to time-fractional heat conduction equation in a half-space in cylindrical coordinates.– Math. Methods Phys.-Mech. Fields, vol.54, No.1, pp.212-219.
• [6] Povstenko Y.Z. (2015): Fractional thermoelasticity, solid mechanics and its application.– Springer, vol. 219, p.293, https://doi.org/10.1007/978-3-319-15335-3.
• [7] Popovich V.S. and Garmatii G.Yu. (1993): Analytic-numerical methods of constructing solutions of heat-conduction problems for thermosensitive bodies with convective heat transfer.– Ukrainian Academy of Sciences, Pidstrigach Institute for Applied Problems of Mechanics and Mathematics, L'viv, Preprint, pp.13-93.
• [8] Popovich V.S. and Fedai B.N. (1997): The axisymmetric problem of thermoelasticity of a multilayer thermosensitive tube.– Journal of Mathematical Sciences, vol.86, No.2, pp.2605-2610.
• [9] Popovich V.S. and Makhorkin I.M. 1998: On the solution of heat-conduction problems for thermosensitive bodies.– Journal of Mathematical Sciences, vol.88, No.3, pp.352-359.
• [10] Kushnir R. and Popovych V.S. (2009): Thermoelasticity of Thermosensitive Solids (in Ukrainien).– SPOLOM, Lviv, p.419.
• [11] Kushnir R. and Popovych V.S. (2011): Heat conduction problems of thermosensitive solids under complex heat exchange.– Heat Conduction - Basic Research, INTECH., pp.131-154, DOI: 10.5772/27970.
• [12] Popovych V.S., Vovk O.M. and Yu H. (2012): Investigation of the static thermoelastic state of a thermosensitive hollow cylinder under convective-radiant heat exchange with environment.– Journal of Mathematical Sciences, vol.187, No.6, pp.726-736.
• [13] Guo Li-C. and Noda N. (2010): An analytical method for thermal stresses of a functionally graded material cylindrical shell under a thermal shock.– Acta Mechanica, vol.214, pp.71-78.
• [14] Cheng Z.Q. and Batra R.C. (2000): Deflection relationships between the homogenous Kirchhoff plate theory and different functionally graded plate theories.– Arch. Mech., vol.52, No.1, pp.143-158.
• [15] Cheng Z.Q. and Batra R.C. (2000): Three-dimensional thermoelastic deformations of a functionally graded elliptic plate.– Composites: Part B, vol.31, pp.97-106.
• [16] Kamdi D. B. and Lamba N. K. (2016): Thermoelastic analysis of functionally graded hollow cylinder subjected to uniform temperature field.– Journal of Applied and Computational Mechanics, vol.2, No.2, pp.118-127.
• [17] Rajneesh K., Manthena V.R., Lamba N.K. and Kedar G.D. (2017): Generalized thermoelastic axisymmetric deformation problem in a thick circular plate with dual phase lags and two temperatures.– Materials Physics and Mechanics, vol.32, No.2, pp.123-132.
• [18] Rajneesh K. and Navneet K. (2020): Analysis of nano-scale beam by eigenvalue approach in modified couple stress theory with thermoelastic diffusion.– Southeast Asian Bulletin of Mathematics, vol.44, pp.515-532.
• [19] Navneet K. and Kamdi D.B. (2020): Thermal behavior of a finite hollow cylinder in context of fractional thermoelasticity with convection boundary conditions.– Journal of Thermal Stresses, vol.43, No.9, pp.1189-1204.
• [20] Lamba N.K. and Deshmukh K.C. (2020): Hygrothermoelastic response of a finite solid circular cylinder.– Multidiscipline Modeling in Materials and Structures, vol.16, No.1, pp.37-52.
• [21] Kamdi D.B. and Navneet K. (2020): Thermal behaviour of an annular fin in context of fractional thermoelasticity with convection boundary conditions.– Annals of Faculty Engineering Hunedoara – International Journal of Engineering, vol.18, No.4, p.9.
• [22] Thakare S. and Warbhe M. (2020): Analysis of time-fractional heat transfer and its thermal deflection in a circular plate by a moving heat source.– International Journal of Applied Mechanics and Engineering, vol.25, No.3, pp.158-168.
• [23] Shivcharan T. and Warbhe M.S. (2021): Time fractional heat transfer analysis in thermally sensitive functionally graded thick hollow cylinder with internal heat source and its thermal stresses.– J. Phys.: Conf. Ser., vol.1913, No.1, pp.1-13.
• [24] Shivcharan T., Warbhe M.S. and Navneet K. (2020): Time fractional heat transfer analysis in non-homogeneous thick hollow cylinder with internal heat generation and its thermal stresses.– International Journal of Thermodynamics, vol. 23, No.4, pp.281-302.
• [25] Hata T. (1982): Thermal stresses in a nonhomogeneous thick plate under steady distribution of temperature.– Journal Thermal Stresses, vol. 5, pp.1-11.
• [26] Noda N. (1986): Thermal stresses in materials with temperature dependent properties.– Thermal Stresses I, Taylor & Francis, North Holland, Amsterdam, pp.391-483.
• [27] Al-Hajri M. and Kalla S.L. (2004): On an integral transform involving Bessel functions - Proceedings of the international conference on Mathematics and its applications, Kuwait, April 5-7.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)