Heat transfer analysis of a fin with temperature-dependent thermal conductivity and heat transfer coefficient

Yıl 2015, Cilt: 3 Sayı: 2, 55 - 69, 19.01.2015

Hadi Mirgolbabaee Davood Domiri Ganji Soheil Tahernejad Ledari

Öz

In this paper Least Square Method (LSM), Collocation Method (CM) and new approach which called Akbari-Ganji’sMethod (AGM) are applied to solve the nonlinear heat transfer equation of fin with power-law temperature-dependent both thermalconductivity and heat transfer coefficient. The major concern is to achieve an accurate answer which has efficient approximation inaccordance to Ruge-Kutta numerical method. Results are presented for the dimensionless temperature distribution and fin efficiencyfor different values of the problem parameters which for the purpose of comparison, obtained equation were calculated withmentioned methods. It was found the proposed solution is very accurate, efficient, and convenient for the discussed problem,furthermore convergence problems for solving nonlinear equations by using AGM appear small so the results demonstrate that theAGM could be applied through other methods in nonlinear problems with high nonlinearity

Anahtar Kelimeler

Akbari-Ganji Method, Collocation Method, Heat Transfer Equation, Least Square Method

Kaynakça

• D.Q. Kern, D.A. Kraus, Extended Surface Heat Transfer, McGraw-Hill, New York, 1972.
• A.H. Bokhari, A.H. Kara, F.D. Zaman, A note on a symmetry analysis and exact solutions of a nonlinear fin equation, Applied
• Mathematics Letters 19 (12) (2006) 1356–1360.
• O.O. Vaneeva, A.G. Johnpillai, R.O. Popovych, C. Sophocl-eous, Group analysis of nonlinear fin equations, Applied Mathematics
• Letters 21 (3) (2008) 248–253.
• M. Pakdemirli, A.Z. Sahin, Similarity analysis of a nonlinear fin equation, Applied Mathematics Letters 19 (4) (2006) 378–384.
• D.D. Ganji, M.J. Hosseini, J. Shayegh, Some nonlinear heat transfer equations solved by three approximate methods, International
• Communications in Heat and Mass Transfer 34 (8) (2007) 1003–1016.
• J.-H.He, “Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999.
• Z. Z. Ganji, D. D. Ganji, A. Janalizadeh, Analytical solution of two-dimensional viscous flow between slowly expanding or
• contracting walls with weak permeability, Mathematical and Computational Applications, Vol. 15, No. 5, pp. 957-961, 2010.
• S. Ghafoori, M. Motevalli, M. G. Nejad, F. Shakeri, D. D. Ganji, and M. Jalaal, ”Efficiency of differential transformation method
• for nonlinear oscillation: Comparison with HPM and VIM,” Current Applied Physics, vol. 11, no. 4, pp. 965-971, 2011.
• J.H. He, X.H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons
• Fractals 29 (2006) 108–113.
• G. Domairry, M. Fazeli, Homotopy analysis method to determine the fin effciency of convective straight fins with temperature- dependent thermal conductivity, Communica-tions in Nonlinear Science and Numerical Simulation 14 (2) (2009) 489–499.
• A.A. Joneidi, D.D. Ganji, M. Babaelahi, Differential trans-formation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductiv-ity, International Communications in Heat and Mass Transfer 36 (7) (2009) 757–762.
• M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Houman B. Rokni, Analytical investigation of Jeffery–Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method, Applied Mathematics and Mechanics 3 (1) 1553–1564, 2012.
• M.R. Akbari, D.D.Ganji, A.Majidian, A.R. Ahmadi, Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM, Frontiers of Mechanical Engineering, Volume 9, Issue 2, pp. 177-190.
• ] M. R. Akbari, D. D. Ganji, A. R. Ahmadi, Sayyid H. Hashemi Kachapi, Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method, Frontiers of Mechanical Engineering Volume 9, Issue 1 , pp 58-70, 2014-03-01.
