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Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses

Year 2020, Volume: 23 Issue: 4, 281 - 302, 27.11.2020

Shivcharan Thakare M. S. Warbhe Navneet Lamba

https://doi.org/10.5541/ijot.730617
https://izlik.org/JA87EG37BX

Abstract

In this article, we assume a two dimensional thermoelastic problem of a nonhomogeneous thick hollow cylinder within the context of fractional order derivative . Convection boundary conditions are applied on the curved surface of cylinder with internal heat generation. Let the material properties other then Poisson’s ratio and density are assumed to be expresses by a simple power law in axial direction. Lower and upper surface are assumed to be thermally insulated. The affect of inhomogeneity on the both thermal and mechanical behavior is examined. Numerical computations are carried out for both homogeneous and nonhomogeneous cylinders and are illustrated graphically are shown in figures with the help of Mathematica software.

Keywords

Time fractional thermal stresses nonhomogeneous cylinder internal heat generation

References

  • [1] Caputo, M., Linear Model of Dissipation whose Q is almost frequency independent-II, Geophys. J. Royal Astron. Soc., 13, 1967, 529–935.
  • [2] Lord, H., Shulman, Y., A Generalized Dynamical Theory of Thermoelasticity,” J. Mech. Phys. Solids, 15(5), 1967, 299–307.
  • [3] Caputo, M., Mainardi, F., A new Dissipation model based on Memory Mechanism,” Pure Appl. Geophys., 91, 1971, 134–147.
  • [4] Caputo, M., Mainardi, F., Linear Model of Dissipation in an Elastic Solids, Rivista Del Nuovo Cimento, 1, 1971, 161–198.
  • [5] Kassir, M. K., Boussinesq Problems for Nonhomogeneous Solid, Journal of the Engineering Mechanics Division, 98(2), 1972, 457-470.
  • [6] Green, A. E., Lindsay, K. A., Thermoelasticity, J. Elastic., 2(1), 1972, 1–7.
  • [7] Caputo, M., Vibrations on an infinite viscoelastic Layer with a Dissipative Memory, J. Acoust. Soc. Am., 56, 1974, 897–904.
  • [8] Edited by the Japan Society of Mechanical Engineers, Elastic Coefficient of Metallic Materials, Japan Society of Mechanical Engineers, 1980.
  • [9] Hata, T., Thermal Stresses in a Nonhomogeneous Thick Plate Under Steady Distribution of Temperature, Journal of Thermal Stresses, 5(1), 1982, 1-11.
  • [10] Sugano, Y., Transient Thermal Stresses in a Non-Homogeneous Doubly connected region, The Japan Society of Mechanical Engineers, 53, 1987, 941-946. [11] Sugano, Y., An expression for Transient Thermal Stress in a Nonhomogeneous Plate with Temperature variation through thickness, Ingenieur-Archiv., 57, 1987, 147-156.
  • [12] Sugano, Y., Transient Thermal Stresses in a Nonhomogeneous Doubly connected region, JSME International Journal Series, 31, 1988. 520-526.
  • [13] Green, A. E., Naghdi, P. M., Thermoelasticity without energy dissipation, J. Elastic., 31(3), 1993, 189–208.
  • [14] Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific Publishing, Singapore, 2000.
