Numerical Simulation of Non-Fourier Temperature Behavior of Functionally Graded Materials in a Slab with Surface Radiation

REFERENCES

• C. Cattaneo , Sullaconduzione de Calore, In Atti del Seminar , Mat. Fis. Univ., Modena, Italy , vol. 3 , pp. 83 – 101 , 1948 . (In Italian.)
   Google Scholar
• P. Vernotte , Les Paradoxes de la Theorie Continue de Lequation de la Chaleur , Compute Rendus , vol. 246 , pp. 3145 – 3155 , 1958 . (In French.)
   Google Scholar
• D. Y. Tzou , Macro-to Microscale Heat Transfer, The Lagging Behaviour , pp. 1 – 65 , Taylor & Francis , Washington , D.C. , 1997 .
   Google Scholar
• D. W. Tang and N. Araki , Non-Fourier Heat Conduction Behavior in Finite Mediums under Pulse Surface Heating , Materials Sci. and Eng. , vol. A292 , pp. 173 – 178 , 2000 .
   Google Scholar
• S. Kiwan , M. A1-Nimr and M. Al-Sharo'a , Trial Solution Methods to Solve the Hyperbolic Heat Conduction Equation , Int. Comm. Heat Mass Transfer , vol. 27 , pp. 865 – 876 , 2000 .
   Web of Science ®Google Scholar
• M. Lewandowska and L. Malinowski , An Analytical Solution of the Hyperbolic Heat Conduction Equation for the Case of a Finite Medium Symmetrically Heated on Both Sides , Int. Comm. in Heat and Mass Transfer , vol. 33 , pp. 61 – 69 , 2006 .
   Web of Science ®Google Scholar
• G. Heidarinejad , R. Shirmohammadi , and M. Maerefat , Heat Wave Phenomena in Solids Subjected to Time-Dependent Surface Heat Flux , Heat Mass Transfer , vol. 44 , pp. 381 – 392 , 2008 .
   Web of Science ®Google Scholar
• T. M. Chen , A Hybrid Green's Function Method for the Hyperbolic Heat Conduction Problems , Int. J. Heat and Mass Transfer , vol. 52 , pp. 4273 – 4278 , 2009 .
   Web of Science ®Google Scholar
• T. M. Chen and C. C. Chen , Numerical Solution for the Hyperbolic Heat Conduction Problems in the Radial-Spherical Coordinate System using a Hybrid Green's Function Method , Int. J. Thermal Sci. , vol. 49 , pp. 1193 – 1196 , 2010 .
   Web of Science ®Google Scholar
• D. E. Glass , M. N. Özişik , D. S. McRae , and B. Vick , On the Numerical Solution of Hyperbolic Heat Conduction , Numer. Heat Transfer, A , vol. 8 , pp. 497 – 504 , 1985 .
   Web of Science ®Google Scholar
• D. E. Glass , M. N. Özişik , and B. Vick , Hyperbolic Heat Conduction with Surface Radiation , Int. J. Heat Mass Transfer , vol. 28 , pp. 1823 – 1830 , 1985 .
   Web of Science ®Google Scholar
• D. E. Glass and M. N. Ozisik , On the Non-Fourier Effects on Transient Temperature Resulting from Periodic On-Off Heat Flux , Int. J. Heat Mass. Transfer , vol. 30 , pp. 1623 – 1631 , 1987 .
   Web of Science ®Google Scholar
• D. E. Glass , M. N. Ozisik , and D. S. McRae , Hyperbolic Heat Conduction with Radiation in an Absorbing and Emitting Medium , Numer. Heat Transfer, Part A , vol. 12 , pp. 321 – 333 , 1987 .
   Web of Science ®Google Scholar
• D. E. Glass , K. K. Tamma , and S. B. Railkar , Numerical Simulation of Hyperbolic Heat Conduction with Convection Boundary Conditions and Pulse Heating Effects , J. Thermophysics and Heat Transfer , vol. 5 , no. 1 , pp. 110 – 116 , 1991 .
