Variation of Parameters Method for Thermal Analysis of Straight Convective- Radiative Fins with Temperature Dependent Thermal Conductivity

Document Type: Research Paper

Authors

Department of Mechanical Engineering, Faculty of Engineering, University of Lagos, Akoka, Lagos, Nigeria.

Abstract

In this study, thermal performance across straight convecting- radiating fin with temperature dependent thermal conductivity is considered. The variation of parameters (VPM) is adopted to analyze the nonlinear higher order differential equations arising due to thermal conductivity and heat transfer coefficient on temperature distribution. Pertinent parameters such as thermo geometric and radiation parameters effect on temperature profile are investigated. Result obtained illustrates that quantitative increase of thermo geometric parameter causes a significant increase in temperature distribution due to increase in ratio of convective to conduction heat transfer which influence is significant toward fin base while increasing radiation parameter leads to decrease in temperature distribution due to increasing heat transfer from fins surface to ambient environment . Comparative analysis of result obtained in study against literature proves to be in satisfactory agreement. Therefore study provides useful insight to fins operational performance in applications such as radiators, boilers, refrigeration devices, oil pipelines amongst others.

Keywords

Main Subjects


[1]          A. Aziz, S. E. Huq, Perturbation solution for convecting fin with variable thermal conductivity, Journal of Heat transfer, Vol. 97, No. 2, pp. 300-301, 1975.

[2]          A. Aziz, Perturbation solution for convective fin with internal heat generation and temperature dependent thermal conductivity, International Journal of Heat and Mass Transfer, Vol. 20, No. 11, pp. 1253-1255, 1977.

[3]          S. Mosayebidorcheh, D. Ganji, M. Farzinpoor, 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 Research, Vol. 3, No. 1, pp. 41-47, 2014.

[4]          D. Ganji, A. Dogonchi, 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, No. 21, pp. 466-474, 2014.

[5]          A. Aziz, M. Bouaziz, A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity, Energy conversion and Management, Vol. 52, No. 8-9, pp. 2876-2882, 2011.

[6]          K. Hosseini, B. Daneshian, N. Amanifard, R. Ansari, Homotopy analysis method for a fin with temperature dependent internal heat generation and thermal conductivity, International Journal of Nonlinear Science, Vol. 14, No. 2, pp. 201-210, 2012.

[7]          S. E. Ghasemi, M. Hatami, D. Ganji, Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation, Case Studies in Thermal Engineering, Vol. 4, pp. 1-8, 2014.

[8]          M. Hatami, G. R. M. Ahangar, D. Ganji, K. Boubaker, Refrigeration efficiency analysis for fully wet semi-spherical porous fins, Energy conversion and management, Vol. 84, pp. 533-540, 2014.

[9]          M. Hatami, D. Ganji, M. Gorji-Bandpy, Numerical study of finned type heat exchangers for ICEs exhaust waste heat recovery, Case Studies in Thermal Engineering, Vol. 4, pp. 53-64, 2014.

[10]        M. Hatami, D. Ganji, M. Gorji-Bandpy, Experimental and thermodynamical analyses of the diesel exhaust vortex generator heat exchanger for optimizing its operating condition, Applied Thermal Engineering, Vol. 75, pp. 580-591, 2015.

[11]        M. Hatami, D. Ganji, Thermal behavior of longitudinal convective–radiative porous fins with different section shapes and ceramic materials (SiC and Si3N4), Ceramics International, Vol. 40, No. 5, pp. 6765-6775, 2014.

[12]        M. Hatami, M. Jafaryar, D. Ganji, M. Gorji-Bandpy, Optimization of finned-tube heat exchangers for diesel exhaust waste heat recovery using CFD and CCD techniques, International Communications in Heat and Mass Transfer, Vol. 57, pp. 254-263, 2014.

[13]        M. T. Atay, S. B. Coşkun, Comparative analysis of power-law fin-type problems using variational iteration method and finite element method, Mathematical Problems in Engineering, Vol. 2008, 2008.

[14]        M. Chowdhury, I. Hashim, O. Abdulaziz, Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 2, pp. 371-378, 2009.

[15]        R. Moitsheki, T. Hayat, M. Malik, Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity, Nonlinear Analysis: Real World Applications, Vol. 11, No. 5, pp. 3287-3294, 2010.

[16]        F. Khani, M. A. Raji, H. H. Nejad, Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 8, pp. 3327-3338, 2009.

