ORIGINAL PAPER
Analysis of Time-Fractional Heat Transfer and its Thermal Deflection in a Circular Plate by a Moving Heat Source
More details
Hide details
1
Department of Mathematics, Sarvodaya Mahavidyalaya, Sindewahi, Chandrapur, India
Online publication date: 2020-08-17
Publication date: 2020-09-01
International Journal of Applied Mechanics and Engineering 2020;25(3):158-168
KEYWORDS
ABSTRACT
Mathematical modeling of a thin circular plate has been made by considering a nonlocal Caputo type time fractional heat conduction equation of order 0 < α ≤ 2, by the action of a moving heat source. Physically convective heat exchange boundary conditions are applied at lower, upper and outer curved surface of the plate. Temperature distribution and thermal deflection has been investigated by a quasi-static approach in the context of fractional order heat conduction. The integral transformation technique is used to analyze the analytical solution to the problem. Numerical computation including the effect of the fractional order parameter has been done for temperature and deflection and illustrated graphically for an aluminum material.
REFERENCES (31)
1.
Povstenko Y.Z. (2005): Fractional heat conduction equation and associated thermal stresses. – J. Therm. Stress, vol.28, pp.83-102.
2.
Povstenko Y.Z. (2009): Thermoelasticity that uses fractional heat conduction equation. – Journal of Mathematical Stresses, vol.162, pp.296-305.
3.
Youssef H.M. (2010): Theory of fractional order generalized thermoelasticity. – J. Heat Transfer, vol.132, pp.1-7.
4.
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.
5.
Jiang X. and Xu M. (2010): The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems. – Physica A, vol.389, pp.3368-3374.
6.
Ezzat M.A. (2011): Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer. – Physica B, vol.406, pp.30-35.
7.
Povstenko Y.Z. (2011): Fractional Cattaneo-type equations and generalized thermoelasticity. – Journal of thermal Stresses, vol.34, No.2, pp.97-114.
8.
Ezzat M.A. (2011): Theory of fractional order in generalized thermoelectric MHD. – Applied Mathematical Modelling, vol.35, pp.4965-4978.
9.
Ezzat M.A. and Ezzat S. (2016): Fractional thermoelasticity applications for porous asphaltic materials. – Petroleum Science, vol.13, No.3, pp.550-560.
10.
Ezzat M.A. and EI-Bary (2016): Modelling of fractional magneto-thermoelasticity for a perfect conducting materials.– Smart Structures and Systems, vol.18, No.4, pp.701-731.
11.
Xiong C. and Niu Y. (2017): Fractional order generalized thermoelastic diffusion theory.– Applied Mathematics and Mechanics, vol.38, No.8, pp.1091-1108.
12.
Khobragade N.L. and Kumar N. (2019): Thermal deflection and stresses of a circular disk due to partially distributed heat supply by application of fractional order theory. – Journal of Computer and Mathematical Sciences, vol.10, No.3, pp.429-437.
13.
Khobragade N.L. and Kumar N. (2019): Study of thermoelastic deformation of a solid circular cylinder by application of fractional order theory. – Journal of Computer and Mathematical Sciences, vol.10, No.3, pp.438-444.
14.
Khobragade N.L. and Lamba N.K. (2019): Magneto-thermodynamic stress analysis of an orthotropic solid cylinder by fractional order theory application. – Research and Reviews: Journal of Physics, vol.8, No.1, pp.37-45.
15.
Khobragade N.L. and Lamba N.K. (2019): Modeling of thermoelastic hollow cylinder by the application of fractional order theory. – Research and Reviews: Journal of Physics, vol.8, No.1, pp.46-57.
16.
Kidawa-Kukla J.(2008): Temperature distribution in a circular plate heated by a moving heat source. – Scientific Research of the Institute of Mathematics and Computer Science, vol.7, No.1, pp.71-76.
17.
Beck J.V., Cole K.D., Haji-Sheikh A. and Litkouhi B. (1992): Heat Conduction using Green’s Functions. – Hemisphere Publishing Corporation, Philadelphia.
18.
Kumar R., Lamba N.K. and Vinod V. (2013): Analysis of thermoelastic disc with radiation conditions on the curved surfaces. – Materials Physics and Mechanics, vol.16, pp.175-186.
19.
Lamba N.K. and Khobragade N.W. (2012): Integral transforms methods for inverse problem of heat conduction with known boundary of a thin rectangular object and its stresses. – Journal of Thermal Science vol.21, No.5, pp.459-465.
20.
Lamba N.K. and Khobragade N.W. (2012): Uncoupled thermoelastic analysis for a thick cylinder with radiation. – Theoretical and Applied Mechanics Letters 2, 021005.
21.
Kamdi D. 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.
22.
Noda N., Hetnarski R.B. and Tanigawa Y. (2003): Thermal Stresses. – Second Edition, Taylor and Francis, New York, pp.376-387.
23.
Sneddon I.N. (1972): The use of Integral Transforms. – New York: McGraw-Hill.
24.
Povstenko Y. (2015): Fractional Thermoelasticity. – New York: Springer.
25.
Hussain E.M. (2014): Fractional order thermoelastic problem for an infinitely long solid circular cylinder. – Journal of Thermal Stresses, vol.38, pp.133-145.
26.
Raslan W. (2014): Application of fractional order theory of thermoelasticity to a 1d problem for a cylindrical cavity. – Arch. Mech., vol.66, pp.257-267.
27.
Hussain E.M. (2015): Fractional order thermoelastic problem for an infinitely long solid circular cylinder. – Journal of Thermal Stresses, vol.38, pp.133-145.
28.
Caputo M. (1967): Linear model of dissipation whose Q is almost frequency independent-II. – Geophys. J. Royal Astron. Soc., vol.13, pp.529-935.
29.
Caputo M. (1974): Vibrations on an infinite viscoelastic layer with a dissipative memory. – J. Acoust. Soc. Am., vol.56, pp.897-904.
30.
Caputo M. and Mainardi F. (1971): A new dissipation model based on memory mechanism. – Pure Appl. Geophys., vol.91, pp.134-147.
31.
Caputo M. and Mainardi F. (1971): Linear model of dissipation in an elastic solid. – Rivista Del NuovoCimento, vol.1, pp.161-198.