  • [15] Awaji, H., Sivakumar, R., Temperature and Stress Distributions in a Hollow Cylinder of Functionally Graded Material: The Case of Temperature-Independent Material Properties, Journal of the American Ceramic Society, 84(5), 2001, 1059-1065.
  • [16] Kim, K. S., Noda, N., Green's Function Approach to Unsteady Thermal Stresses in an Infinite Hollow Cylinder of Functionally Graded Material, Acta Mechanica, 156(3), 2002, 145-161.
  • [17] Noda, N., Hetnarski, R. B., Tanigawa, Y., Thermal Stresses 2nd Edition, Taylor and Francis, New York, 2003.
  • [18] Al-Hajri, M., Kalla, S. L., On an Integral Transform involving Bessel Functions, Proceedings of the international conference on Mathematics and its applications, Kuwait, April 5-7, 2004.
  • [19] Khobragade, N. L., Deshmukh, K. C., Thermal Deformation in a Thin Circular Plate due to a Partially Distributed Heat Supply, Sadhana, 30(4), 2005, 555-563.
  • [20] Ootao, Y., Tanigawa Y., Transient Thermoelastic analysis for a Functionally Graded Hollow Cylinder, Journal of Thermal Stresses, 29, 2005, 1031-1046.
  • [21] Povstenko, Y. Z., Fractional Heat Conduction Equation and Associated Thermal Stresses, Journal of Thermal Stresses, 28, 2005, 83-102.
  • [22] Mukhopadhay, S., Kumar, R., A Study of Generalized Thermoelastic interactions in an unbounded medium with a Spherical Cavity, Computers and Mathematics with Applications, 56, 2008, 2329-2339.
  • [23] Kar, A., Kanoria, M., Generalized Thermoelasticity problem of a Hollow Sphere under Thermal Shock, European Journal of Pure and Applied Mathematics, 2, 2009, 125-146. 2009.
  • [24] Hosseini, S. M., Akhlaghi, M., Analytical Solution in Transient Thermoelasticity of Functionally Graded Thick Hollow Cylinders, Math. Methods Appl. Sci., 32(15), 2009, 2019-2034.
  • [25] Ootao, Y., Transient Thermoelastic analysis for a Multilayered Hollow Cylinder with Piecewise Power Law Nonhomogenity, Journal of Solid Mechanics and Materials Engineering, 4, 2010, 1167-1177.
  • [26] Sherief, H., El-Sayed, A. M. A., Abd El-Latief, A. M., Fractional Order Theory of Thermoelasticity, International Journal of Solids Structure, 47(2), 2010, 269–275.
  • [27] Povstenko, Y. Z., Fractional Radial Heat Conduction in an infinite medium with a Cylindrical Cavity and associated Thermal Stresses, Mech. Res. Commun., 37, 2010, 436-440.
  • [28] Ehteram, M. A., Sadighi, M., Tabrizi, H. B., Analytical Solution for Thermal Stresses of Laminated Hollow Cylinders under Transient Nonuniform Thermal Loading, Mechanika, 17(1), 2011, 30-37.
  • [29] Povstenko, Y. Z., Non-Axisymmetric Solutions to Time-Fractional Diffusion-Wave Equation in an Infinite Cylinder, Fract. Calc. Appl. Anal., 14(3), 2011, 418–435.
  • [30] Povstenko, Y. Z., Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates, Advances in Differential Equations, Article no. 930297, 2011.
  • [31] Povstenko, Y. Z., Non-Axisymmetric Solutions to Time-Fractional Heat Conduction Equation in a Half-Space in Cylindrical Coordinates, Math. Methods Phys.-Mech. Fields, 54(1), 2011, 212–219.