[17]        G. Domairry, M. Fazeli, Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 2, pp. 489-499, 2009.

[18]        S. B. Coşkun, M. T. Atay, Fin efficiency analysis of convective straight fins with temperature dependent thermal conductivity using variational iteration method, Applied Thermal Engineering, Vol. 28, No. 17-18, pp. 2345-2352, 2008.

[19]        E. M. Languri, D. Ganji, N. Jamshidi, Variational Iteration and Homotopy perturbation methods for fin efficiency of convective straight fins with temperature dependent thermal conductivity. 5th WSEAS Int, in Proceeding of, 25-27.

[20]        G. O. andGbeminiyi Sobamowo, Galerkin’s Method of Weighted Residual for a Convective Straight Fin with Temperature-dependent Conductivity and Internal Heat Generation, International Journal of Engineering and Technology, Vol. 6, No. 12, 2016.

[21]        U. Filobello-Niño, H. Vazquez-Leal, K. Boubaker, Y. Khan, A. Perez-Sesma, A. Sarmiento-Reyes, V. Jimenez-Fernandez, A. Diaz-Sanchez, A. Herrera-May, J. Sanchez-Orea, Perturbation method as a powerful tool to solve highly nonlinear problems: the case of Gelfand's equation, Asian Journal of Mathematics & Statistics, Vol. 6, No. 2, pp. 76, 2013.

[22]        C. Lim, B. Wu, Modified Mickens procedure for certain non-linear oscillators, Academic Press, 2002.

[23]        Y. Cheung, S. Chen, S. Lau, A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators, International Journal of Non-Linear Mechanics, Vol. 26, No. 3-4, pp. 367-378, 1991.

[24]        R. W. Lewis, P. Nithiarasu, K. N. Seetharamu, 2004, Fundamentals of the finite element method for heat and fluid flow, John Wiley & Sons,

[25]        M. Sobamowo, L. Jayesimi, M. Waheed, Magnetohydrodynamic squeezing flow analysis of nanofluid under the effect of slip boundary conditions using variation of parameter method, Karbala International Journal of Modern Science, 2018.

[26]        G. Oguntala, R. A. Abd-Alhameed, Thermal Analysis of Convective-Radiative Fin with Temperature-Dependent Thermal Conductivity Using Chebychev Spectral Collocation Method, 2018.

[27]        M. Goodarzi, M. Mohammadi, M. Khooran, F. Saadi, Thermo-mechanical vibration analysis of FG circular and annular nanoplate based on the visco-pasternak foundation, Journal of Solid Mechanics Vol, Vol. 8, No. 4, pp. 788-805, 2016.

[28]        A. Farajpour, A. Rastgoo, M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment, Physica B: Condensed Matter, Vol. 509, pp. 100-114, 2017.

[29]        M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, Effect of surface energy on the vibration analysis of rotating nanobeam, Journal of Solid Mechanics, Vol. 7, No. 3, pp. 299-311, 2015.

[30]        M. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version of differential quadrature method, 2011.

[31]        M. Mohammadi, A. Farajpour, M. Goodarzi, H. Mohammadi, Temperature effect on vibration analysis of annular graphene sheet embedded on visco-Pasternak foundation, 2013.

[32]        M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, 2014.

[33]        M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory, Micro & Nano Letters, Vol. 11, No. 6, pp. 302-307, 2016.

[34]        A. Farajpour, M. H. Yazdi, A. Rastgoo, M. Loghmani, M. Mohammadi, Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates, Composite Structures, Vol. 140, pp. 323-336, 2016.

[35]        M. Mohammadi, A. Farajpour, A. Moradi, M. Ghayour, Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites Part B: Engineering, Vol. 56, pp. 629-637, 2014.

[36]        A. Farajpour, M. Danesh, M. Mohammadi, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 3, pp. 719-727, 2011.

[37]        A. Farajpour, M. Mohammadi, A. Shahidi, M. Mahzoon, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 10, pp. 1820-1825, 2011.

[38]        M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.

[39]        A. Farajpour, A. Shahidi, M. Mohammadi, M. Mahzoon, Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, Vol. 94, No. 5, pp. 1605-1615, 2012.

[40]        M. Mohammadi, M. Ghayour, A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B: Engineering, Vol. 45, No. 1, pp. 32-42, 2013.