Hybrid Laplace transform technique for non-linear transient thermal problems

Abstract A hybrid numerical method combining the application of the Laplace transform technique and the finite-difference method (FDM) or the finite-element method (FEM) is presented for non-linear transient thermal problems. The space domain in the governing equation is discretized by FDM or FEM and the non-linear terms are linearized by Taylor's series expansion. The time-dependent terms are removed from the linearized equations by Laplace transformation, and so, the results at a specific time can be calculated without step-by-step computation in the time domain. To show the efficiency and accuracy of the present method several one-dimensional non-linear transient thermal problems are studied.

[1]  Han-Taw Chen,et al.  Hybrid Laplace transform/finite difference method for transient heat conduction problems , 1988 .

[2]  Kumar K. Tamma,et al.  A new hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer , 1988 .

[3]  Thomas J. R. Hughes,et al.  Unconditionally stable algorithms for nonlinear heat conduction , 1977 .

[4]  F. Durbin,et al.  Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method , 1974, Comput. J..

[5]  Han-Taw Chen,et al.  Hybrid Laplace transform/finite element for one-dimensional transient heat conduction problems , 1987 .

[6]  A. Aziz,et al.  Application of perturbation techniques to heat-transfer problems with variable thermal properties , 1976 .

[7]  T. Goodman.  The Heat-Balance Integral—Further Considerations and Refinements , 1961 .

[8]  Han-Taw Chen,et al.  Hybrid Laplace transform/finite element method for one-dimensional transient heat conduction problems , 1987 .

[9]  E. A. Thornton,et al.  A finite element thermal analysis procedure for several temperature-dependent parameters , 1978 .

[10]  G. Honig,et al.  A method for the numerical inversion of Laplace transforms , 1984 .

[11]  S. Orivuori.  Efficient method for solution of nonlinear heat conduction problems , 1979 .

[12]  Kumar K. Tamma,et al.  Hybrid transfinite element methodology for nonlinear transient thermal problems , 1987 .

[13]  Alberto Cardona,et al.  Solution of non‐linear thermal transient problems by a reduction method , 1986 .

[14]  Kumar K. Tamma,et al.  Transfinite element methodology for non‐liner/linear transient thermal modelling/analysis: Progress and recent advances , 1988 .

[15]  J. Kujawski.  Analysis of the collocation time finite element method for the non‐linear heat transfer equation , 1987 .

[16]  Harvey Dubner,et al.  Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform , 1968, JACM.

[17]  B. Krajewski.  On a direct variational method for nonlinear heat transfer , 1975 .

[18]  A. K. Noor,et al.  Hybrid perturbation/Bubnov-Galerkin technique for nonlinear thermal analysis , 1983 .

[19]  A. Muthunayagam,et al.  Transient Conduction in a Finite Slab with Variable Conductivity , 1975 .

[20]  B. Vujanović.  Application of the optimal linearization method to the heat transfer problem , 1973 .