### Thermal Performance and Optimum Design Analysis of Fin with Variable Thermal Conductivity Using Double Decomposition Method

#### Abstract

In this paper, thermal performance and optimum design analysis of straight fin with variable thermal conductivity is carried out using double decomposition method. The developed heat transfer models are used to analyze the thermal performance, establish the optimum thermal design parameters and also, investigate the effects of thermo-geometric parameters and thermal conductivity (non-linear) parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. From the results, it shows that the fin temperature distribution, the total heat transfer, the fin effectiveness, and the fin efficiency are significantly affected by the thermo-geometric and thermal parameters of the fin. The analysis revealed that the operational parameters must be carefully chosen to ensure that the fin retains its primary purpose of removing heat from the primary surface. The results obtained in this analysis provides platform for improvement in the design of fin in heat transfer equipment.

#### Full Text:

PDF#### References

Khani, F. and Aziz, A. (2010). Thermal analysis of a longitudinal trapezoidal fin with temperature dependent thermal conductivity and heat transfer coefficient, Commun Nonlinear SciNumerSciSimult15, pp. 590–601.

Ndlovu, P. L. and Moitsheki , J. R. (2013). Analytical Solutions for Steady Heat Transfer in Longitudinal Fins with Temperature-Dependent Properties, Mathematical Problems in Engineering, Volume 2013, pp. 14 pages.

Aziz, A and Enamul-Huq, S. M. (1973). Perturbation solution for convecting fin with temperature dependent thermal conductivity, J Heat Transfer97, pp. 300–301.

Aziz, A (1977). Perturbation solution for convecting fin with internal heat generation and temperature dependent thermal conductivity, Int. J Heat Mass Transfer20, 1253-5.

Campo, A. and Spaulding, R. J. “Coupling of the methods of successive approximations and undetermined coefficients for the prediction of the thermal behaviour of uniform circumferential fins,” Heat and Mass Transfer, vol. 34, no. 6, pp. 461–468, 1999.

Ching-Huang Chiu, Cha’o-Kuang Chen (2002).A decomposition method for solving the convectice longitudinal fins with variable thermal conductivity, International Journal of Heat and Mass Transfer 45, pp. 2067-2075.

Arslanturk, A. (2005). A decomposition method for fin efficiency of convective straight fin with temperature dependent thermal conductivity, IntCommun Heat Mass Transfer32, pp. 831–841.

Ganji, D. D. (2006). The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer, Phys Lett A355, pp. 337–341.

He, J. H. (1999). Homotopy perturbation method, Comp Methods ApplMechEng178, pp. 257–262.

Chowdhury M. S. H., Hashim I. (2008). Analytical solutions to heat transfer equations by homotopy-perturbation method revisited, Physical Letters A372, pp. 1240-1243.

Rajabi.A. (2007).Homotopy perturbation method for fin efficiency of convective straight fins with temperature dependent thermal conductivity .Physics Letters A364. P.p.33-37

Mustafa Inc (2008). Application of Homotopy analysis method for fin efficiency of convective straight fin with temperature dependent thermal conductivity. Mathematics and Computers Simulation 79 p.p 189 – 200.

Coskun, S. B. and Atay M. T. (2007). Analysis of Convective Straight and Radial Fins with Temperature Dependent Thermal Conductivity Using Variational Iteration Method with Comparision with respect to finite Element Analysis. Mathematical problem in Engineering vol.2007 ,Article ID 42072, 15 pages

Languri, E. M., Ganji, D.D, Jamshidi, N. (2008) Variational Iteration and Homotopy perturbation methods for fin efficiency of convective straight fins with temperature dependent thermal conductivity. 5th WSEAS Int .Conf .On FLUID MECHANICS (fluids 08) Acapulco, Mexico January 25 -27.

Coskun, S. B. and Atay, M. T. (2008). Fin efficiency analysis of convective straight fin with temperature dependent thermal conductivity using variational iteration method, ApplThermEng28, pp. 2345–2352.