  • [32] Ezzat, M. A., EL-Karamany, A. S., Fractional Order Theory of a perfect conducting Thermoelastic Medium, Can. J. Phys., 89, 2011, 311–318.
  • [33] Ezzat, M. A., EL-Karamany, A. S., Theory of Fractional Order in Electro - Thermoelasticity, Eur. J. Mech. A/Solids, 30, 2011, 491–500.
  • [34] Ezzat, M. A., EL-Karamany, A. S., Fractional Order Heat conduction law in Magneto-Thermoelasticity involving two Temperatures, Z. Angew. Math. Phys., 62(5), 2011, 937–952.
  • [35] Ezzat, M. A., EL-Karamany, A. S., On Fractional Thermoelasticity, Math. Mech. Solids, 16(3), 2011, 334–346.
  • [36] Ezzat, M. A., State Space approach to Thermoelectric Fluid with Fractional Order Heat Transfer, Heat Mass Trans., 48, 2012, 71–82.
  • [37] Ootao, Y., Tanigawa Y., Transient Thermoelastic Analysis for a Functionally Graded Hollow Circular Disk with Piecewise Power Law Nonhomogenity, Journal of Thermal Stresses, 35, 2012, 75-90.
  • [38] Sherief, H., El-Sayed, A. M., Behiry, S. H., Raslan, W. E., Using Fractional Derivatives to Generalize the Hodgkin–Huxley Model, Fractional Dynamics and Control, 2012, 275–282.
  • [39] Sur, A., Kanoria, M., Fractional Order two-Temperature Thermoelasticity with wave speed, Acta Mechanica, 223, 2012, 2685-2701.
  • [40] Ezzat, M. A., EL-Karamany, A. S., Ezzat, S. M., Two-Temperature Theory in Magneto-Thermoelasticity with Fractional Order dual-phase-lag Heat Transfer, Nuc. Eng. Des., 252,2012, 267–277.
  • [41] Ezzat, A. S., EL-Karamany, A. S. Fayik, M. A., Fractional Order Theory in Thermoelastic Solid with three-phase lag Heat Transfer, Arch. Appl. Mech., 82(4),2012, 557–572.
  • [42] Youssef, H. M., Two-Dimensional Thermal Shock problem of Fractional Order Generalized Thermoelasticity, Acta Mech., 223, 2012, 1219-1231.
  • [43] Sherief, H., Abd El-Latief, A. M., Application of Fractional Order Theory of Thermoelasticity to a 1D problem for a half-space, ZAMM, 2, 2013, 1-7.
  • [44] Ezzat, M. A., EL-Karamany, A. S., EL-Bary, A. A., Fayik, M. A., Fractional calculus in One-dimensional Isotropic Thermo-viscoelasticity,” Comp. Rendus Mecanique, 341, 2013, 553–566.
  • [45] Tenreiro, J., Alexandra, M., Trujillo, J., Science Metrics on Fractional Calculus Development since 1966, Fract. Calc. Appl. Anal., 16, 2013, 479–500.
  • [46] Aksoy, S., Kurşun, A., Çetin, E., Haboğlu, M. R., Stress analysis of Laminated Cylinders subject to the Thermo-Mechanical Loads, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 8(2), 2014, 244-249.
  • [47] Fu, J., Chen, Z., Qian, L., Hu, K., Transient Thermoelastic analysis of a Solid Cylinder containing a Circumferential Crack using the C–V Heat Conduction Model, Journal of Thermal Stresses, 37(11), 2014, 1324-1345.
  • [48] Jabbari, M., Hashemitaheri, M., Mojahedin, A., Eslami, M. R., Thermal Buckling analysis of Functionally Graded thin Circular Plate made of Saturated Porous Materials, Journal of Thermal Stresses, 37(2), 2014, 202-220.
  • [49] Sur, A., Kanoria, M., Fractional Order Generalized Thermoelastic Functionally Graded solid with variable material properties, Journal of Solid Mechanics, 6, 2014, 54-69.
