Hybrid Spline Difference Method for Heat Transfer and Thermal Stresses in Annular Fins

REFERENCES

• M. Gross and P. Betsch , Galerkin-Based Energy-Momentum Consistent Time-Stepping Algorithms for Classical Nonlinear Thermo-Elastodynamics , Math. Comput. Simul. , vol. 82 , pp. 718 – 770 , 2011 .
   Web of Science ®Google Scholar
• A. Ghoufi and P. Malfreyt , Calculation of the Surface Tension and Pressure Components from a Non-exponential Perturbation Method of the Thermodynamic Route , J. Chem. Phys. , vol. 136 , no. 024104 , 2012 .
   PubMed Web of Science ®Google Scholar
• S. Panda and M. C. Ray , Nonlinear Finite Element Analysis of Functionally Graded Plates Integrated with Patches of Piezoelectric Fiber Reinforced Composite , Finite Elem. Anal. Design , vol. 44 , pp. 493 – 504 , 2008 .
   Web of Science ®Google Scholar
• A. H. Akbarzadeh , M. Abbasi , and S. K. Hosseini , Dynamic Analysis of Functionally Graded Plates using the Hybrid Fourier-Laplace Transform under Thermomechanical Loading , Meccanica , vol. 46 , pp. 1373 – 1392 , 2011 .
   Web of Science ®Google Scholar
• C. H. Chiu and C. K. Chen , Application of Adomian's Decomposition Procedure to the Analysis of Convective-Radiative Fins , J. Heat Transfer—Trans. ASME , vol. 125 , pp. 312 – 316 , 2003 .
   Web of Science ®Google Scholar
• A. Valiani , V. Caleffi , and A. Zanni , Case Study: Malpasset Dam-Break Simulation using a Two-Dimensional Finite Volume Method , J. Hydraulic Eng.—ASCE , vol. 128 , pp. 460 – 472 , 2002 .
   Web of Science ®Google Scholar
• G. Jacobsohn , A Discrete Taylor Series Method for the Solution of Two-Point Boundary-Value Problems , J. Franklin Inst.—Eng. Appl. Math. , vol. 338 , pp. 61 – 68 , 2001 .
   Web of Science ®Google Scholar
• H. S. Peng and C. L. Chen , Hybrid Differential Transformation and Finite Difference Method to Annular Fin with Temperature-Dependent Thermal Conductivity, Int. J. Heat Mass Transfer , vol. 54, pp. 2427–2433, 2011.
   Web of Science ®Google Scholar
• P. Wang and R. Kahawita , Numerical Integration of Partial Differential Equations Using Cubic Splines , Int. J. Comput. Math. , vol. 13 , no. 3–4 , pp. 271 – 286 , 1983 .
   Web of Science ®Google Scholar
• A. Y. Al Bayati , R. K. Saeed , and F. K. Hama-Salh , Lacunary Interpolation by Quartic Splines with Application to Quadratures , Int. J. Open Prob. Comput. Math. , vol. 3 , no. 3 , 2010 .
   Google Scholar
• H. S. Peng , C. L. Chen , and G. S. Li , Application of Residual Correction Method to Laser Heating Process , Int. J. Heat Mass Transfer , vol. 55 , pp. 316 – 324 , 2012 .
   Web of Science ®Google Scholar
• F. Peng and X. Han , Parametric Splines on a Hyperbolic Paraboloid , J. Comput. Appl. Math. , vol. 229 , pp. 183 – 191 , 2009 .
   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 , no. 4 , pp. 293 – 306 , 2009 .
   Web of Science ®Google Scholar
• H. Ding and Y. Zhang , Parameters Spline Methods for the Solution of Hyperbolic Equations , Appl. Math. Comput. , vol. 204 , pp. 938 – 941 , 2008 .
   Web of Science ®Google Scholar
• C. C. Wang , L. P. Chao , and W. J. Liao , Hybrid Spline Difference Method (HSDM) for Transient Heat Conduction , Numer. Heat Transfer B , vol. 61 , no. 2 , pp. 129 – 146 , 2012 .
   Web of Science ®Google Scholar
• C. H. Chiu and C. K. Chen , Application of the Decomposition Method to Thermal Stresses in Isotropic Circular Fins with Temperature-Dependent Thermal Conductivity , Acta Mech. , vol. 157 , pp. 147 – 158 , 2002 .
   Web of Science ®Google Scholar
• A. Martin and I. D. Boyd , Variant of the Thomas Algorithm for Opposite-Bordered Tridiagonal Systems of Equations , Int. J. Numer. Meth. Biomed. Eng. , vol. 26 , no. 6 , pp. 752 – 759 , 2010 .
   Web of Science ®Google Scholar