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Thermal performance of porous fins with temperature-dependent heat generation via the homotopy perturbation method and collocation method

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Języki publikacji
EN
Abstrakty
EN
An analysis has been performed to study the problem of the thermal performance of a nonlinear problem of the porous fin with temperature-dependent internal heat generation. Highly accurate semi-analytical methods called the collocation method (CM) and the homotopy perturbation method (HPM) are introduced and then are used to obtain a nonlinear temperature distribution equation in a longitudinal porous fin. This study is performed using passage velocity from the Darcy’s model to formulate the heat transfer equation through porous media. The heat generation is assumed to be a function of temperature. The effects of the natural convection parameter Nc, internal heat generation εg, porosity Sh and generation number G parameter on the dimensionless temperature distribution are discussed. Also, numerical calculations called the fourth order Runge-Kutta method were carried out for the various parameters entering into the problem for validation. Results reveal that analytical approaches are very effective and convenient. Also it is found that these methods can achieve more suitable results compared to numerical methods.
Rocznik
Strony
53--65
Opis fizyczny
Bibliogr. 30 poz., rys., tab.
Twórcy
  • Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
  • Young Researchers Club, Sari Branch, Islamic Azad University, Sari, Iran
autor
  • Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
  • Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Bibliografia
  • [1] Gawin D., Majorana C.E, Schrefler B.A., Numerical analysis of hygro-thermic behaviour and damage of concrete at high temperature, Mechanic of Cohesive-Frictional Materials 1999, 4, 37-74.
  • [2] Gawin D., Pesavento F., Schrefler B.A., Numerical modelling of concrete strains by means of effective stress, with application to concrete at early ages and at high temperatures, Proc. of 17th International Conference on Computer Method in Mechanics, Łódź-Spała, Poland, Short Papers, eds. K. Dems, D. Gawin, M. Lefik, Z. Więckowski, Lodz, Poland 2007, 149-150.
  • [3] Kiwan S., Thermal analysis of natural convection in porous fins, Transport in Porous Media 2006, 67, 17-29.
  • [4] Kiwan S., Effect of radiative losses on heat transfer from porous fins, Int. J. Thermal Sci. 2007, 46, 1046-1055
  • [5] Kiwan S., Zeitoun O., Natural convection in a horizontal cylindrical annulus using porous fins, Int. J. Numer. Method H. 2008, 18, 618-634.
  • [6] Nayfeh A.H., Perturbation Methods, Wiley, New York 2000.
  • [7] Ganji D.D., Kachapi S.H.H., Analytical and numerical method in engineering and applied science, Progress in Nonlinear Science 2011, 3, 1-579.
  • [8] Ganji D.D., Kachapi S.H.H., Analysis of nonlinear equations in fluids, Progress in Nonlinear Science 2011, 3, 1-294.
  • [9] He J.H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, Internat. J. Non-Linear Mech. 2000, 35, 1, 37-43.
  • [10] He J.H., Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci. Numer. Simul. 2005, 6, 207-208.
  • [11] He J.H., Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals 2005, 26, 695-700.
  • [12] Torabi M., Yaghoobi H., Saeddodin S., Assessment of Homotopy Perturbation Method in nonlinear convective-radiative nonfourier conduction heat transfer equation with variable coefficient, Thermal Science 2011, 15, 2, 263-274.
  • [13] Esmaeilpour M., Ganji D.D., Mohseni E., Application of homotopy perturbation method to micropolar flow in a porous channel, J. Porous Media 2009, 12, 5, 451-459.
  • [14] Ganji D.D., Rostamiyan Y., Rahimi Petroudi I., Khazayi Nejad M., Analytical investigation of nonlinear model arising in heat transfer through the porous fin, Thermal Sciences (in press).
  • [15] Vahabzadeh A., Fakour M., Ganji D.D., Rahimipetroudi I., Analytical accuracy of the one dimensional heat transfer in geometry with logarithmic various surfaces, Central European Journal of Engineering 2014, 4, 4, 341-351.
  • [16] Rostamiyan Y., Ganji D.D., Rahimipetroudi I., Khazayinejad M., Analytical investigation of nonlinear model arising in heat transfer through the porous fin, Thermal Science 2014, 18, 2, 409-417.
  • [17] Singh J., Gupta K.P., Rai N.K., Variation Iteration Method to solve moving boundary problem with temperature dependent physical properties, Thermal Science 2011, 15, 2, 229-239.
  • [18] He J.H., Variational iteration method - some recent results and new interpretations, Journal of Computational and Applied Mathematics 2007, 207, 1, 3-17.
  • [19] He J.H., Wu X.H., Construction of solitary solution and compaction-like solution by variational iteration method, Chaos Solitons & Fractals 2006, 29, 1, 108-113.
  • [20] Momani S., Abuasad S., Application of He’s variational iteration method to Helmholtz equation, Chaos Solitons & Fractals 2006, 27, 5, 1119-1123.
  • [21] Ganji D.D., Jamshidi N., Ganji Z.Z., HPM and VIM methods for finding the exact solutions of the nonlinear dispersive equations and seventh-order Sawada-Kotera equation, International Journal of Modern Physics B 2009, 23, 1, 39-52.
  • [22] Ganji D.D., Tari H., Jooybari M.B., Variational iteration method and homotopy perturbation method for nonlinear evolution equations, Computers and Mathematics with Applications 2007, 54, 1018-1027.
  • [23] Ganji D.D., Afrouzi G.A., Talarposhti R.A., Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations, Physics Letters A 2007, 368, 450-457.
  • [24] He J.H., Variational iteration method - a kind of nonlinear analytical technique: Some examples, International Journal of Non-linear Mechanics 1999, 34, 4, 699-708.
  • [25] He J.H., Approximate analytical solution for seepage with fractional derivatives in porous media, Computational Methods in Applied Mechanics and Engineering 1998, 167, 57-68.
  • [26] Aziz A., Bouaziz M.N., A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity, Energy Conversion and Management 2011, 52, 2876-82.
  • [27] Hatami M., Hasanpour A., Ganji D.D., Heat transfer study through porous fins (Si3N4and AL) with temperature-dependent heat generation, Energy Conversion and Management 2013, 74, 9-16.
  • [28] Hatami M., Ganji D.D., Thermal behavior of longitudinal convective-radiative porous fins with different section shapes and ceramic materials (SiC and Si3N4), Ceramics International, http://dx.doi.org/10.1016/j.cera-mint.2013.11.140
  • [29] Rahimipetroudi I., Ganji D.D., Khazayinejad M., Rahimi J., Rahimi E., Rahimifar A., Transverse magnetic field on Jeffery-Hamel problem with Cu-water nanofluid between two non-parallel plane walls by using collocation method, Case Studies in Thermal Engineering 2014, 4, 193-201.
  • [30] Aziz A., Heat Conduction with Maple, R.T. Edwards, Philadelphia (PA) 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a9ff7bd8-2015-42bd-8823-458facbf95cb
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