Short-time Analysis of Magnetothermoelastic Wave Under Fractional Order Heat Conduction Law

REFERENCES

• H. W. Lord and Y. H. Shulman , A Generalized Dynamical Theory of thermoelasticity , J. Mech. Phys. Solids , vol. 15 , pp. 299 – 309 , 1967 .
   Web of Science ®Google Scholar
• J. Ignaczak , Uniqueness in Generalized Thermoelasticity , J. Thermal Stresses , vol. 2 , pp. 171 – 175 , 1979 .
   Web of Science ®Google Scholar
• J. Ignaczak , A Note on Uniqueness in Thermoelasticity with One Relaxation Time , J. Thermal Stresses , vol. 5 , pp. 257 – 263 , 1982 .
   Web of Science ®Google Scholar
• R. S. Dhaliwal and H. Sherief , Generalized Thermoelasticity for Anisotropic Media , Quart. Appl. Math. vol. 33 , pp. 1 – 8 , 1980 .
   Web of Science ®Google Scholar
• A. E. Green and K. A. Lindsay , Thermoelasticity , J. Elastic. , vol. 2 , pp. 1 – 7 , 1972 .
   Google Scholar
• J. Ignaczak and M. Ostoja-Starzewski , Thermoelasticity with Finite Wave Speeds, Oxford Science Publications, 2010.
   Google Scholar
• M. R. Eslami , R. B. Hetnarski , J. Ignaczak , N. Noda , N. Sumi , and Y. Tanigawa , Theory of Elasticity and Thermal Stresses , Springer , vol. 197 , p . 786, 2013.
   Google Scholar
• A. E. Green and P. M. Naghdi , A Re-examination of the Basic Results of Thermomechanics , Proc. Roy. Soc. London. Ser. A , vol. 432 , pp. 171 – 194 , 1991 .
   Web of Science ®Google Scholar
• A. E. Green and P. M. Naghdi , On Undamped Heat Waves in an Elastic Solid , J. Thermal Stresses , vol. 15 , pp. 253 – 264 , 1992 .
   Web of Science ®Google Scholar
• A. E. Green and P. M. Nagdhi , Thermoelasticity without Energy Dissipation , J. Elasticity , vol. 31 , pp. 189 – 208 , 1993 .
   Web of Science ®Google Scholar
• A. Bagri and M. R. Eslami , Generalized Coupled Themoelasticity of Disks Based on Lord-Shulman Model , J. Thermal Stresses , vol. 27 , pp. 691 – 704 , 2004 .
   Web of Science ®Google Scholar
• A. Kar and M. Kanoria , Thermoelastic Interaction with Energy Dissipation in a Transversely Isotropic Thin Circular Disc , Euro. J. Mech. A/Solids , vol. 26 , pp. 969 – 981 , 2007 .
   Web of Science ®Google Scholar
• A. Kar and M. Kanoria , Thermoelastic Interaction with Energy Dissipation in an Unbounded Body with a Spherical Hole , Int. J. Solids and Structures , vol. 44 , pp. 2961 – 2971 , 2007 .
   Web of Science ®Google Scholar
• D. S. Chandrasekharaiah , Thermoelastic Plane Waves Without Energy Dissipation , Mech. Res. Commun. , vol. 23 , pp. 549 – 555 , 1996 .
   Web of Science ®Google Scholar
• D. S. Chandrasekharaiah , A Note on the Uniqueness of Solution in the Linear Theory of Thermoelasticity without Energy Dissipation , J. Elastic. , vol. 43 , pp. 279 – 283 , 1996 .
   Web of Science ®Google Scholar
• M. Islam , S. H. Mallik , and M. Kanoria , Dynamic Response in Two-dimensional Transversely Isotropic Thick Plate with Spatially Varying Heat Sources and Body Forces , J. Appl. Math. Mech.-Engl. Ed. , vol. 32 , pp. 1315 – 1332 , 2011 .