• M. Hatami, R. Nouri, D. D. Ganji, Forced convection analysis for MHD Al2O3–water nano fluid flow over a horizontal plate, Journal of Molecular Liquids 187 (2013), pp. 294–301
• Alireza Sadeghirad, Iradj Mahmoudzadeh Kani, Mohammad Rahimian, Ali Vaziri Astaneh, A numerical approach based on the meshless collocation method in elastodynamics, Acta Mechanica Sinica, December 2009, Volume 25, Issue 6, pp 857-870.
• S.E. Ghasemi, M. Hatami, G.H.R. Mehdizadeh Ahangar, D.D. Ganji. Electrohydrodynamic flow analysis in a circular cylindrical conduitusing Least Square Method. Published by Elsevier B.V. November 2013.
• M.Hatami , D.D.Ganji. Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods. Case Studies in Thermal Engineering, Volume 2, March 2014, Pages 14-22.
• A. Aziz, S.M.E. Hug, Perturbation solution for convecting fin with variable thermal conductivity, Journal of Heat Transfer, Trans ASME 97 (1975) 300–301.
• A. Aziz, J.Y. Benzies, Application of perturbation techniques to heat-transfer problems with variable thermal properties, International Journal of Heat and Mass Transfer 19 (3) (1976) 271–276.
• Stern RH, Rasmussen H .Left ventricular ejection: Model solution by collocation, an approximate analytical method. ComputBoilMed1996; 26:255–61.
• Vaferi B, Salimi V, Dehghan Baniani D ,Jahan miri A ,Khedri S . Prediction of transient pressure response in the petroleum reservoirs using orthogonal collocation. J Petrol Sci and Eng2012; http://dx.doi.org/10.1016/j.petrol.2012.04.023.
• Hatami M, Hasanpour A, Ganji D.D. Heat transfer study through porous fins (Si3N4andAL) with temperature-dependent heat generation. Energy Convers Manage 2013; 74:9–16.
• Bouaziz MN, Aziz A. Simple and accurate solution for convective–radiative fin with temperature dependent thermal conductivity using double optimal linearization. Energy Convers Manage 2010; 51:76–82.
• Aziz A, Bouaziz MN. A least squares method for alongitudinal fin with temperature dependent internal heat generation and thermal conductivity. Energy ConversManage2011; 52:2876–82.
• Shaoqin G, Huoyuan D. Negative norm least-squares methods for the incompressible magneto-hydrodynamic equations. Act Math Sci 2008; 28B (3): 675–84.
• Hatami M, Nouri R, Ganji D.D. Forced convection analysis for MHD Al2O3–water nano fluid flow over a horizontal plate. J Mol Liq 2013; 187:294–301.
• Hatami M, Sheikholeslami M, Ganji DD. Laminar flow and heat transfer of nano fluid between contracting and rotating disks by least square method. Powder Technol2014; 253:769–79.
• Hatami M, Hatami J, Ganji D.D. Computer simulation of MHD blood conveying gold nanoparticles as a third grade non- Newtonian nanofluid in a hollow porous vessel. Comput Methods Programs Biomed 2014; 113:632–41.
• Hatami M, Ganji D.D. Thermal performance of circular convective–radiative porous fins with different section shapes and materials. Energy Convers Manage 2013; 76:185–93.
• Hatami M, Ganji D.D. Heat transfer and nanofluid flow in suction and blowing process between parallel disks in presence of variable magnetic field .J Mol Liq2014;190:159–68.
• Hatami M, Ganji D.D. Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods. Case Studies Therm Eng 2014; 2:14–22.
• Hatami M, Domairry G. Transient vertically motion of asoluble particle in a Newtonian fluid media. Powder Techno l2014; 253:481–5.
• Domairry G, Hatami M. Squeezing Cu–water nanofluid flow analysis between parallel plates by DTM-Pad´e Method. J Mol Liq 2014; 193:37–44.
• Ahmadi AR, Zahmtkesh A, Hatami M, Ganji D.D. A comprehensive analysis of the flow and heat transfer for a nanofluid over an unsteady stretching flat plate. Powder Techno l2014; 258:125–33.
• Sobhan Mosayebidorcheh, D.D.Ganji, Masoud 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, Volume 3, Issue 1, March 2014, Pages 41-47.