Analysis of Convective-Radiative Fins by Using Hybrid Spline Difference Method

Abstract:

This study used rectangular fins with constant heat transfer coefficient as material to discuss convective and radiative heat transfer, so as to prove that the hybrid spline difference method proposed in this study is an easy to operate method with high accuracy. According to the computational process described in this paper, the hybrid spline difference method is as simple as finite difference method and is easy to use. The complex computational process of traditional spline method can be simplified by using this method, but the numerical accuracy can be increased to second order. Therefore, the high accuracy numerical method of hybrid spline difference method replacing traditional spline method for future heat transfer analyses is expectable.

• Periodical: Applied Mechanics and Materials (Volumes 284-287)
• Pages: 3345-3351
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.284-287.3345
• Online since: January 2013
• Authors: Chi Chang Wang, Wu Jung Liao, Lu Ping Chao
• Keywords: Fin, Finite Difference Method (FDM), High Accuracy, Hybrid Spline Difference Method, Parametric Spline

References

[1] M. Gross and P. Betsch, Galerkin-based energy-momentum consistent time-stepping algorithms for classical nonlinear thermo-elastodynamics, Mathematics and Computers in Simulation, Vol. 82, pp.718-770, (2011).

DOI: 10.1016/j.matcom.2011.10.009

[2] A. Ghoufi and P. Malfreyt, Calculation of the surface tension and pressure components from a non-exponential perturbation method of the thermodynamic route, Journal of Chemical Physics, Vol. 136, No. 024104, (2012).

DOI: 10.1063/1.3676056

[3] S. Panda and M. C. Ray, Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite, Finite Elements in Analysis and Design, Vol. 44, pp.493-504, (2008).

DOI: 10.1016/j.finel.2008.01.001

[4] C. H. Chiu and C. K. Chen, Application of Adomian's decomposition procedure to the analysis of convective-radiative fins, Journal of Heat Transfer-Transactions of the ASME, Vol. 125, pp.312-316, (2003).

DOI: 10.1115/1.1532012

[5] G. Jacobsohn, A discrete Taylor series method for the solution of two-point boundary-value problems, Journal of the Franklin Institute-Engineering and Applied Mathematics, Vol. 338, pp.61-68, (2001).

DOI: 10.1016/s0016-0032(00)00064-8

[6] H. S. Peng and C. L. Chen, Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity, International Journal of Heat and Mass Transfer, Vol. 54, pp.2427-2433, (2011).

DOI: 10.1016/j.ijheatmasstransfer.2011.02.019

[7] P. Wang and R. Kahawita, Numerical integration of partial differential equations using cubic splines, Int. J. of Compt. Math., Vol. 13, No. 3-4, pp.271-286, (1983).

DOI: 10.1080/00207168308803369

[8] Abbas Y. Al Bayati, Rostam K. Saeed and Faraidun K. Hama-Salh, Lacunary interpolation by quartic splines with application to quadratures, Int. J. Open Problems Compt. Math., Vol. 3, No. 3, (2010).

[9] H. S. Peng, C. L. Chen and G. S. Li, Application of residual correction method to laser heating process, Int. J. of Heat and Mass Transfer, Vol. 55, pp.316-324, (2012).

DOI: 10.1016/j.ijheatmasstransfer.2011.09.021

[10] F. Peng and X. Han, Parametric splines on a hyperbolic paraboloid, J. of Compt. and Appl. Math., Vol. 229, pp.183-191, (2009).

[11] C. C. Wang and Z. Y. Lee, Uniform-parameter spline method for solving non-fourier heat conduction problems, Numerical Heat Transfer Part B, Vol. 56, No. 4, pp.293-306. (2009).

DOI: 10.1080/10407790903244378

[12] H. Ding and Y. Zhang, Parameters spline methods for the solution of hyperbolic equations, Appl. Math. and Compt., Vol. 204, pp.938-941, (2008).

DOI: 10.1016/j.amc.2008.08.003