   Web of Science ®Google Scholar
• S. K. Roychoudhuri , On a Thermoelastic Three-phase-lag Model , J. Thermal Stresses , vol. 30 , pp. 231 – 238 , 2007 .
   Web of Science ®Google Scholar
• R. Quintanilla and R. Racke , A Note on Stability in Three-Phase-Lag Heat Conduction , Int. J. Heat Mass Transf. , vol. 51 , pp. 24 – 29 , 2008 .
   Web of Science ®Google Scholar
• R. Quintanilla , Spatial Behaviour of Solutions of the Three-Phase-Lag Heat Equation , Appl. Math. Comput. , vol. 213 , pp. 153 – 162 , 2009 .
   Web of Science ®Google Scholar
• M. Kanoria and S. H. Mallik , Generalized Thermoviscoelastic Interaction Due to Periodically Varying Heat Source with Three-Phase-Lag Effect, Eur. J. Mech. A/Solids , vol. 29, pp. 695–703, 2010.
   Web of Science ®Google Scholar
• A. Kar and M. Kanoria , Generalized Thermoelastic Functionally Graded Orthotropic Hollow Sphere Under Thermal Shock with Three-Phase-Lag Effect , Eur. J. Mech. A/Solids , vol. 28 , pp. 757 – 767 , 2009 .
   Web of Science ®Google Scholar
• A. Kar and M. Kanoria , Generalized Thermoe-Visco-Elastic Problem of a Spherical Shell with Three-phase-lag Effect , Appl. Math. Model. , vol. 33 , pp. 3287 – 3298 , 2009 .
   Web of Science ®Google Scholar
• A. Kar and M. Kanoria , Analysis of Thermoelastic Response in a Fiber Reinforced thin Annular Disc with Three-Phase-Lag Effect , Euro. J. Pure Appl. Math. , vol. 4 , pp. 304 – 321 , 2011 .
   Google Scholar
• M. Islam and M. Kanoria , Study of Dynamical Response in a Transversely Isotropic Thick Plate Due to Heat Source , J. Thermal Stresses , vol. 34 , pp. 702 – 723 , 2011 .
   Web of Science ®Google Scholar
• S. Banik , and M. Kanoria , Generalized Thermoelastic Interaction in Afunctionally Graded Isotropic Unbounded Medium Due to Varying Heat Source with Three-phase-lag Effect , Mathamatics and Mechanics of Solids , vol. 18 ( 3 ), pp. 231 – 245 , 2013 .
   Web of Science ®Google Scholar
• M. E. Gurtin and W. O. Williams , On the Clausius-Duhem Inequality , Z. Angew. Math. Phys. , vol. 7 , pp. 626 – 633 , 1966 .
   Web of Science ®Google Scholar
• M. E. Gurtin and W. O. Williams , An Axiomatic Foundation for Continuum Thermodynamics , Arch. Ration. Mech. Anal. , vol. 26 , pp. 83 – 117 , 1967 .
   Web of Science ®Google Scholar
• P. J. Chen and M. E. Gurtin , On a Theory of Heat Conduction Involving Two Temperatures , Z. Angew. Math. Phys. , vol. 19 , pp. 614 – 627 , 1968 .
   Web of Science ®Google Scholar
• P. J. Chen , M. E. Gurtin , and W. O. Williams , A Note on Non Simple Heat Conduction , Z. Angew. Math. Phys. , vol. 19 , pp. 969 – 970 , 1968 .
   Web of Science ®Google Scholar
• P. J. Chen , M. E. Gurtin , and W. O. Williams , On the Thermodynamics of Non-simple Elastic Materials with Two Temperatures , Z. Angew. Math. Phys. , vol. 20 , pp. 107 – 112 , 1969 .
   Web of Science ®Google Scholar
• W. E. Warren and P. J. Chen , Wave Propagation in Two Temperatures Theory of Thermoelasticity , Acta Mech. , vol. 16 , pp. 83 – 117 , 1973 .