  • [50] Hussain, E. M., Fractional Order Thermoelastic Problem for an Infinitely Long Solid Circular Cylinder, Journal of Thermal Stresses, 38, 2014, 133-145.
  • [51] Raslan, W., Application of Fractional Order Theory of Thermoelasticity to a 1D problem for a Cylindrical Cavity, Arch. Mech, 66, 2014, 257-267.
  • [52] Povstenko, Y., Fractional Thermoelasticity, New York, Springer, 2015.
  • [53] Hussain, E. M., Fractional Order Thermoelastic Problem for an infinitely Long Solid Circular Cylinder, Journal of Thermal Stresses, 38, 2015, 133-145.
  • [54] Kedar, G. D., Deshmukh, K. C., Inverse Heat Conduction Problem in a Semi-infinite Hollow Cylinder and its Thermal Deflection by Quasi-static Approach, International Journal of Applied Mathematics and Computation, 6(2), 2015, 15-21.
  • [55] Raslan, W. E., Application of Fractional Order Theory of Thermoelasticity in a Thick Plate under Axisymmetric Temperature distribution, Journal of Thermal Stresses, 38(7), 2015, 733–743.
  • [56] Ezzat, M. A., EL-Karamany, A. S., EL-Bary, A. A., On Thermo-viscoelasticity with variable Thermal conductivity and Fractional-Order Heat Transfer, Int. J. Thermophys., 36(7), 1684–1697, 2015.
  • [57] Ezzat, M. A., EL-Karamany, A. S., EL-Bary, A. A., Thermo-viscoelastic materials with Fractional Relaxation Operators,” Appl. Math. Modell., 39, 2015, 7499–7512.
  • [58] Ezzat, M. A., EL-Bary, A. A., Unified Fractional Derivative Models of Magneto-Thermo-viscoelasticity theory, Archives of Mechanics, 68, 2016, 285–308.
  • [59] Xiong, C., Guo, Y., Effect of variable properties and Moving Heat Source on Magneto Thermoelastic Problem under Fractional Order Thermoelasticity, Advanced in Material Science and Engineering, 2016, 1–12.
  • [60] Sherief, H. H., Hamza, F A., Modeling of variable Thermal Conductivity in a Generalized Thermoelastic infinitely Long Hollow Cylinder, Meccanica, 51, 2016, 551–558.
  • [61] Zhang, X. Y., Li, X. F., Transient Response of a Hygrothermoelastic Cylinder based on Fractional Diffusion Wave Theory, Journal of Thermal Stresses, 40, 2017, 1575–1594.
  • [62] Zhang, X. Y., Peng Y., Li, X.-F., Time-Fractional Hygrothermoelastic problem for a Sphere Subjected to Heat and Moisture Flux, Journal of Heat Transfer,140,122002, 2018.
  • [63] Khobragade, N. L., Kumar, N., 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, 10(3), 2019, 429-437.
  • [64] Khobragade, N. L., Kumar, N., Study of Thermoelastic Deformation of a Solid Circular Cylinder by Application of Fractional Order Theory, Journal of Computer and Mathematical Sciences, 10(3), 2019, 438-444.
  • [65] Khobragade, N. L., Lamba, N. K., Magneto-thermodynamic Stress Analysis of an Orthotropic Solid Cylinder by Fractional Order Theory Application, Research & Reviews: Journal of Physics, 8(1), 2019, 37-45.
  • [66] Khobragade, N. L., Lamba, N. K., Modeling of Thermoelastic Hollow Cylinder by the Application of Fractional Order Theory, Research & Reviews: Journal of Physics, 8, (1), 2019, 46-57.