Atay, M. T. and Coskun, S. B. (2008).Comparative Analysis of Power-Law Fin-Type Problems Using Variational Iteration Method and Finite Element Method, Mathematical Problems in Engineering, 9 pages.

Domairry, G and Fazeli, M. (2009) Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity. Communication in Nonlinear Science and Numerical Simulation 14 .p.p 489-499.

Chowdhury M. S. H., Hashim I., Abdulaziz O (2009).Comparison of homotopy analysis method and homotopy-permutation method for purely nonlinear fin-type problems, Communications in Nonlinear Science and Numerical Simulation 14, pp. 371-378.

Khani F., Ahmadzadeh Raji M., HamediNejad H. (2009). Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient, Commun Nonlinear SciNumerSimulat 14, pp. 3327-3338.

Moitheki, R.J. Hayat, T. and Malik, M.Y. (2010). Some exact solutions of the fin problem with a power law temperature dependent thermal conductivity .Nonlinear Analysis real world Application 11 p.p 3287 – 3294.

K. Hosseini , B. Daneshian, N. Amanifard, R. Ansari (2012). Homotopy Analysis Method for a Fin with Temperature Dependent Internal Heat Generation and Thermal Conductivity. International Journal of Nonlinear Science. 14, 2, 201-210.

Joneidi, A.A., Ganji, D.D., Babaelahi, M. (2009) Differential Transformation Method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity. International communication in Heat and Mass transfer 36 p.p757-762

Moradi. A and Ahmadikia, H. (2010). Analytical Solution for different profiles of fin with temperature dependent thermal conductivity. Hindawi Publishing Corporation Mathematical Problem in Engineering volume 2010, Article ID 568263, 15.

Moradi, A and Ahmadikia, H (2011). Investigation of effect thermal conductivity on straight fin performance with DTM, International Journal of Engineering and Applied Sciences (IJEAS).1, 42 -54

Mosayebidorcheh S., Ganji D. D., MasoudFarzinpoor (2014), Approximate Solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient, Propulsion and Power Reasearch, pp. 41-47.

Ghasemi, S. E., Hatami, M. and Ganji, D. D. (2014). Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation, Cases Studies in Thermal Engineering. 4, 1-8.

Sadri, S.; Raveshi, M. R., and Amiri, S. (2012). Efficiency analysis of straight fin with variable heat transfer coefficient and thermal conductivity. Journal of Mechanical Science and Technology, 26;4:1283-1290.

Ganji D. D. and A. S. Dogonchi (2014). Analytical investigation of convective heat transfer of a longitudinal fin with temperature-dependent thermal conductivity, heat transfer coefficient and heat generation, International Journal of Physical Sciences. Vol. 9(21), pp. 466-474.

Fernandez, A. (2009). On some approximate methods for nonlinear models. Appl Math Comput., 215:168-74.

Aziz, A. and Bouaziz , M. N. (2011). A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity, Energy Conversion and Management, 52: 2876-2882.

Adomian G and Rach R (1993). Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition. J Math Anal. 174:118–37.

Yue-Tzu Yang, Shih-Kai Chien, Cha’o-Kuang Chen (2008). A double decomposition method for solving the periodic base temperature in convective longitudinal fins. Energy Conversion and Management 49; 2910–2916

Yue-Tzu Yang, Shih-Kai Chien, Cha’o-Kuang Chen (2010). A double decomposition method for solving the annular hyperbolic profile fins with variable thermal conductivity .Heat transfer Eng. 31; 1165–1172.

Chiu, C. H. and Chen, C. K. (2003). Application of Adomian decomposition procedure to analysis of convective-radiative fins, Journal of Heat transfer 125; 312–316.

**PRINT ISSN No.: 2180-1053**

E ISSN No.: 2289-8123E ISSN No.: 2289-8123