Thermal Analysis of Longitudinal Fin with Temperature-Dependent Properties and Internal heat Generation by a Novel Intelligent Computational Approach Using Optimized Chebyshev Polynomials

References

[1] H. Chen, J. Ma, H. Liu, Least square spectral collocation method for nonlinear heat transfer in moving porous plate with convective and radiative boundary conditions, Int. J. Thermal Sci. 132 (2018), 335–343.10.1016/j.ijthermalsci.2018.06.020Suche in Google Scholar

[2] J. Ma, Y. Sun, B. Li, Spectral collocation method for transient thermal analysis of coupled conductive, convective and radiative heat transfer in the moving plate with temperature dependent properties and heat generation, Int. J. Heat Mass Trans. 114 (2017), 469–482.10.1016/j.ijheatmasstransfer.2017.06.082Suche in Google Scholar

[3] J. Ma, Y. Sun, B. Li, Simulation of combined conductive, convective and radiative heat transfer in moving irregular porous fins by spectral element method, Int. J. Thermal Sci. 118 (2017), 475–487.10.1016/j.ijthermalsci.2017.05.008Suche in Google Scholar

[4] H. Mirgolbabaee, D. D. Ganji, S. T. Ledari, Heat transfer analysis of a fin with temperature-dependent thermal conductivity and heat transfer coefficient, New Trends Math. Sci. 3 (2) (2015), 55–69.Suche in Google Scholar

[5] R. Gorla, R. Darvishi, M. Khani, Effects of variable thermal conductivity on natural convection and radiation in porous fins, Int. Commun. Heat Mass Trans. 38 (2013), 638–645.10.1016/j.icheatmasstransfer.2010.12.024Suche in Google Scholar

[6] A. Moradi, T. Hayat, A. Alsaedi, Convection-radiation thermal analysis of triangular porous fins with temperature-dependent thermal conductivity by dtm, Energy Convers. Manage. 77 (2014), 70–77.10.1016/j.enconman.2013.09.016Suche in Google Scholar

[7] P. L. Ndlovu, R. J. Moitsheki, “Analytical Solutions for Steady Heat Transfer in Longitudinal Fins with Temperature- Dependent Properties,” Mathematical Problems in Engineering, vol. 2013, Article ID 273052, 14 pages, 2013. https://doi.org/10.1155/2013/273052.Suche in Google Scholar

[8] R. Moitsheki, T. Hayat, M. Malik, Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity, Nonlinear Anal.: Real World Appl. 11 (5) (2010), 3287–3294.10.1016/j.nonrwa.2009.11.021Suche in Google Scholar

[9] S. Kim, C.-H. Huang, A series solution of the non-linear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient, J. Phys. D: Appl. Phys. 40 (2007), 2979–2987.10.1088/0022-3727/40/9/046Suche in Google Scholar

[10] D. Ganji, The application of he’s homotopy perturbation method to nonlinear equations arising in heat transfer, Phys. Lett. A 335 (2006), 337–341.10.1016/j.physleta.2006.02.056Suche in Google Scholar

[11] H. Tari, D. Ganji, H. Babazadeh, The application of he’s variational iteration method to nonlinear equations arising in heat transfer, Phys. Lett. A 363 (2007), 213–217.10.1016/j.physleta.2006.11.005Suche in Google Scholar

[12] S. E. Ghasemi, M. Hatami, D. Ganji, Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation, Case Stud. Therm. Eng. 4 (2014), 1–8.10.1016/j.csite.2014.05.002Suche in Google Scholar

[13] J. Heemskerk, F. V. Kuik, H. Knaap, J. Beenakker, The thermal conductivity of gases in a magnetic field: The temperature dependence, Physica 71 (3) (1974), 484–514.10.1016/0031-8914(74)90017-2Suche in Google Scholar

[14] M. Neek-Amal, R. Moussavi, H. Sepangi, Monte Carlo simulation of size effects on thermal conductivity in a two-dimensional Ising system, Phys. A 371 (2) (2006), 424–432.10.1016/j.physa.2006.03.026Suche in Google Scholar

[15] M. A. Mahmoud, Thermal radiation effects on {MHD} flow of a micropolar fluid over a stretching surface with variable thermal conductivity, Physica A 375 (2) (2007), 401–410.10.1016/j.physa.2006.09.010Suche in Google Scholar

[16] R. Ellahi, E. Shivanian, S. Abbasbandy, T. Hayat, Numerical study of magnetohydrodynamics generalized couette flow of Eyring-Powell fluid with heat transfer and slip condition, Int. J. Numer. Meth. Heat Fluid Flow 26 (5) (2016), 1433–1445.10.1108/HFF-04-2015-0131Suche in Google Scholar