Year 2020, Volume: 23 Issue: 4, 281 - 302, 27.11.2020

Shivcharan Thakare M. S. Warbhe Navneet Lamba

https://doi.org/10.5541/ijot.730617
https://izlik.org/JA87EG37BX

Abstract

References

  • [1] Caputo, M., Linear Model of Dissipation whose Q is almost frequency independent-II, Geophys. J. Royal Astron. Soc., 13, 1967, 529–935.
  • [2] Lord, H., Shulman, Y., A Generalized Dynamical Theory of Thermoelasticity,” J. Mech. Phys. Solids, 15(5), 1967, 299–307.
  • [3] Caputo, M., Mainardi, F., A new Dissipation model based on Memory Mechanism,” Pure Appl. Geophys., 91, 1971, 134–147.
  • [4] Caputo, M., Mainardi, F., Linear Model of Dissipation in an Elastic Solids, Rivista Del Nuovo Cimento, 1, 1971, 161–198.
  • [5] Kassir, M. K., Boussinesq Problems for Nonhomogeneous Solid, Journal of the Engineering Mechanics Division, 98(2), 1972, 457-470.
  • [6] Green, A. E., Lindsay, K. A., Thermoelasticity, J. Elastic., 2(1), 1972, 1–7.
  • [7] Caputo, M., Vibrations on an infinite viscoelastic Layer with a Dissipative Memory, J. Acoust. Soc. Am., 56, 1974, 897–904.
  • [8] Edited by the Japan Society of Mechanical Engineers, Elastic Coefficient of Metallic Materials, Japan Society of Mechanical Engineers, 1980.
  • [9] Hata, T., Thermal Stresses in a Nonhomogeneous Thick Plate Under Steady Distribution of Temperature, Journal of Thermal Stresses, 5(1), 1982, 1-11.
  • [10] Sugano, Y., Transient Thermal Stresses in a Non-Homogeneous Doubly connected region, The Japan Society of Mechanical Engineers, 53, 1987, 941-946. [11] Sugano, Y., An expression for Transient Thermal Stress in a Nonhomogeneous Plate with Temperature variation through thickness, Ingenieur-Archiv., 57, 1987, 147-156.
  • [12] Sugano, Y., Transient Thermal Stresses in a Nonhomogeneous Doubly connected region, JSME International Journal Series, 31, 1988. 520-526.
  • [13] Green, A. E., Naghdi, P. M., Thermoelasticity without energy dissipation, J. Elastic., 31(3), 1993, 189–208.
  • [14] Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific Publishing, Singapore, 2000.
  • [15] Awaji, H., Sivakumar, R., Temperature and Stress Distributions in a Hollow Cylinder of Functionally Graded Material: The Case of Temperature-Independent Material Properties, Journal of the American Ceramic Society, 84(5), 2001, 1059-1065.
  • [16] Kim, K. S., Noda, N., Green's Function Approach to Unsteady Thermal Stresses in an Infinite Hollow Cylinder of Functionally Graded Material, Acta Mechanica, 156(3), 2002, 145-161.
  • [17] Noda, N., Hetnarski, R. B., Tanigawa, Y., Thermal Stresses 2nd Edition, Taylor and Francis, New York, 2003.
  • [18] Al-Hajri, M., Kalla, S. L., On an Integral Transform involving Bessel Functions, Proceedings of the international conference on Mathematics and its applications, Kuwait, April 5-7, 2004.
  • [19] Khobragade, N. L., Deshmukh, K. C., Thermal Deformation in a Thin Circular Plate due to a Partially Distributed Heat Supply, Sadhana, 30(4), 2005, 555-563.
  • [20] Ootao, Y., Tanigawa Y., Transient Thermoelastic analysis for a Functionally Graded Hollow Cylinder, Journal of Thermal Stresses, 29, 2005, 1031-1046.
  • [21] Povstenko, Y. Z., Fractional Heat Conduction Equation and Associated Thermal Stresses, Journal of Thermal Stresses, 28, 2005, 83-102.
  • [22] Mukhopadhay, S., Kumar, R., A Study of Generalized Thermoelastic interactions in an unbounded medium with a Spherical Cavity, Computers and Mathematics with Applications, 56, 2008, 2329-2339.
  • [23] Kar, A., Kanoria, M., Generalized Thermoelasticity problem of a Hollow Sphere under Thermal Shock, European Journal of Pure and Applied Mathematics, 2, 2009, 125-146. 2009.
  • [24] Hosseini, S. M., Akhlaghi, M., Analytical Solution in Transient Thermoelasticity of Functionally Graded Thick Hollow Cylinders, Math. Methods Appl. Sci., 32(15), 2009, 2019-2034.