   Web of Science ®Google Scholar
• D. Iesan , On the Linear Coupled Thermoelasticity with Two Temperatures , J. Appl. Math. Phys. , vol. 21 , pp. 583 – 591 , 1970 .
   Web of Science ®Google Scholar
• R. Quintanilla , Exponential Stability and Uniqueness in Thermoelasticity with Two Temperture , Dynam. Contin. Discrete Impul. Syst. A , vol. 11 , pp. 57 – 68 , 2004 .
   Web of Science ®Google Scholar
• R. Quintanilla , On Existence, Structural Stability, Convergence and Spatial Behavior in Thermoelasticity with Two Temperatures , Acta Mech. , vol. 168 , pp. 61 – 73 , 2004 .
   Web of Science ®Google Scholar
• P. Puri and P. M. Jordan , On the Propagation of Harmonic Plane Waves Under the Two-temperature Theory , Int. J. Eng. Sci. , vol. 44 , pp. 1113 – 1126 , 2006 .
   Web of Science ®Google Scholar
• H. M. Youssef , Theory of Two-temperature Generalized Thermoelasticity , IMA J. Appl. Math. , vol. 71 , pp. 1 – 8 , 2006 .
   Web of Science ®Google Scholar
• A. S. El-Karamany and M. A. Ezzat , On the Two-Temperature Green-Naghdi Thermoelasticity Theories , J. Thermal Stresses , vol. 34 , pp. 1207 – 1226 , 2011 .
   Web of Science ®Google Scholar
• R. Quintanilla , A Well Posed Problem for the Dual-Phase-Lag Heat Conduction , J. Thermal Stresses , vol. 31 , pp. 260 – 269 , 2008 .
   Web of Science ®Google Scholar
• R. Quintanilla , A Well Posed Problem for the Three-Dual-Phase-Lag Heat Conduction , J. Thermal Stresses , vol. 32 , pp. 1270 – 1278 , 2009 .
   Web of Science ®Google Scholar
• H. M. Youssef and A. H. Al-Harby , State-Space Approach of Two Temperature Generalized Thermoelasticity of Infinite Body with a Spherical Cavity Subjected to Different Type Thermal Loading , Arch. Appl. Mech. , vol. 77 , pp. 675 – 687 , 2007 .
   Web of Science ®Google Scholar
• H. M. Youssef and E. A. Al-Lehaibi , State-Space Approach of Two Temperature Generalized Thermoelasticity of One Dimensional Problem , Int. J. Solid Struct. , vol. 44 , pp. 1550 – 1562 , 2007 .
   Web of Science ®Google Scholar
• S. Banik and M. Kanoria , Two Temperature Generalized Thermoelastic Interactions in an Infinite Body with a Spherical Cavity, Int. J. Thermo Physics , vol. 32, pp. 1247–1270, 2011.
   Web of Science ®Google Scholar
• S. Banik , and M. Kanoria , Effects of Three-Phase-Lag on Two Temperature Generalized Thermoelasticity for Infinite Medium with Spherical Cavity , J. Appl. Math. Mech.-Engl. Ed. , vol. 33 ( 4 ), pp. 483 – 498 , 2012 .
   Web of Science ®Google Scholar
• S. Mukhopadhyay and R. Kumar , Thermoelastic Interactions on Two-Temperature Generalized Thermoelasticity in an Infinite Medium with a Cylindrical Cavity , J. Thermal Stresses , vol. 32 , pp. 341 – 360 , 2009 .
   Web of Science ®Google Scholar
• H. M. Youssef , Two Dimensional Problem of Two-Temperature Generalized Thermoelastic Half Space Subjected to Ramp-Type Heating , J. Comput. Math. Model. , vol. 19 , pp. 201 – 216 , 2008 .
