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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 59, 2011 - Issue 1
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Original Articles

Application of Hybrid Differential Transformation and Finite Difference Method on the Laser Heating Problem

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Pages 28-42 | Received 09 Sep 2010, Accepted 14 Oct 2010, Published online: 28 Jan 2011

REFERENCES

  • J. F. Ready , Effects Due to Absorption of Laser Radiation , J. Appl. Phys. , vol. 36 , no. 2 , pp. 462 – 468 , 1965 .
  • B. F. Blackwell , Temperature Profile in Semi-infinite Body with Exponential Source and Convective Boundary Condition , J. Heat Transfer , vol. 112 , pp. 567 – 571 , 1990 .
  • O. O. Diniz Neto and C. A. S. Lima , Nonlinear Three-Dimensional Temperature Profiles in Pulsed Laser Heated Solids , J. Phys. D-Appl. Phys. , vol. 27 , pp. 1795 – 1804 , 1994 .
  • B. S. Yilbas , M. Sami , and A. Al-Farayedhi , Closed-Form and Numerical Solutions to the Laser Heating Process , Proc. of the Institution of Mechanical Engineers, Part C, J. Mechanical Eng. Sci. , vol. 212 , pp. 141 – 151 , 1998 .
  • J. C. Rozzi , F. E. Pfefferkorn , F. P. Incropera , and Y. C. Shin , Transient Thermal Response of a Rotating Cylindrical Silicon Nitride Workpiece Subjected to a Translating Laser Source, Part I: Comparison of Surface Temperature Measurements with Theoretical Results , J. Heat Transfer , vol. 120 , pp. 899 – 906 , 1998 .
  • B. S. Yilbas , M. Sami , and K. Danisman , A Laser Succesive Pulse Heating of a Moving Slab: A Kinetic Theory Approach , Japan J. Appl. Phys. , vol. 37 , pp. 1855 – 1864 , 1998 .
  • B. S. Yilbas and M. Kalyon , Repetitive Laser Pulse Heating with a Convective Boundary Condition at the Surface , J. Phys. D-Appl. Phys. , vol. 34 , pp. 222 – 231 , 2001 .
  • Y. F. He , D. Du , Z. G. Sun , Q. Chen , and J. L. Pan , Analytical Solution and Experimental Verification for Pulsed Laser Heating Process with Convective Boundary Condition , Science in China Ser. E Eng. & Mater. Sci. , vol. 47 , no. 3 , pp. 305 – 319 , 2004 .
  • M. Kalyon and B. S. Yilbas , Repetitive Laser Pulse Heating Analysis: Pulse Parameter Variation Effects on Closed Form Solution , Appl. Surf. Sci. , vol. 252 , pp. 2242 – 2250 , 2006 .
  • J. K. Zhou , Differential Transformation and its Applications for Electrical Circuits , Huazhong University Press , Wuhan , China , 1986 (in Chinese) .
  • S. H. Ho and C. K. Chen , Analysis of General Elastically End Restrained Non-Uniform Beams using Differential Transform , Appl. Math. Model. , vol. 22 , pp. 219 – 234 , 1998 .
  • C. Mei , Differential Transformation Approach for Free Vibration Analysis of a Centrifugally Stiffened Timoshenko Beam , J. Vib. Acoust.—Trans. ASME , vol. 128 , pp. 170 – 175 , 2006 .
  • S. H. Ho and C. K. Chen , Free Vibration Analysis of Non-Homogeneous Rectangular Membranes using a Hybrid Method , J. Sound Vibr. , vol. 233 , no. 3 , pp. 547 – 555 , 2000 .
  • C. K. Chen and S. H. Ho , Application of Differential Transformation to Eigenvalue Problems , Appl. Math. Comput. , vol. 79 , pp. 173 – 188 , 1996 .
  • C. K. Chen and S. P. Ju , Application of Differential Transformation to Transient Advective-Dispersive Transport Equation , Appl. Math. Comput. , vol. 155 , pp. 25 – 38 , 2004 .
  • B. L. Kuo , Application of the Differential Transformation Method to the Solutions of Falkner-Skan Wedge Flow , Acta Mech. , vol. 164 , pp. 161 – 174 , 2003 .
  • A. J. Arenas , G. González-Parra , and B. M. Chen-Charpentier , Dynamical Analysis of the Transmission of Seasonal Diseases using the Differential Transformation Method , Math. Comput. Model. , vol. 50 , pp. 765 – 776 , 2009 .
  • M. J. Jang and C. L. Chen , Analysis of the Response of a Strongly Nonlinear Damped System using a Differential Transformation Technique , Appl. Math. Comput. , vol. 88 , pp. 137 – 151 , 1997 .
  • H. S. Chu and C. Y. Lo , Application of the Hybrid Differential Transform-Finite Difference Method to Nonlinear Transient Heat Conduction Problems , Numer. Heat Transfer A , vol. 53 , no. 3 , pp. 295 – 307 , 2008 .
  • C. Y. Lo and B. Y. Chen , Application of the Hybrid Differential Transform/Control-Volume Method to Hyperbolic Heat Conduction Problems , Numer. Heat Transfer B , vol. 55 , no. 3 , pp. 219 – 231 , 2009 .
  • M. J. Jang , C. L. Chen , and Y. C. Liu , On Solving the Initial-Value Problems using the Differential Transformation Method, Appl. Math. Comput. , vol. 115, no. 2–3, pp. 145–160, 2000.
  • M. J. Jang , C. L. Chen , and Y. C. Liu , Two-Dimensional Differential Transformation Method for Partial Differential Equations , Appl. Math. Comput. , vol. 121 , pp. 261 – 270 , 2001 .

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