An approximate spectral method for accurate solution of Fourier and non-Fourier heat conduction problems

JSME International Journal, Series B: Fluids and Thermal Engineering

Volumn 46, Issue 4, 2003, Pages 519-527

  Rahmani, Ramin Khosravi ^a   Keith, Theo Gordon ^a   Cottam, Russell ^b  

^a Toledo   (United States)

^b NASA GLENN RESEARCH CENTER   (United States)

Author keywords

Chebyshev polynomials; Parabolic and hyperbolic heat conduction; Pseudo spectral

Indexed keywords

BOUNDARY LAYERS; COMPUTATIONAL METHODS; GIBBS FREE ENERGY; POLYNOMIALS;

CHEBYSHEV EXPANSION COEFFICIENT;

HEAT CONDUCTION;

HEAT CONDUCTION; HEAT TRANSFER; MATHEMATICAL METHOD;

EID: 0347300544     PISSN: 13408054     EISSN: None     Source Type: Journal    
DOI: 10.1299/jsmeb.46.519     Document Type: Article

References (27)

1. Boyd, J.P., Lecture Notes in Engineering : Chebyshev & Fourier Spectral Methods, (1989), Springer-Verlag, Berlin.
2. Canuto, C., Hussaini, M.Y., Quarteroni, A. and Zang, T.A., Spectral Methods in Fluid Dynamics, (1988), Springer-Verlag, Berlin.
3. Gottlieb, D. and Orszag, S.A., Numerical Analysis of Spectral Methods: Theory and Applications, (1977), SIAM, Philadelphia.
4. Berntsson, F., A Spectral Method for Solving the Sideways Heat Equation, Inverse Problems, Vol. 15 (1999), pp. 891-906.
5. Shu, C.W. and Wong, P., A Note on the Accuracy of Spectral Methods Applied to Nonlinear Conservation Laws, Journal of Scientific Computing, Vol. 10 (1995), pp. 357-369.
6. Zhang, S.Q. and Tangborn, A.V., Flow Regimes in Two-Dimensional Mixed Convection with Spatially Periodic Lower Wall Heating, Physics of Fluids, Vol. 6 (1994), pp. 3285-3293.
7. Paik, S. and Nguyen, H.D., Momentum and Heat Transfer of a Translating Liquid Droplet under a Thermal Plasma Environment, Physics Plasmas, Vol. 1 (1994), pp. 2383-2397.
8. Kao, K. and Chow, C., Linear Stability of Compressible Taylor-Couette Flow, Physics of Fluids, Vol. 4 (1992), pp. 984-996.
9. Godon, P. and Livio, M., On the Nonlinear Hydrodynamic Stability of Thin Keplerian Disks, The Astrophysical Journal, Vol. 521 (1999), pp. 319-327.
10. Mulholland, L.S., Huang, W.Z. and Sloan, D.M., Pseudospectral Solution of Near-Singular Problems Using Numerical Coordinate Transformations Based on Adaptively, SIAM Journal on Scientific Computing, Vol. 19 (1998), pp. 1261-1289.
11. Majda, A., McDonough, J. and Osher, S., The Fourier Method for Nonsmooth Initial Data, Mathmatics of Computation, Vol. 32 (1978), pp. 1041-1081.
12. Abarbanel, S., Gottlieb, D. and Tadmor, E., Spectral Methods for Discontious Problems, NASA CR 117974, (1985), NASA Langley Research Center, Hampton, VA.
13. Hussaini, M.Y. and Zang, T.A., Spectral Methods in Fluid Dynamics, NASA CR 178103, (1986), NASA Langley Research Center, Hampton, VA.
14. Carey, G.F. and Tsai, M., Hyperbolic Heat Transfer with Reflection, Numerical Heat Transfer, Vol. 5 (1982), pp. 309-327.
15. Glass, D.E., Ozisik, M.N., McRae, D.S. and Vick, B., On the Numerical Solution of Hyperbolic Heat Conduction, Numerical Heat Transfer, Vol. 8 (1985), pp. 497-504.
16. Glass, D.E., Ozisik, M.N., McRae, D.S. and Vick, B., Hyperbolic Heat Conduction with Temperature-Dependent Thermal Conductivity, Journal of Applied Physics, Vol. 59 (1986), pp. 1861-1865.
17. Frankel, J.I., Vick, B. and Ozisik, M.N., Flux Formulation of Hyperbolic Heat Conduction, Journal of Applied Physics, Vol. 58 (1985), pp. 3340-3345.
18. Hays-Stang, K.J. and Haji-Sheikh, A., A Unified Solution for Heat Conduction in Thin Films, Int. J. of Heat and Mass Transfer, Vol. 42 (1999), pp. 455-465.
19. Antaki, P.J., Solution for Non-Fourier Dual Phase Lag Heat Conduction in a Semi-Infinite Slab with Surface Heat Flux, Int. J. Heat Mass Transfer, Vol. 41, No. 14 (1998), pp. 2253-2258.
20. Abdel-Hamid, B., Modelling Non-Fourier Heat Conduction with Periodic Thermal Oscillation Using the Finite Integral Transform, Applied Mathematical Modelling, Vol. 23 (1999), pp. 899-914.
21. Lin, J., The Non-Fourier Effect on the Fin Performance under Periodic Thermal Conditions, Applied Mathematical Modelling, Vol. 22 (1998), pp. 629-640.
22. Liu, L.H. and Tan, H.P., Non-Fourier Effects on Transient Coupled Radiative-Conductive Heat Transfer in One-Dimensional Semitransparent Medium Subjected to a Periodic Irradiation, J. of Quantitative Spectroscopy & Radiative Transfer, Vol. 71 (2001), pp. 11-24.
23. Chu, H., Lin, S. and Lin, C., Non-Fourier Heat Conduction with Radiation in an Absorbing, Emitting, and Isotropically Scattering Medium, J. of Quantitative Spectroscopy & Radiative Transfer, Vol. 73 (2002), pp. 571-582.
24. Wang, G.X. and Prasad, V., Microscale Heat and Mass Transfer and Non-Equilibrium Phase Change in Rapid Solidification, Materials Science and Engineering Vol. A292 (2000), pp. 142-148.
25. Haji-Sheikh, A., Minkowycz, W.J. and Sparrow, E.M., Certain Anomalies in the Analysis of Hyperbolic Heat Conduction, Journal of Heat Transfer, Vol. 24 (2002), pp. 307-318.
26. Gottlieb, D., Shu, C., Solomonoff, A. and Vandeven, H., On The Gibb's Phenomenon, NASA Contractor Report 189609, Contract No. NASI-18605 (1992).
27. Morse, P.M. and Feshback, H., Methods of Thermal Physics, (1953), McGraw-Hill, New York.