   Google Scholar
• M. Islam , A. Kar , and M. Kanoria , Two-Temperature Generalized Thermoelasticity in a Fiber Reinforced Hollow Cylinder Under Thermal Shock , Int. J. Comp. Methods Eng. Sci. Mech. , vol. 14 , pp. 367 – 390 , 2013 .
   Google Scholar
• R. Kumar , R. Prasad , and S. Mukhopadhyay , Variational and Reciprocal Principles in Two Temperature Generalized Thermoelasticity , J. Thermal Stresses , vol. 33 , pp. 161 – 171 , 2010 .
   Web of Science ®Google Scholar
• R. Kumar , R. Prasad , and S. Mukhopadhyay , Some Theorems on Two Temperature Generalized Thermoelasticity , Arch Appl. Mech. , vol. 81 , pp. 1031 – 1040 , 2011 .
   Web of Science ®Google Scholar
• G. Paria , On Magneto-Thermo-Elastic Plane Waves , Proc. Camb. Phil. Soc. , vol. 58 , pp. 527 – 531 , 1962 .
   Web of Science ®Google Scholar
• A. Nayfeh and S. Nemat-Nasser , Thermo-elastic Waves in a Solids with Thermal Relaxation , Acta. Mech. , vol. 12 , pp. 43 – 69 , 1971 .
   Web of Science ®Google Scholar
• A. Nayfeh and S. Nemat-Nasser , Electro-Magneto-Thermo-Elastic Plane Waves in Solid with Thermal Relaxation , J. Appl. Mech. , vol. 39 , pp. 108 – 113 , 1972 .
   Web of Science ®Google Scholar
• S. K. Roychoudhuri , and G. Chatterjee , A Coupled Magneto-Thermo-Elastic Problem in a Perfectly Conducting Elastic Half-Space with Thermal Relaxation , Int. J. Math and Mech. Sci. , vol. 13 ( 3 ), pp. 567 – 578 , 1990 .
   Google Scholar
• R. K. T. Hsieh , Mechanical Modelling of New Electromagnetic Materials, Proc. IUTAM Symposium, Stockholm, Sweden, 2–6 April, 1990 .
   Google Scholar
• M. A. Ezzat , State Space Approach to Generalized Magneto-thermoelasticity with Two Relaxation Times in a Medium of Perfect Conductivity , J. Eng. Sci. , vol. 35 , no. 8 , pp. 741 – 752 , 1997 .
   Web of Science ®Google Scholar
• M. A. Ezzat , M. I. Othman , and A. S. El-Karamany , Electro-magneto-thermo-elastic Plane Waves with Thermal Relaxation in a Medium of Perfect Conductivity , J. Thermal Stresses , vol. 24 , pp. 411 – 432 , 2011 .
   Google Scholar
• H. H. Sherief and H. M. Youssef , Short Time Solution for a Problem in Magneto Thermoelasticity with Thermal Relaxation , J. Thermal Stresses , vol. 27 , pp. 537 – 559 , 2004 .
   Web of Science ®Google Scholar
• A. Baksi and R. K. Bera , Eigen Function Method for the Solution of Magneto-thermoelastic Problems with Thermal Relaxation and Heat Source in Three Dimension , Math. Comp. Modelling , vol. 42 , pp. 533 – 552 , 2005 .
   Web of Science ®Google Scholar
• P. Das , and M. Kanoria , Magneto-thermo-elastic Response in a Perfectly Conducting Medium with Three-Phase-Lag Effect , Acta Mech. , vol. 223 , no. 4 , pp. 811 – 828 2012 .
   Web of Science ®Google Scholar
• P. Das , A. Kar , and M. Kanoria , Analysis of Magneto-thermo-elastic Response in a Transversely Isotropic Hollow Cylinder Under Thermal Shock with Three-Phase-Lag Effect , J. Thermal Stresses , vol. 36 , pp. 239 – 258 , 2013 .