  • [25] Ootao, Y., Transient Thermoelastic analysis for a Multilayered Hollow Cylinder with Piecewise Power Law Nonhomogenity, Journal of Solid Mechanics and Materials Engineering, 4, 2010, 1167-1177.
  • [26] Sherief, H., El-Sayed, A. M. A., Abd El-Latief, A. M., Fractional Order Theory of Thermoelasticity, International Journal of Solids Structure, 47(2), 2010, 269–275.
  • [27] Povstenko, Y. Z., Fractional Radial Heat Conduction in an infinite medium with a Cylindrical Cavity and associated Thermal Stresses, Mech. Res. Commun., 37, 2010, 436-440.
  • [28] Ehteram, M. A., Sadighi, M., Tabrizi, H. B., Analytical Solution for Thermal Stresses of Laminated Hollow Cylinders under Transient Nonuniform Thermal Loading, Mechanika, 17(1), 2011, 30-37.
  • [29] Povstenko, Y. Z., Non-Axisymmetric Solutions to Time-Fractional Diffusion-Wave Equation in an Infinite Cylinder, Fract. Calc. Appl. Anal., 14(3), 2011, 418–435.
  • [30] Povstenko, Y. Z., Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates, Advances in Differential Equations, Article no. 930297, 2011.
  • [31] Povstenko, Y. Z., Non-Axisymmetric Solutions to Time-Fractional Heat Conduction Equation in a Half-Space in Cylindrical Coordinates, Math. Methods Phys.-Mech. Fields, 54(1), 2011, 212–219.
  • [32] Ezzat, M. A., EL-Karamany, A. S., Fractional Order Theory of a perfect conducting Thermoelastic Medium, Can. J. Phys., 89, 2011, 311–318.
  • [33] Ezzat, M. A., EL-Karamany, A. S., Theory of Fractional Order in Electro - Thermoelasticity, Eur. J. Mech. A/Solids, 30, 2011, 491–500.
  • [34] Ezzat, M. A., EL-Karamany, A. S., Fractional Order Heat conduction law in Magneto-Thermoelasticity involving two Temperatures, Z. Angew. Math. Phys., 62(5), 2011, 937–952.
  • [35] Ezzat, M. A., EL-Karamany, A. S., On Fractional Thermoelasticity, Math. Mech. Solids, 16(3), 2011, 334–346.
  • [36] Ezzat, M. A., State Space approach to Thermoelectric Fluid with Fractional Order Heat Transfer, Heat Mass Trans., 48, 2012, 71–82.
  • [37] Ootao, Y., Tanigawa Y., Transient Thermoelastic Analysis for a Functionally Graded Hollow Circular Disk with Piecewise Power Law Nonhomogenity, Journal of Thermal Stresses, 35, 2012, 75-90.
  • [38] Sherief, H., El-Sayed, A. M., Behiry, S. H., Raslan, W. E., Using Fractional Derivatives to Generalize the Hodgkin–Huxley Model, Fractional Dynamics and Control, 2012, 275–282.
  • [39] Sur, A., Kanoria, M., Fractional Order two-Temperature Thermoelasticity with wave speed, Acta Mechanica, 223, 2012, 2685-2701.
  • [40] Ezzat, M. A., EL-Karamany, A. S., Ezzat, S. M., Two-Temperature Theory in Magneto-Thermoelasticity with Fractional Order dual-phase-lag Heat Transfer, Nuc. Eng. Des., 252,2012, 267–277.
  • [41] Ezzat, A. S., EL-Karamany, A. S. Fayik, M. A., Fractional Order Theory in Thermoelastic Solid with three-phase lag Heat Transfer, Arch. Appl. Mech., 82(4),2012, 557–572.
  • [42] Youssef, H. M., Two-Dimensional Thermal Shock problem of Fractional Order Generalized Thermoelasticity, Acta Mech., 223, 2012, 1219-1231.
  • [43] Sherief, H., Abd El-Latief, A. M., Application of Fractional Order Theory of Thermoelasticity to a 1D problem for a half-space, ZAMM, 2, 2013, 1-7.
  • [44] Ezzat, M. A., EL-Karamany, A. S., EL-Bary, A. A., Fayik, M. A., Fractional calculus in One-dimensional Isotropic Thermo-viscoelasticity,” Comp. Rendus Mecanique, 341, 2013, 553–566.
  • [45] Tenreiro, J., Alexandra, M., Trujillo, J., Science Metrics on Fractional Calculus Development since 1966, Fract. Calc. Appl. Anal., 16, 2013, 479–500.
  • [46] Aksoy, S., Kurşun, A., Çetin, E., Haboğlu, M. R., Stress analysis of Laminated Cylinders subject to the Thermo-Mechanical Loads, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 8(2), 2014, 244-249.