   Web of Science ®Google Scholar
• D. E. Glass , M. N. Ozisik , and W. S. Kim , On the Numerical Solution of Hyperbolic Heat Conduction , Numer. Heat Transfer, Part A , vol. 18 , pp. 503 – 516 , 1990 .
   Web of Science ®Google Scholar
• D. E. Glass , M. N. Ozisik , and W. S. Kim , Hyperbolic Stefan Problem with Applied Surface Heat Flux and Temperature-Dependent Thermal Conductivity , Numer. Heat Transfer A , vol. 18 , pp. 503 – 516 , 1991 .
   Web of Science ®Google Scholar
• B. Pulvirenti , A. Barletta , and E. Zanchini , Finite-Difference Solution of Hyperbolic Heat Conduction with Temperature-Dependent Properties , Numer. Heat Transfer A , vol. 34 , pp. 169 – 183 , 1998 .
   Web of Science ®Google Scholar
• J. Fang-Ming and L. Deng-Ying , Experimental Results and Theoretical Analyse of Non-Fourier Heat Conduction Phenomenon in Porous Material , J. of Eng. Thermophysics , vol. 1 , pp. 77 – 80 , 2001 .
   Google Scholar
• S. Torii , Propagation Phenomena During Symmetrical Collision of Thermal Waves in Thin Film, Int. J. of Transport Phenomena , vol. 3, pp. 357–364, 2001.
   Google Scholar
• H. S. Chu , S. Lin , and C. H. Lin , On Non-Fourier Heat Conduction with Radiation in an Absorbing, Emitting, and Isotropically Scattering Medium , J. Quant. Spectrosc. Radiat. Transfer , vol. 73 , pp. 571 – 582 , 2002 .
   Web of Science ®Google Scholar
• S. Torii and W. Yang , Heat Transfer Mechanisms in Thin Film with Laser Heat Source , Int. J. Heat Mass Transfer , vol. 48 , pp. 537 – 544 , 2005 .
   Web of Science ®Google Scholar
• M. Goharkhah , S. Amiri , and B. Baghapour , Numerical Investigation for Determining Temperature Peaks in a Finite Slab With Volumetric Heat Generation Based on the Hyperbolic Model of Heat Conduction, ASME, 7th Int. Conf. on Nanochannels, Microchannels, and Minichannels, Pohang, South Korea, pp. 491–495, 2009 .
   Google Scholar
• R. Ghazizadeh , M. Maerefat , and A. Azimi , Explicit and Implicit Finite Difference Schemes for Fractional Cattaneo Equation , J. of Computational Physics , vol. 229 , pp. 7042 – 7057 , 2010 .
   Web of Science ®Google Scholar
• C. C. Yen and C. Y. Wu , Modelling Hyperbolic Heat Conduction in a Finite Medium with Periodic Thermal Disturbance and Surface Radiation , Appl. Mathematical Modelling , vol. 27 , pp. 397 – 408 , 2003 .
   Web of Science ®Google Scholar
• H. T. Chen and J. Y. Lin , Numerical Analysis for Hyperbolic Heat Conduction , Int. J. Heat Mass Transfer , vol. 36 , pp. 2891 – 2898 , 1993 .
   Web of Science ®Google Scholar
• K. C. Liu and H. T. Chen , Numerical Analysis for the Hyperbolic Heat Conduction Problem under a Pulsed Surface Disturbance , Appl. Mathematics and Computation , vol. 159 , pp. 887 – 901 , 2004 .
   Web of Science ®Google Scholar
• K. C. Liu , C. N. Lin , and J. S. Wang , Numerical Solutions for the Hyperbolic Heat Conduction Problems in a Layered Solid Cylinder with Radiation Surface , Appl. Mathematics and Computation , vol. 164 , pp. 805 – 820 , 2005 .
   Web of Science ®Google Scholar
• W. K. Yeung and T. T. Lam , A Numerical Scheme for Non-Fourier Heat Conduction, Part I: One-Dimensional Problem Formulation, and Applications , Numer. Heat Transfer B , vol. 33 , pp. 215 – 233 , 1998 .
