### A Haar Wavelet Study on Convective-Radiative Fin under Continuous Motion with Temperature-Dependent Thermal Conductivity

#### Abstract

In this paper, the Haar wavelet method is applied to find an approximate solution for heat transfer in moving fins with temperature-dependent thermal conductivity losing heat through both convection and radiation to the surroundings. The effects of various significant parameters involved in the problem, such as the thermal conductivity parameter *a*, sink temperature , convection-radiation parameter *N _{c}*, radiation-conduction parameter

*N*, and Peclet number

_{r}*Pe*on the temperature profile of the fin, is discussed and physical interpreted through illustrative graphs.

doi:10.14456/WJST.2014.40

#### Keywords

#### Full Text:

PDF#### References

DQ Kern and AD Kraus. Extended Surface Heat Transfer. McGraw-Hill, New York, 1972.

AD Kraus, A Aziz and J Welty. Extended Surface Heat Transfer. John Wiley and Sons, New York, 2001.

JH Lienhard IV and JH Lienhard V. A Heat Transfer Textbook. Phlogiston Press, Cambridge, Massachusetts, 2003.

CH Chiu and CK Chen. A decomposition method for solving the convective longitudinal fins with variable thermal conductivity. Int. J. Heat Mass Tran. 2002; 45, 2067-75.

C Arslanturk. A decomposition method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Int. Commun. Heat Mass Tran. 2005; 32, 831-41.

A Rajabi. Homotopy perturbation method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Phys. Lett. A 2007; 364, 33-7.

G Domairry and M Fazeli. Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Commun. Nonlinear Sci. Numer. Simulat. 2009; 14, 489-99.

AA Joneidi, DD Ganji and M Babelahi. Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity. Int. Commun. Heat Mass Tran. 2009; 36, 757-62.

DB Kulkarni and MM Joglekar. Residue minimization technique to analyze the efficiency of convective straight fins having temperature-dependent thermal conductivity. Appl. Math. Comput. 2009; 215, 2184-91.

R Das. A simplex search method for a conductive-convective fin with variable conductivity. Int. J. Heat Mass Tran. 2011; 54, 5001-9.

A Aziz and JY Benzies Application of perturbation techniques to heat-transfer problems with variable thermal properties. Int. J. Heat Mass Tran. 1976; 19, 271-6.

H Nguyen and A Aziz. Heat transfer from convecting-radiating fins of different profile shapes. Warme und Stoffubertragung 1992; 27, 67-72.

LT Yu and CK Chen. Application of Taylor transformation to optimize rectangular fins with variable thermal parameters. Appl. Math. Model. 1998; 22, 11-21.

MN Bouaziz and A Aziz. Simple and accurate solution for convective-radiative fin with temperature dependent thermal conductivity using double optimal linearization. Energ. Convers. Manage. 2010; 51, 2276-782.

A Aziz and F Khani. Convection-radiation from a continuous moving fin of variable thermal conductivity. J. Franklin Inst. 2011; 348, 640-51.

A Aziz and RJ Lopez. Convection-radiation from a continuously moving, variable thermal conductivity sheet or rod undergoing thermal processing. Int. J. Therm. Sci. 2011; 50, 1523-31.

M Torabi, H Yaghoobi and A Aziz. Analytical solution for convective-radiative continuously moving fin with temperature-dependent thermal conductivity. Int. J. Thermophys. 2012; 33, 924-41.

CF Chen and CH Hsiao. Haar wavelet method for solving lumped and distributed-parameter systems. IEEE Proc. Control Theory Appl. 1997; 144, 87-94.

CH Hsiao and WJ Wang. Haar wavelet approach to nonlinear stiff systems. Math. Comput. Simulat. 2001; 57, 347-53.

CH Hsiao. Haar wavelet approach to linear stiff systems. Math. Comput. Simulat. 2004; 64, 561-7.

K Maleknejad, F Mirzaee and S Abbasbandy. Solving linear integro-differential equations system by using rationalized Haar functions method. Appl. Math. Comput. 2004; 155, 317-28.

U Lepik. Numerical solution of differential equations using Haar wavelets. Math. Comput. Simulat. 2005; 68, 127-43.

U Lepik. Haar wavelet method for nonlinear integro-differential equations. Appl. Math. Comput. 2006; 176, 324-33.

R Kalpana and SR Balachandar. Haar wavelet method for the analysis of transistor circuits. Int. J. Electron. Commun. 2007; 61, 589-94.

E Babolian and A Shahsavaran. Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets. J. Comput. Appl. Math. 2009; 225, 87-95.

G Hariharan, K Kannan and KR Sharma. Haar wavelet method for solving Fisher’s equation. Appl. Math. Comput. 2009; 211, 284-92.

S Ul-Islam, I Aziz and B Sarler. The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets. Math. Comput. Model. 2010; 52, 1577-90.

S Zhi and C Yong-yan. A spectral collocation method based on Haar wavelets for Poisson equations and biharmonic equations. Math. Comput. Model. 2011; 54, 2858-68.

S Zhi and C Yong-yan. Application of Haar wavelet method to eigen value problems of high order differential equations. Appl. Math. Model. 2012; 36, 4020-6.

S Zhi and C Yong-yan. Solving 2D and 3D Poisson equations and biharmonic equations by the Haar wavelet method. Appl. Math. Model. 2012; 36, 5143-61.

### Refbacks

- There are currently no refbacks.

**Online ISSN: 2228-835X****http://wjst.wu.ac.th **

**Last updated:**18 January 2018