Recent advances in the understanding of the precise physical thermal behaviour of various solids under the effect of fractional-order derivatives have boosted the study of thermoelasticity, which is primarily important in various industrial designs of usable structural materials. We investigated a thin circular plate that was subjected to additional sectional heating on its top and lower surfaces while creating thermal insulation around its outside border. In this work, we maintained the heat transfer equation while accounting for the impact of Caputo-Fabrizio fraction-order derivatives. According to specified boundary constraints, the integral transformation approach is used to assess the analytical solution of the displacement, temperature change, and thermal stresses. Furthermore, various functions and fractional parameters are computed using the material properties of aluminium metal plates for numerical purposes.

circular plate, sectional heating, integral transform, thermal stress.

Received: May 20, 2024; Revised: September 2, 2024; Accepted: September 16, 2024

How to cite this article: Indrajeet Varhadpande, V. R. K. Murthy and N. K. Lamba, Thermal behaviour of a circular plate under Caputo-Fabrizio fractional impact with sectional heating, Advances in Differential Equations and Control Processes 31(4) (2024), 511-530. https://doi.org/10.17654/0974324324027

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

References:
[1] A. H. Elsheikh, J. Guo and K.-M. Lee, Thermal deflection and thermal stresses in a thin circular plate under an axisymmetric heat source, J. Therm. Stress. 42 (2019), 361-373.
[2] K. R. Gaikwad, Axi-symmetric thermoelastic stress analysis of a thin circular plate due to heat generation, Int. J. Dyn. Syst. Differ. Equ. 9 (2019), 187-202.
[3] E. Dats, E. Murashkin and N. Stadnik, On heating of thin circular elastic-plastic plate with the yield stress depending on temperature, Procedia Eng. 173 (2017), 891-896.
[4] K. S. Parihar and S. S. Patil, Transient heat conduction and analysis of thermal stresses in thin circular plate, J. Therm. Stress. 34 (2011), 335-351.
[5] 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 (2020), 293-303.
[6] K. Rajneesh and D. Shaloo, Deformation of modified couple stress thermoelastic diffusion in a thick circular plate due to heat sources, CMST 25 (2019), 167-176.
[7] E. Dats, S. Mokrin and E. Murashkin, Calculation of the residual stress field of the thin circular plate under unsteady thermal action, Key Eng. Mater. 685 (2016), 37-41.
[8] S. Singh and P. Lata, Effect of two temperature and nonlocality in an isotropic thermoelastic thick circular plate without energy dissipation, Partial Differ. Equ. Appl. Math. 7 (2023), 100512.
[9] Y. Nakajo and K. Hayashi, Response of simply supported and clamped circular plates to thermal impact, J. Sound Vib. 122 (1988), 347-356.
[10] A. E. Abouelregal, M. V. Moustapha, T. A. Nofal, S. Rashid and H. Ahmad, Generalized thermoelasticity based on higher-order memory-dependent derivative with time delay, Results Phys. 20 (2021), 103705.
[11] S. G. Khavale and K. R. Gaikwad, Fractional ordered thermoelastic stress analysis of a thin circular plate under axi-symmetric heat supply, Int. J. Nonlinear Anal. Appl. 14 (2023), 207-219.
[12] I. Kaur and K. Singh, Fractional order strain analysis in thick circular plate subjected to hyperbolic two temperature, Partial Differ. Equ. Appl. Math. 4 (2021) 100130.
[13] P. Lata, Time harmonic interactions in fractional thermoelastic diffusive thick circular plate, Coupled Syst. Mech. 8 (2019), 39-53.
[14] S. Patnaik, S. Sidhardh and F. Semperlotti, Nonlinear thermoelastic fractional-order model of nonlocal plates: application to postbuckling and bending response, Thin-Walled Struct. 164 (2021), 107809.
[15] S. Thakare and M. S. Warbhe, Thermal response of a thick circular plate with internal heat sources in time fractional frame, SAMRIDDHI J. Phys. Sci. Eng. Technol. 14 (2022), 189-199.
[16] N. K. Lamba, Thermosensitive response of a functionally graded cylinder with fractional order derivative, Int. J. Appl. Mech. Eng. 27 (2022), 107-124.
[17] D. S. Mashat, A. M. Zenkour and A. E. Abouelregal, Fractional order thermoelasticity theory for a half-space subjected to an axisymmetric heat distribution, Mech. Adv. Mater. Struct. 22 (2015), 925-932.
