پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 692 |
| تعداد مقالات | 10,048 |
| تعداد مشاهده مقاله | 71,051,008 |
| تعداد دریافت فایل اصل مقاله | 62,502,654 |
Fractional ordered thermoelastic stress analysis of a thin circular plate under axi-symmetric heat supply | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 17، دوره 14، شماره 4، تیر 2023، صفحه 207-219 اصل مقاله (659.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29131.4067 | ||
| نویسندگان | ||
| Satish G Khavale1؛ Kishor R Gaikwad* 2 | ||
| 1Department of Engineering Science, Amrutvahini College of Engineering, Sangamner, Maharashtra, 422608, India | ||
| 2P. G. Department of Mathematics, N. E. S., Science College, Nanded, Maharashtra, 431605, India | ||
| تاریخ دریافت: 07 آذر 1401، تاریخ بازنگری: 29 بهمن 1401، تاریخ پذیرش: 01 اسفند 1401 | ||
| چکیده | ||
| The main objective of the current study is to investigate the fractional ordered thermoelastic stress analysis of a thin circular plate under axi-symmetric heat supply. Initially, the plate is characterized by the initial temperature $T_{0}(r, z)$. The boundary value problem is formulated with a circular plate model where the perimetric edge is clamped and convection, and the upper and lower surfaces are subjected to heat convection with convection coefficient $h_{c}$ and fluid temperature $T_{\infty}$. The variable separable technique and Green's function approach scheme have been employed to solve the heat conduction equation. The impacts of the fractional ordered derivative of some other parameters on temperature, deflection, and stress profiles will be analyzed in detail. For instance, the results indicate that the temperature and thermal deflection are directly proportional to the fractional order parameter $\alpha$. Also, the parameter $\alpha$ represents the weak, normal, and strong conductivity, within the range of $0 < \alpha < 1$, $\alpha = 1$ and $1 < \alpha < 2$ respectively. | ||
| کلیدواژهها | ||
| Caputo fractional derivative؛ Green’s function؛ Axi-symmetric heat source؛ Thin circular plate؛ Mittag-Leffler functions | ||
| مراجع | ||
|
[1] A. Bayat, H. Moosavi and Y. Bayat, Thermo-mechanical analysis of functionally graded thick spheres with linearly time dependent temperature, Sci. Iran. B. 22 (2015), 1801—1812. [2] N.M. Dien, Nonlinear sequential fractional boundary value problems involving generalized ψ-Caputo fractional derivatives, Filomat, 36 (2022), no. 15, 5047–5058. [3] M.A. Ezzat, A. Karamany and A.A. El-Bary, Application of fractional order theory of thermoelasticity to 3D time dependent thermal shock problem for a half-space, Mech. Adv. Materials Struc. 226 (2016), 27—35. [4] K.R. Gaikwad, Analysis of thermoelastic deformation of a thin hollow circular disk due to partially distributed heat supply, J. Thermal Stresses 36 (2013), 207–224. [5] K.R. Gaikwad, Mathematical modelling of thermoelastic problem in a circular sector disk subject to heat generation, Int. J. Adv. Appl. Math. Mech. 2 (2015), 183–195. [6] K.R. Gaikwad, Two-dimensional steady-state temperature distribution of a thin circular plate due to uniform internal energy generation, Cogent Math. 3 (2016), 1–10. [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 (2012), 485–498. [8] K.R. Gaikwad and K.P. Ghadle, On a certain thermoelastic problem of temperature and thermal stresses in a thick circular plate, Aust. J. Basic Appl. Sci. 6 (2012), 34–48. [9] K.R. Gaikwad and S.G. Khavale, Time fractional heat conduction problem in a thin hollow circular disk and it’s thermal deflection, Easy Chair 1672 (2019), 1–11. [10] K.R. Gaikwad and S.G. Khavale, Time fractional 2D thermoelastic problem of thin hollow circular disk and it’s associated thermal stresses, Bull. Marathwada Math. Soc. 21 (2020), no. 1-2, 37-–47. [11] K.R. Gaikwad and S.G. Khavale, Fractional order transient thermoelastic stress analysis of a thin circular sector disk, Int. J. Thermodyn. 