[17] S. Abbasbandy, E. Shivanian, Exact analytical solution of a nonlinear equation arising in heat transfer, Phys. Lett. A 374 (4) (2010), 567–574.10.1016/j.physleta.2009.11.062Suche in Google Scholar

[18] R. Ellahi, E. Shivanian, S. Abbasbandy, S. Rahman, T. Hayat, Analysis of steady flows in viscous fluid with heat/mass transfer and slip effects, Int. J. Heat Mass Trans. 55 (23-24) (2012), 6384–6390.10.1016/j.ijheatmasstransfer.2012.06.026Suche in Google Scholar

[19] L. A. Soltani, E. Shivanian, R. Ezzati, Convection–radiation heat transfer in solar heat exchangers filled with a porous medium: Exact and shooting homotopy analysis solution, Appl. Thermal Eng. 103 (2016), 537–542.10.1016/j.applthermaleng.2016.04.107Suche in Google Scholar

[20] E. Shivanian, H. R. Khodabandehlo, Application of meshless local radial point interpolation (mlrpi) on a one-dimensional inverse heat conduction problem, Ain Shams Eng. J. 7 (3) (2016), 993–1000.10.1016/j.asej.2015.07.009Suche in Google Scholar

[21] S. Abbasbandy, E. Shivanian, K. Vajravelu, S. Kumar, A new approximate analytical technique for dual solutions of nonlinear differential equations arising in mixed convection heat transfer in a porous medium, Int. J. Numer. Meth. Heat Fluid Flow 27 (2) (2017), 486–503.10.1108/HFF-11-2015-0479Suche in Google Scholar

[22] M. Sobamowo, Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using galerkin’s method of weighted residual, Appl. Thermal Eng. 99 (2016), 1316–1330.10.1016/j.applthermaleng.2015.11.076Suche in Google Scholar

[23] A. Aziz, M. Bouaziz, A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity, Energy Convers. Manage. 52 (8) (2011), 2876–2882.10.1016/j.enconman.2011.04.003Suche in Google Scholar

[24] R. W. Lewis, P. Nithiarasu, K. N. Seetharamu, “Fundamentals of the Finite Element Method for Heat and Fluid Flow,” John Wiley & Sons Ltd, The Atrium Southern Gate, Chichester, 2004. doi:10.1002/0470014164.Suche in Google Scholar

[25] S. Kim, C.-H. Huang, A series solution of the non-linear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient, J. Phys. D: Appl. Phys. 40 (9) (2007), 2979.10.1088/0022-3727/40/9/046Suche in Google Scholar

[26] K. Hosseini, B. Daneshian, N. Amanifard, R. Ansari, Homotopy analysis method for a fin with temperature dependent internal heat generation and thermal conductivity, Int. J. Nonl. Sci. 14 (2) (2012), 201–210.Suche in Google Scholar

[27] M. Anbarloei, E. Shivanian, Exact closed-form solution of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient, J. Heat Trans. 138 (11) (2016), 114501.10.1115/1.4033809Suche in Google Scholar

[28] M. Sobamowo, O. Kamiyo, O. Adeleye, Thermal performance analysis of a natural convection porous fin with temperature- dependent thermal conductivity and internal heat generation, Thermal Sci. Eng. Progress 1 (2017), 39–52.10.1016/j.tsep.2017.02.007Suche in Google Scholar

[29] S. Abbasbandy, E. Shivanian, Exact analytical solution of a nonlinear equation arising in heat transfer, Phys. Lett. A 374 (4) (2010), 567–574.10.1016/j.physleta.2009.11.062Suche in Google Scholar

[30] S. Abbasbandy, E. Shivanian, I. Hashim, Exact analytical solution of forced convection in a porous-saturated duct, Commun. Nonlinear Sci. Numer. Simul. 16 (10) (2011), 3981–3989.10.1016/j.cnsns.2011.01.009Suche in Google Scholar

[31] A.-M. Wazwaz, Adomian decomposition method for a reliable treatment of the Emden–Fowler equation, Appl. Math. Comput. 161 (2) (2005), 543–560.10.1016/j.amc.2003.12.048Suche in Google Scholar

[32] S. Momani, Z. Odibat, Analytical solution of a time-fractional Navier–Stokes equation by Adomian decomposition method, Appl. Math. Comput. 177 (2) (2006), 488–494.10.1016/j.amc.2005.11.025Suche in Google Scholar