  • [47] Fu, J., Chen, Z., Qian, L., Hu, K., Transient Thermoelastic analysis of a Solid Cylinder containing a Circumferential Crack using the C–V Heat Conduction Model, Journal of Thermal Stresses, 37(11), 2014, 1324-1345.
  • [48] Jabbari, M., Hashemitaheri, M., Mojahedin, A., Eslami, M. R., Thermal Buckling analysis of Functionally Graded thin Circular Plate made of Saturated Porous Materials, Journal of Thermal Stresses, 37(2), 2014, 202-220.
  • [49] Sur, A., Kanoria, M., Fractional Order Generalized Thermoelastic Functionally Graded solid with variable material properties, Journal of Solid Mechanics, 6, 2014, 54-69.
  • [50] Hussain, E. M., Fractional Order Thermoelastic Problem for an Infinitely Long Solid Circular Cylinder, Journal of Thermal Stresses, 38, 2014, 133-145.
  • [51] Raslan, W., Application of Fractional Order Theory of Thermoelasticity to a 1D problem for a Cylindrical Cavity, Arch. Mech, 66, 2014, 257-267.
  • [52] Povstenko, Y., Fractional Thermoelasticity, New York, Springer, 2015.
  • [53] Hussain, E. M., Fractional Order Thermoelastic Problem for an infinitely Long Solid Circular Cylinder, Journal of Thermal Stresses, 38, 2015, 133-145.
  • [54] Kedar, G. D., Deshmukh, K. C., Inverse Heat Conduction Problem in a Semi-infinite Hollow Cylinder and its Thermal Deflection by Quasi-static Approach, International Journal of Applied Mathematics and Computation, 6(2), 2015, 15-21.
  • [55] Raslan, W. E., Application of Fractional Order Theory of Thermoelasticity in a Thick Plate under Axisymmetric Temperature distribution, Journal of Thermal Stresses, 38(7), 2015, 733–743.
  • [56] Ezzat, M. A., EL-Karamany, A. S., EL-Bary, A. A., On Thermo-viscoelasticity with variable Thermal conductivity and Fractional-Order Heat Transfer, Int. J. Thermophys., 36(7), 1684–1697, 2015.
  • [57] Ezzat, M. A., EL-Karamany, A. S., EL-Bary, A. A., Thermo-viscoelastic materials with Fractional Relaxation Operators,” Appl. Math. Modell., 39, 2015, 7499–7512.
  • [58] Ezzat, M. A., EL-Bary, A. A., Unified Fractional Derivative Models of Magneto-Thermo-viscoelasticity theory, Archives of Mechanics, 68, 2016, 285–308.
  • [59] Xiong, C., Guo, Y., Effect of variable properties and Moving Heat Source on Magneto Thermoelastic Problem under Fractional Order Thermoelasticity, Advanced in Material Science and Engineering, 2016, 1–12.
  • [60] Sherief, H. H., Hamza, F A., Modeling of variable Thermal Conductivity in a Generalized Thermoelastic infinitely Long Hollow Cylinder, Meccanica, 51, 2016, 551–558.
  • [61] Zhang, X. Y., Li, X. F., Transient Response of a Hygrothermoelastic Cylinder based on Fractional Diffusion Wave Theory, Journal of Thermal Stresses, 40, 2017, 1575–1594.
  • [62] Zhang, X. Y., Peng Y., Li, X.-F., Time-Fractional Hygrothermoelastic problem for a Sphere Subjected to Heat and Moisture Flux, Journal of Heat Transfer,140,122002, 2018.
  • [63] Khobragade, N. L., Kumar, N., 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, 10(3), 2019, 429-437.
  • [64] Khobragade, N. L., Kumar, N., Study of Thermoelastic Deformation of a Solid Circular Cylinder by Application of Fractional Order Theory, Journal of Computer and Mathematical Sciences, 10(3), 2019, 438-444.
  • [65] Khobragade, N. L., Lamba, N. K., Magneto-thermodynamic Stress Analysis of an Orthotropic Solid Cylinder by Fractional Order Theory Application, Research & Reviews: Journal of Physics, 8(1), 2019, 37-45.
  • [66] Khobragade, N. L., Lamba, N. K., Modeling of Thermoelastic Hollow Cylinder by the Application of Fractional Order Theory, Research & Reviews: Journal of Physics, 8, (1), 2019, 46-57.
There are 65 citations in total.