   Web of Science ®Google Scholar
• S. C. Mishra , T. B. Pavan Kumar , and B. Mondal , Lattice Boltzmann Method Applied to the Solution of Energy Equation of a Radiation and Non-Fourier Heat Conduction Problem , Numer. Heat Transfer A , vol. 54 , pp. 798 – 818 , 2008 .
   Web of Science ®Google Scholar
• J. Zhou , Y. Zhang , and J. K. Chen , Non-Fourier Heat Conduction Effect on Laser-Induced Thermal Damage in Biological Tissues , Numer. Heat Transfer A , vol. 54 , pp. 1 – 19 , 2008 .
   Web of Science ®Google Scholar
• C.-C. Wang and Z.-Y. Lee , Uniform Parameter Spline Method for Solving Non-Fourier Heat Conduction Problems , Numer. Heat Transfer B , vol. 56 , pp. 293 – 306 , 2009 .
   Web of Science ®Google Scholar
• C.-Y. Lo and B.-Y. Chen , Application of Hybrid Differential Transform/Control-Volume Method to Hyperbolic Heat Conduction Problems , Numer. Heat Transfer B , vol. 55 , pp. 219 – 231 , 2009 .
   Web of Science ®Google Scholar
• R. Čiegis , Numerical Solution of Hyperbolic Heat Conduction Equation , Mathematical Modelling and Analysis , vol. 14 , pp. 11 – 24 , 2009 .
   Web of Science ®Google Scholar
• M. Pakdemirli and A. Z. Şahin , Approximate Symmetries of Hyperbolic Heat Conduction Equation with Temperature Dependent Thermal Properties , Mathematical and Computational Applications , vol. 10 , pp. 139 – 145 , 2005 .
   Google Scholar
• R. Cai , C. Gou , and H. Li , Algebraically Explicit Analytical Solutions of Unsteady 3-D Nonlinear Non-Fourier (Hyperbolic) Heat Conduction , Int. J. Thermal Sciences , vol. 45 , pp. 893 – 896 , 2006 .
   Web of Science ®Google Scholar
• M. Goharkhah , S. Amiri , and H. Shokouhmand , Effect of Spatial Variation of Thermal Conductivity on Non-Fourier Heat Conduction in a Finite Slab , J. Mechanical Sci. and Tech. , vol. 23 , pp. 3393 – 3398 , 2009 .
   Web of Science ®Google Scholar
• X. Q. Fang and C. Hu , Dynamic Effective Thermal Properties of Functionally Graded Fibrous Composites using Non-Fourier Heat Conduction, Computational Materials Sci. , vol. 42, pp. 194–202, 2008.
   Web of Science ®Google Scholar
• M. H. Babaei and Z. T. Chen , Hyperbolic Heat Conduction in a Functionally Graded Hollow Sphere , Int. J. Thermophysics , vol. 29 , pp. 1457 – 1469 , 2008 .
   Web of Science ®Google Scholar
• I. Keles and C. Conker , Transient Hyperbolic Heat Conduction in Thick-Walled FGM Cylinders and Spheres with Exponentially-Varying Properties , Euro. J. of Mechanics A/Solids , vol. 30 , pp. 449 – 455 , 2011 .
   Web of Science ®Google Scholar
• S. Chi and Y. Chung , Mechanical Behavior of Functionally Graded Material Plates Under Transverse Load-Part I: Analysis , Int. J. Solids and Structures , vol. 43 , pp. 3657 – 3674 , 2006 .
   Web of Science ®Google Scholar
• G. H. Rahimi and A. R. Davoodinik , Thermal Behavior Analysis of the Functionally Graded Timoshenko's Beam , IUST Inte. J. of Eng. Sci. , vol. 19 , pp. 105 – 113 , 2008 .
   Google Scholar
• Y. Tanigawa , M. Matsumoto and T. Akai , Optimization of Material Composition to Minimize Thermal Stresses in Nonhomogeneous Plate Subjected to Unsteady Heat Supply , JSME Int. J. , vol. 40 , pp. 84 – 93 , 1997 .
   Web of Science ®Google Scholar