Journal of Applied and Computational Mechanics

Haar Wavelet Collocation Method for Thermal Analysis of Porous Fin with Temperature-dependent Thermal Conductivity and Internal Heat Generation

Document Type : Research Paper

Authors

1 Faculty of Engineering and Informatics University of Bradford, BD7 1DP West Yorkshire, UK

2 School of Electrical Engineering and Computer Science, Faculty of Engineering and Informatics University of Bradford West Yorkshire, UK

Abstract

In this study, the thermal performance analysis of porous fin with temperature-dependent thermal conductivity and internal heat generation is carried out using Haar wavelet collocation method. The effects of various parameters on the thermal characteristics of the porous fin are investigated. It is found that as the porosity increases, the rate of heat transfer from the fin increases and the thermal performance of the porous fin increases. The numerical solutions by the Haar wavelet collocation method are in good agreement with the standard numerical solutions.

Keywords

Main Subjects

[1] S. Kiwan, A. Al-Nimr. “Using porous fins for heat transfer enhancement”. ASME Journal of Heat Transfer 123, pp. 790–5, 2001.
[2] S. Kiwan, “Effect of radiative losses on the heat transfer from Porous fins”. International Journal of Thermal Science, 46(a), pp. 1046-1055, 2007.
[3] S. Kiwan. “Thermal Analysis of natural convection porous fins”. Transport in Porous Media 67(b), pp. 17-29, 2007.
[4] S. Kiwan, O. Zeitoun, “Natural convection in a horizontal cylindrical annulus using porous fins”. International Journal on Numerical Heat Fluid Flow, 18(5), pp. 618-634, 2008.
[5] R. S. Gorla, A. Y. Bakier. “Thermal analysis of natural convection and radiation in porous fins”. International Communication in Heat and Mass Transfer, 38, pp. 638-645, 2011.
[6] B. Kundu, D. Bhanji. “An Analytical Prediction for Performance and Optimum Design Analysis of Porous fins”. International Journal on Refrigeration, 34, pp. 337-352, 2011.
[7] B. Kundu, D. Bhanja, K. S. Lee. “A Model on the basis of Analytics for Computing Maximum Heat Transfer in porous fins”. International Journal of Heat and Mass Transfer, 55, pp. 7611-7622, 2012.
[8] D. Bhanja, B. Kundu. “Thermal analysis of a constructal T-shaped porous fin with radiation effects”. International Journal on Refrigeration, 34(6), pp.1483–96, 2011.
[9] B. Kundu, “Performance and optimization Analysis of SRC profile fins subject to simultaneous Heat and Mass Transfer”. International Journal of Heat and Mass Transfer, 50, pp. 1545-1558, 2007.
[10] A. Taklifi, C. Aghanajafi, H. Akrami. “The Effect of MHD on a porous fin attached to a vertical isothermal surface”. Transp Porous Med., 85, pp, 215–31, 2010.
[11] S. Saedodin, S. Sadeghi, S. “Temperature distribution in long porous fins in natural convection condition”. Middle-east Journal of Scientific Research. 13(6), pp. 812-817, 2013.
[12] M. T. Darvishi, R. Gorla, R.S., Khani, F., Aziz, A.-E. “Thermal Performance of a porous radial fin with natural convection and radiative heat losses”. Journal of Thermal Science, 19(2), pp. 669-678, 2015.
[13] Moradi, A., Hayat, T. and Alsaedi, A. “Convective-radiative thermal analysis of triangular fins with temperature-dependent thermal conductivity by DTM”. Energy Conversion and Management, 77, pp. 70–77, 2014.
[14] H. Ha, Ganji D. D and Abbasi M. “Determination of Temperature Distribution for Porous Fin with Temperature-Dependent Heat Generation by Homotopy Analysis Method”. Journal of Applied Mechanical Engineering, 4(1), 2005.
[15] M. Hatami, D. D. Ganji. “Thermal Performance of circular convective-radiative porous fins with different section shapes and materials”. Energy Conversion and Management, 76, pp.185−193, 2013.
[16] H. A. Hoshyar, I. Rahimipetroudi, D. D. Ganji, A. R. Majidian. “Thermal performance of porous fins with temperature-dependent heat generation via Homotopy perturbation method and collocation method”. Journal of Applied Mathematics and Computational Mechanics. 14(4), pp. 53-65, 2015.
[17] Y. Rostamiyan, D. D. Ganji, I. R. Petroudi, and M. K. Nejad. “Analytical Investigation of Nonlinear Model Arising in Heat Transfer through the Porous Fin”. Journal of Thermal Science, 182, pp. 409-417, 2014.
[18] S. E. Ghasemi, P. Valipour, M. Hatami, D. D. Ganji. “Heat transfer study on solid and porous convective fins with temperature-dependent heat-generation using efficient analytical method” Journal of Central South University 21, pp. 4592−4598, 2014. 
[19] S. Singh, D. Kumar and K. N. Rai. “Wavelet Collocation Solution for Convective Radiative Continuously Moving Fin with temperature-dependent Thermal Conductivity”. International Journal of Engineering and Advanced Technology, 2(4), pp.10-16, 2013.
[20] S. Singh, D. Kumar and K. N. Rai. “Convective-radiative fin with temperature-dependent thermal conductivity, heat transfer coefficient and wavelength dependent surface emissivity”. Propulsion and Power Research, 3(4), pp. 207-221, 2014.
[21] S. Singh, D. Kumar and K. N. Rai. “Wavelet Collocation Solution for Non-linear Fin Problem with Temperature-dependent Thermal Conductivity and Heat Transfer Coefficient”. International Journal of Nonlinear Analysis Application, 6(1), pp. 105-118, 2015.
[22] A. S. V. R Kanta, and N. U. Kumar. “A Haar Wavelet Study on Convective Radiative under continuously Moving Fin with temperature-dependent thermal conductivity”. Walailak Journal of Science and Engineering, 11(3), pp. 211-224, 2014.
[23] A. S. V. R Kanta, and N. U. Kumar. “Application of the Haar Wavelet Method on a Continuously Moving Convective Radiative Fin with Variable thermal conductivity”. Heat Transfer- Asian Research, pp. 1-17, 2013.
[24] I. R. Petroudi, D. D. Ganji, A.  B. Shotorban, M. K. Nejad, E. Rahimi, R. Rohollahtabar and F. Taherinia.  “Semi-Analytical Method for Solving Nonlinear Equation Arising in Natural Convection Porous fin”. Journal of Thermal Science, 16(5), pp. 1303-1308, 2012. 
Journal of Applied and Computational Mechanics
Volume 3, Issue 3
August 2017
Pages 185-191