25 (2022), no. 1, 1-–8. [12] K.R. Gaikwad and Y.U. Naner, Analysis of transient thermoelastic temperture distribution of a thin circular plate and its thermal deflection under uniform heat generation, J. Thermal Stress 44 (2021), no. 1, 75–85. [13] K.R. Gaikwad, Y.U. Naner and S.G. Khavale, Time fraectional thermoelastic stress anlysis of a thin rectangular plate, NOVYI MIR Res. J. 6 (2021), no. 1, 42–56. [14] K.R. Gaikwad, Y.U. Naner and S.G. Khavale, Transient thermoelastic bending analysis of a rectangular plate with a simply supported edge under heat source: Green’s function approach, Int. J. Nonlinear Anal. Appl. 14 (2022), no. 1, 805—818. [15] E.M. Hussain, Fractional order thermoelastic problem for an infinitely long solid circular cylinder, J. Thermal Stresses 38 (2014), 133—145. [16] A. Kar and M. Kanoria, Generalized thermoelasticity problem of a hollow sphere under thermal shock, Eur. J. Pure Appl. Math. 2 (2009), 125—146. [17] S.G. Khavale and K.R. Gaikwad, Generalized theory of magneto-thermo-viscoelastic Spherical cavity problem under Fractional order derivative: State Space Approach, Adv. Math.: Sci. J. 9 (2020), 9769–9780. [18] S.G. Khavale and K.R. Gaikwad, Fractional order thermoelatic problem of thin hollow circular disk and its thermal stresses under axi-symmetric heat supply, Design Engin. 2021 (2021), no. 9, 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), no. 1, 1–15. [20] S.G. Khavale and K.R. Gaikwad, Analysis of non-integer order thermoelastic temperature distribution and thermal deflection of thin hollow circular disk under the axi-symmetric heat supply, J. Korean Soc. Ind. Apll. Math. 26 (2022), no. 1, 67-–75. [21] S.G. Khavale and K.R. Gaikwad, Two-dimensional generalized magneto-thermo-viscoelasticity problem for a spherical cavity with one relaxation time using fractional derivative, Int. J. Thermodyn. 25 (2022), no. 2, 89—97. [22] B.G. Korenev, Bessel Functions and Their Applications. Boca Raton: CRC Press, 2003. [23] S. Mukhopadhay and R. Kumar, A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity, Comput. Math. Appl. 56 (2008), 2329—2339. [24] N.M. Ozisik, Boundary Value Problem Of Heat Conduction, International Textbook Company, Scranton, Pennsylvania, 1968. [25] I. Podlubny, Fractional differential Equation, Academic Press, San Diego, 1999. [26] Y.Z. Povstenko, Fractional heat conduction equation and associated thermal stresses, J. Thermal Stresses 28 (2005), 83–102. [27] Y.Z. Povstenko, Thermoelasticity that uses fractional heat conduction equation, J. Math. Science, 162 (2009), 296–305. [28] Y.Z. Povstenko, Fractional Thermoelasticity, Springer, New York, 2015. [29] PTC Mathcad Prime-7.0.0.0, [Online]. Available: https://support.ptc.com/help/mathcad/r7.0/en/ (accessed Dec. 1, 2021). [30] W. Raslan, Application of fractional order theory of thermoelasticity to a 1D problem for a cylindrical cavity, Arch. Mech. 66 (2014), 257–267. [31] W. Raslan, Application of fractional order theory of thermoelasticity in a thick plate under axisymmetric temperature distribution, J. Thermal Stresses 38 (2015), 733–743. [32] M.A. Ragusa and A. Razani, Existence of a periodic solution for a coupled system of differential equations, AIP Conf. Proc. 2425 (2022), Article ID 370004. [33] A. Selvam, S. Sabarinathan, S. Noeiaghdam and V. Govindan, Fractional Fourier transform and Ulam stability of fractional differential equation with fractional Caputo type derivative, J. Funct. Spaces 2022 (2022), Article ID 3777566. [34] H.H. Sherief, A. El-Said and A. Abd El-Latief, Fractional order theory of thermoelasticity, Int.J. Solids Struct. 47 (2010) 269–275. [35] I.N. Sneddon, The use of Integral Transform, McGraw Hill, New York, 1972. [36] A. Sur and M. Kanoria, Fractional order two-temperature thermoelasticity with wave speed, Acta Mech. 223 (2012) 2685–2701. [37] A. Sur and M. Kanoria, Fractional order generalized thermoelastic functionally graded solid with variable material properties, J. Solid Mech. 6 (2014), 54–69. [38] J.J. Tripathi, G.D. Kedar and K.C. Deshmukh, Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply, Acta Mech. 226 (2015), 2121–2134. [39] H.M. Youssef, Two-dimensional thermal shock problem of fractional order generalized thermoelasticity, Acta Mech. 223 (2012), 1219–1231. | ||
|
آمار تعداد مشاهده مقاله: 17,048 تعداد دریافت فایل اصل مقاله: 10,560 |
||