   Web of Science ®Google Scholar
• R. Kimmich , Strange Kinetics, Porous Media, and NMR , J. Chem. Phys. , vol. 284 , pp. 243 – 285 , 2002 .
   Google Scholar
• F. Mainardi and R. Gorenflo , On Mittag-Lettler-type Function in Fractional Evolution Processes , J. Comput. Appl. Math. , vol. 118 , pp. 283 – 299 , 2000 .
   Web of Science ®Google Scholar
• Y. Fujita , Integrodifferential Equation Which Interpolates the Heat Equation and Wave Equation (II), Osaka J. Math. , vol. 27, pp. 797–804, 1990.
   Web of Science ®Google Scholar
• Y. Z. Povstenko , Fractional Heat Conductive and Associated Thermal Stress , J. Thermal Stresses , vol. 28 , pp. 83 – 102 , 2004 .
   Web of Science ®Google Scholar
• Y. Z. Povstenko , Fractional Catteneo-type Equations and Generalized Thermoelasticity , J. Thermal Stresses , vol. 34 , pp. 94 – 114 , 2011 .
   Web of Science ®Google Scholar
• H. H. Sherief , A. El-Said , and A. Abd El-Latif , Fractional Order Theory of Thermoelasticity , Int. J. Solids Struct. , vol. 47 , pp. 269 – 275 , 2010 .
   Web of Science ®Google Scholar
• H. M. Youssef , Theory of Fractional Order Generalized Thermoelasticity , J. Heat Trans., (ASME) , vol. 132 , no. 6 , pp. 1 – 7 , 2010 .
   PubMed Web of Science ®Google Scholar
• A. S. El-Karamany and M. A. Ezzat , Convolution Variational Principles Reciprocal and Uniqueness Theorems in Linear Fractional Two-Temperature Thermoelasticity , J. Thermal Stresses , vol. 34 , no. 3 , pp. 264 – 284 , 2011 .
   Web of Science ®Google Scholar
• A. Sur and M. Kanoria , Fractional Order Two-Temperature Thermoelasticity with Finite Wave Speed , Acta Mech. , vol. 223 , pp. 2685 – 2701 , 2012 .
   Web of Science ®Google Scholar
• A. Sur and M. Kanoria , Fractional Order Generalized Thermo-visco-elastic Problem of a Spherical Shell with Three-phase-lag Effect , Latin Amer. J. Solid Struct. , vol. 11 , pp. 1132 – 1162 , 2014 .
   Web of Science ®Google Scholar
• M. Islam and M. Kanoria , One-Dimensional Problem of a Fractional Order Two Temperature Generalized Thermo-Piezoelasticity , Math. Mech. Solids , vol. 19 , pp. 672 – 693 , 2014 .
   Web of Science ®Google Scholar
• G. Honig and U. Hirdes , A Method For the Numerical Inversion of Laplace Transform , J. Comp. Appl. Math. , vol. 10 , pp. 113 – 132 , 1984 .
   Web of Science ®Google Scholar
• R. B. Hetnarski and M. R. Eslami , Thermal Stresses-Advanced Theory and Applications , Vol. 158 , pp. 560 , Springer , New York , 2009 .
   Google Scholar
• L. Y. Bahar and R. B. Hetnarski , State Space Approach to Thermoelasticity , J. Thermal Stresses , vol. 1 , pp. 135 – 145 , 1978 .
   Web of Science ®Google Scholar
• M. A. Ezzat and A. S. El-Karamany , Fractional Order Heat Conduction Law in Magneto-thermoelasticity Involving Two Temperatures , ZAMP , vol. 62 , pp. 937 – 952 , 2011 .
   Web of Science ®Google Scholar
• H. M. Youssef and E. A. Al-Lehaibi , State Space Approach of Two-Temperature Generalized Thermoelasticity of One-dimensional Problem , Int. J. Solid Struct. , vol. 44 , pp. 1550 – 1562 , 2007 .
   Web of Science ®Google Scholar