Details

Primary Language English
Subjects Material Production Technologies
Journal Section Research Article
Authors

Shivcharan Thakare This is me

M. S. Warbhe This is me

Navneet Lamba

Publication Date November 27, 2020
DOI https://doi.org/10.5541/ijot.730617
IZ https://izlik.org/JA87EG37BX
Published in Issue Year 2020 Volume: 23 Issue: 4

Cite

APA Thakare, S., Warbhe, M. S., & Lamba, N. (2020). Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses. International Journal of Thermodynamics, 23(4), 281-302. https://doi.org/10.5541/ijot.730617
AMA 1.Thakare S, Warbhe MS, Lamba N. Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses. International Journal of Thermodynamics. 2020;23(4):281-302. doi:10.5541/ijot.730617
Chicago Thakare, Shivcharan, M. S. Warbhe, and Navneet Lamba. 2020. “Time Fractional Heat Transfer Analysis in Nonhomogeneous Thick Hollow Cylinder With Internal Heat Generation and Its Thermal Stresses”. International Journal of Thermodynamics 23 (4): 281-302. https://doi.org/10.5541/ijot.730617.
EndNote Thakare S, Warbhe MS, Lamba N (November 1, 2020) Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses. International Journal of Thermodynamics 23 4 281–302.
IEEE [1]S. Thakare, M. S. Warbhe, and N. Lamba, “Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses”, International Journal of Thermodynamics, vol. 23, no. 4, pp. 281–302, Nov. 2020, doi: 10.5541/ijot.730617.
ISNAD Thakare, Shivcharan - Warbhe, M. S. - Lamba, Navneet. “Time Fractional Heat Transfer Analysis in Nonhomogeneous Thick Hollow Cylinder With Internal Heat Generation and Its Thermal Stresses”. International Journal of Thermodynamics 23/4 (November 1, 2020): 281-302. https://doi.org/10.5541/ijot.730617.
JAMA 1.Thakare S, Warbhe MS, Lamba N. Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses. International Journal of Thermodynamics. 2020;23:281–302.
MLA Thakare, Shivcharan, et al. “Time Fractional Heat Transfer Analysis in Nonhomogeneous Thick Hollow Cylinder With Internal Heat Generation and Its Thermal Stresses”. International Journal of Thermodynamics, vol. 23, no. 4, Nov. 2020, pp. 281-02, doi:10.5541/ijot.730617.
Vancouver 1.Shivcharan Thakare, M. S. Warbhe, Navneet Lamba. Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses. International Journal of Thermodynamics. 2020 Nov. 1;23(4):281-302. doi:10.5541/ijot.730617

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