[33] D. Ganji, The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer, Phys. Lett. A 355 (4) (2006), 337–341.10.1016/j.physleta.2006.02.056Suche in Google Scholar

[34] C. Chen, Y. Liu, Solution of two-point boundary-value problems using the differential transformation method, J. Opt. Theo. Appl. 99 (1) (1998), 23–35.10.1023/A:1021791909142Suche in Google Scholar

[35] S. Abbasbandy, E. Shivanian, K. Vajravelu, Mathematical properties of h-curve in the frame work of the homotopy analysis method, Commun. Nonl. Sci. Numer. Simulation 16 (11) (2011), 4268–4275.10.1016/j.cnsns.2011.03.031Suche in Google Scholar

[36] S. Abbasbandy, E. Magyari, E. Shivanian, The homotopy analysis method for multiple solutions of nonlinear boundary value problems, Commun. Nonl. Sci. Numer. Simul. 14 (9-10) (2009), 3530–3536.10.1016/j.cnsns.2009.02.008Suche in Google Scholar

[37] S. Abbasbandy, E. Shivanian, Prediction of multiplicity of solutions of nonlinear boundary value problems: Novel application of homotopy analysis method, Commun. Nonl. Sci. Numer. Simul. 15 (12) (2010), 3830–3846.10.1016/j.cnsns.2010.01.030Suche in Google Scholar

[38] S. Abbasbandy, E. Shivanian, Predictor homotopy analysis method and its application to some nonlinear problems, Commun. Nonl. Sci. Numer. Simul. 16 (6) (2011), 2456–2468.10.1016/j.cnsns.2010.09.027Suche in Google Scholar

[39] D. R. Croft, D. G. Lilley, Heat transfer calculations using finite difference equations. No. 283. London: Applied Science Publishers, Elsevier Science & Technology 1977.Suche in Google Scholar

[40] Y. Sun, J. Ma, B. Li, Z. Guo, Predication of nonlinear heat transfer in a convective-radiative fin with temperature- dependent properties by the collocation spectral method, Numer. Heat Trans., Part B: Fundam. 69 (1) (2016), 68–83.10.1080/10407782.2015.1081043Suche in Google Scholar

[41] Y. Sun, J. Ma, Application of collocation spectral method to solve a convective-radiative longitudinal fin with temperature dependent internal heat generation, thermal conductivity and heat transfer coefficient, J. Comput. Theor. Nanosci. 12 (9) (2015), 2851–2860.10.1166/jctn.2015.4189Suche in Google Scholar

[42] T. Rivlin, Chebyshev polynomials, John Wiley and sons, New York.Suche in Google Scholar

[43] N. H. Asmar, Partial differential equations with Fourier series and boundary value problems, Courier Dover Publications, New Jersey, 2016.Suche in Google Scholar

[44] R. M. Slevinsky, H. Safouhi, New formulae for higher order derivatives and applications, J. Comput. Appl. Math. 233 (2) (2009), 405–419.10.1016/j.cam.2009.07.038Suche in Google Scholar

[45] N. Karmarkar, A new polynomial-time algorithm for linear programming, in: Proceedings of the sixteenth annual ACM symposium on Theory of computing, pp. 302–311, ACM, New York, 1984.10.1145/800057.808695Suche in Google Scholar

[46] S. J. Wright, Primal-dual interior-point methods, SIAM, Philadelphia, PA, 1997.10.1137/1.9781611971453Suche in Google Scholar

[47] M. Wright, The interior-point revolution in optimization: history, recent developments, and lasting consequences, Bull. Am. Math. Soc. 42 (1) (2005), 39–56.10.1090/S0273-0979-04-01040-7Suche in Google Scholar

[48] W. Yan, L. Wen, W. Li, C. Chung, K. Wong, Decomposition– coordination interior point method and its application to multi-area optimal reactive power flow, Int. J. Elect. Power Energy Syst. 33 (1) (2011), 55–60.10.1016/j.ijepes.2010.08.004Suche in Google Scholar

[49] N. Duvvuru, K. Swarup, A hybrid interior point assisted differential evolution algorithm for economic dispatch, IEEE Trans. Power Syst. 26 (2) (2011), 541–549.10.1109/TPWRS.2010.2053224Suche in Google Scholar

[50] M. A. Z. Raja, R. Samar, Numerical treatment for nonlinear mhd Jeffery–Hamel problem using neural networks optimized with interior point algorithm, Neurocomputing 124 (2014), 178–193.10.1016/j.neucom.2013.07.013Suche in Google Scholar