[18] S. Khavale and K. Gaikwad, Design engineering fractional order thermoelastic problem of thin hollow circular disk and its thermal stresses under axi-symmetric heat supply, Des. Eng. Tor. 2021 (2021), 13851-13862.
[19] S. G. Khavale and K. R. Gaikwad, 2D problem for a sphere in the fractional order theory thermoelasticity to axisymmetric temperature distribution, Adv. Math. Sci. J. 11 (2022), 1-15.
[20] Y. J. Yu and Z. C. Deng, Fractional order theory of Cattaneo-type thermoelasticity using new fractional derivatives, Appl. Math. Model. 87 (2020), 731-751.
[21] D. Baleanu, A. Jajarmi, H. Mohammadi and S. Rezapour, A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative, Chaos Solitons Fractals 134 (2020), 109705.
[22] S. Ullah, M. A. Khan, M. Farooq, Z. Hammouch and D. Baleanu, A fractional model for the dynamics of tuberculosis infection using Caputo-Fabrizio derivative, Discrete Contin. Dyn. Syst. 13 (2020), 975-993.
[23] T. M. Atanacković, S. Pilipović and D. Zorica, Properties of the Caputo-Fabrizio fractional derivative and its distributional settings, Fract. Calc. Appl. Anal. 21 (2018), 29-44.
[24] S. Qureshi, N. A. Rangaig and D. Baleanu, New numerical aspects of Caputo-Fabrizio fractional derivative operator, Mathematics 7 (2019), 374.
[25] M. Al-Refai and A. M. Jarrah, Fundamental results on weighted Caputo-Fabrizio fractional derivative, Chaos Solitons Fractals 126 (2019), 7-11.
[26] A. Atangana and E. F. D. Goufo, The Caputo-Fabrizio fractional derivative applied to a singular perturbation problem, Int. J. Math. Model. Numer. Optim. 9 (2019), 241-253.
[27] D. Baleanu, B. Agheli and M. M. Al Qurashi, Fractional advection differential equation within Caputo and Caputo-Fabrizio derivatives, Adv. Mech. Eng. 8 (2016), 1-8.
[28] A. Giusti, A comment on some new definitions of fractional derivative, Nonlinear Dyn. 93 (2018) 1757-1763.
[29] O. J. J. Algahtani, Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order: Allen Cahn model, Chaos Solitons Fractals 89 (2016), 552-559.
[30] F. E.-G. Bouzenna, M. T. Meftah and M. Difallah, Application of the Caputo-Fabrizio derivative without singular kernel to fractional Schrödinger equations, Pramana 94 (2020), 92.
[31] A. E. Abouelregal, A. H. Sofiyev, H. M. Sedighi and M. A. Fahmy, Generalized heat equation with the Caputo-Fabrizio fractional derivative for a nonsimple thermoelastic cylinder with temperature-dependent properties, Phys. Mesomech. 26 (2023), 224-240.
[32] N. Kumar and D. B. Kamdi, Thermal behavior of a finite hollow cylinder in context of fractional thermoelasticity with convection boundary conditions, J. Therm. Stress. 43 (2020) 1189-1204.
[33] N. K. Lamba and K. C. Deshmukh, Hygrothermoelastic response of a finite solid circular cylinder, Multidiscip. Model. Mater. Struct. 16 (2019), 37-52.
[34] N. K. Lamba, Impact of memory-dependent response of a thermoelastic thick solid cylinder, J. Appl. Comput. Mech. 9 (2023), 1135-1143.
[35] N. K. Lamba and K. C. Deshmukh, Memory dependent response in an infinitely long thermoelastic solid circular cylinder, Perm National Research Polytechnic University 1 (2024), 5-12.
[36] J. Verma, N. K. Lamba and K. C. Deshmukh, Memory impact of hygrothermal effect in a hollow cylinder by theory of uncoupled-coupled heat and moisture, Multidiscip. Model. Mater. Struct. 18 (2022), 826-844.
[37] V. R. Manthena, N. K. Lamba and G. D. Kedar, Thermoelastic analysis of a rectangular plate with nonhomogeneous material properties and internal heat source, J. Solid Mech. 1 (2018), 200.
[38] N. K. Lamba and N. W. Khobragade, Uncoupled thermoelastic analysis for a thick cylinder with radiation, Theor. Appl. Mech. Lett. 2 (2012), 021005.
[39] V. Manthena, N. Lamba and G. Kedar, Thermoelastic analysis of a nonhomogeneous hollow cylinder with internal heat generation, Applications and Applied Mathematics: An International Journal (AAM) 12 (2017), 946-967.
[40] Indrajeet Varhadpande, V. R. K. Murthy and N. K. Lamba, Ramp heating response in thermoelastic thick annular disc with convective heat exchange boundaries under fractional order derivatives, Neuroquantology 20 (2022), 506-514.
[41] Indrajeet Varhadpande, V. R. K. Murthy and N. K. Lamba, Caputo-Fabrizio fractional order response in thermoelastic thick circular plate with heat source, European Chemical Bulletin Journal 12(Special Issue 5) (2023), 5389-5400.
[42] M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl. 1 (2015), 73-85.