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Application of an Integral Numerical Technique for a Temperature-Dependent Thermal Conductivity Fin with Internal Heat Generation

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Journal of Engineering Physics and Thermophysics Aims and scope

A numerical study of convective heat transfer in a longitudinal fin with temperature-dependent thermal conductivity and internal heat generation is undertaken. Integral calculations are implemented on each generic element of the discretized problem domain. The resulting systems of nonlinear equations are solved efficiently because of the coefficient matrix sparsity to yield both the dependent variable and its flux. In order to validate the formulation, the effects of the thermogeometric parameter, nonlinearity due to the temperature-dependent thermal conductivity, and of the heat transfer coefficient on the fin temperature distribution are investigated. The results are found to be in agreement with those for similar problems described in the literature and with the physics of the problem.

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References

  1. D. Q. Kern and A. D. Kraus, Extended Surface Heat Transfer, McGraw-Hill, New York (1972).

  2. Y. Cengel and A. Ghajar, Heat and Mass Transfer: Fundamentals and Applications, McGraw-Hill, New York (2011).

  3. A. Aziz and J. Y. Benzies, Application of perturbation techniques to heat transfer with variable thermal properties, Int. J. Heat Mass Transf., 19, 271–276 (1976).

  4. M. Pakdemirli and A. Z. Sahin, Similarity analysis of a nonlinear fin equation, Appl. Math. Lett., 19, 378–384 (2006).

  5. A. H. Bokhari, A. H. Kara, and F. D. Zaman, A note on symmetry analysis and exact solutions of a nonlinear fin equation, Appl. Math. Lett., 19, 1356–1360 (2006).

  6. P. Mebine and N. Olali, Leibnitz–MacLaurin method for solving temperature distribution in straight fins with temperature dependent thermal conductivity, J. Sci. Eng. Res., 3, No. 2, 97–105 (2016).

  7. S. B. Coskun and M. T. Atay, Fin efficiency analysis of convective straight fins with temperature dependent thermal conductivity using variational iteration method, Appl. Therm. Eng., 28, 2345–2352 (2008).

  8. A. Aziz and S. M. Enamul Hug, Perturbation solution for convecting fin with variable thermal conductivity, ASME J. Heat Transf., 97, 300–301 (1975).

  9. A. Campo and R. J. Spaulding, Coupling of methods of successive approximations and undetermined coefficients for the prediction of thermal behavior of uniform circumferential fins, Heat Mass Transf., 25, No. 6, 461–468 (1999).

  10. A. D. Kraus, A. Aziz, and J. Welty, Extended Surface Heat Transfer, Wiley, New York (2001).

  11. H. Fatoorechi and H. Abolghasemi, Investigation of nonlinear problems of heat conduction in tapered cooling fins via symbolic programming, Appl. Appl. Math.: An Int. J., 7, No. 2, 717–734 (2012).

  12. R. J. Moitsheki, Steady one-dimensional heat flow in a longitudinal triangular and parabolic fin, Commun. Nonlinear Sci. Numer. Simul., 16, 3971–3980 (2011).

  13. F. Khani and A. Aziz, Thermal analysis of a longitudinal trapezoidal fin with temperature dependent thermal conductivity and heat transfer coefficient, Commun. Nonlinear Sci. Numer. Simul., 15, 590–601 (2010).

  14. M. G. Sobamowo, Analysis of convective longitudinal fin with temperature dependent thermal conductivity and internal heat generation, Alexandria Eng. J., 56, 1–11 (2017).

  15. A. Arslanturk, A decomposition method for fin efficiency of convective straight fin with temperature dependent thermal conductivity, Int. Commun. Heat Mass Transf., 32, 831–841 (2005).

  16. Ching-Huang Chu and Chao-Kung Chen, A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, Int. J. Heat Mass Transf., 45, 2067–2075 (2002).

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Authors and Affiliations

  1. Computational Science Program, Addis Ababa University, Arat Kilo Campus, Addis Ababa, Ethiopia

    O. O. Onyejekwe, G. Tamiru, T. Amha, F. Habtamu, Y. Demiss, N. Alemseged & B. Mengistu

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  1. O. O. Onyejekwe
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  2. G. Tamiru
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  3. T. Amha
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  4. F. Habtamu
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  5. Y. Demiss
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  6. N. Alemseged
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  7. B. Mengistu
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Correspondence to O. O. Onyejekwe.

Additional information

Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 6, pp. 1629–1636, November–December, 2020.

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Onyejekwe, O.O., Tamiru, G., Amha, T. et al. Application of an Integral Numerical Technique for a Temperature-Dependent Thermal Conductivity Fin with Internal Heat Generation. J Eng Phys Thermophy 93, 1574–1582 (2020). https://doi.org/10.1007/s10891-020-02262-w

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  • DOI: https://doi.org/10.1007/s10891-020-02262-w

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