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Exact solution of the nonlinear fin problem with exponentially temperature-dependent thermal conductivity and heat transfer coefficient

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Abstract

This article studies a class of fin problems with two nonlinear terms arising from thermal conductivity and convection heat transfer coefficient. A one-dimensional convective straight fin is analysed for exponentially temperature-dependent thermal conductivity and exponentially temperature-dependent heat transfer coefficient. The exact fin temperature excess, heat transfer rate and fin efficiency are obtained and presented graphically. The obtained results show the strong influences of exponent indexes of thermal conductivity and convection transfer coefficient as well as thermogeometric fin parameter on the fin efficiency and heat flow.

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References

  1. M Gholinia, S Gholinia, K Hosseinzadeh and D D Ganji, Results Phys. 9, 1525 (2018)

    Article  ADS  Google Scholar 

  2. K Hosseinzadeh, A Asadi, A Mogharrebi, J Khalesi, S Mousavisani and D Ganji, Case Stud. Therm. Eng. 14, 100482 (2019)

    Article  Google Scholar 

  3. T Hayat, M Kanwal, S Qayyum, M I Khan and A Alsaedi, Pramana – J. Phys. 93(4): 54 (2019)

    Article  ADS  Google Scholar 

  4. K Hosseinzadeh, A J Amiri, S S Ardahaie and D D Ganji, Case Stud. Therm. Eng. 10, 595 (2017)

    Article  Google Scholar 

  5. S Iram, M Nawaz and A Ali, Pramana – J. Phys. 91(4): 47 (2018)

    Article  ADS  Google Scholar 

  6. M R Zangooee, K Hosseinzadeh and D D Ganji, Case Stud. Therm. Eng. 14, 100460 (2019)

    Article  Google Scholar 

  7. K Hosseinzadeh, A R Mogharrebi, A Asadi, M Paikar and D D Ganji, J. Mol. Liq. 300, 112347 (2020)

    Article  Google Scholar 

  8. A D Kraus, A Aziz and J Welty, Extended surface heat transfer (John Wiley & Sons, 2002)

  9. H M Hung and F C Appl, J. Heat Transfer 89(2), 155 (1967)

    Article  Google Scholar 

  10. S A Atouei, K Hosseinzadeh, M Hatami, S E Ghasemi, S A R Sahebi and D D Ganji, Appl. Therm. Eng. 89, 299 (2015)

    Article  Google Scholar 

  11. E Yasar, Y Yildirim and I B Giresunlu, Pramana – J. Phys. 87(2): 18 (2016)

    Article  ADS  Google Scholar 

  12. M H Chang, Int. J. Heat Mass Transfer 48(9), 1819 (2005)

    Article  Google Scholar 

  13. S Abbasbandy and E Shivanian, Phys. Lett. A 374(4), 567 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  14. C H Chiu and K C Chen, Int. J. Heat Mass Transfer 45(10), 2067 (2002)

    Article  Google Scholar 

  15. C Arslanturk, Int. Commun. Heat Mass Transfer 32(6), 831 (2005)

    Article  Google Scholar 

  16. Y T Yang, S K Chien and C K Chen, Energy Convers. Manage. 49(10), 2910 (2008)

    Article  Google Scholar 

  17. A A Joneidi, D D Ganji and M Babaelahi, Int. Commun. Heat Mass Transfer 36(7), 757 (2009)

    Article  Google Scholar 

  18. M Torabi, H Yaghoobi and A Aziz, Int. J. Thermophys. 33(5), 924 (2012)

    Article  ADS  Google Scholar 

  19. S B Coskun and M T Atay, Appl. Therm. Eng. 28(17–18), 2345 (2008)

    Article  Google Scholar 

  20. M Miansari, D D Ganji and M Miansari, Phys. Lett. A 372(6), 779 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  21. S Abbasbandy, Phys. Lett. A 360(1), 109 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  22. M Inc, Math. Comput. Simul. 79(2), 189 (2008)

    Article  Google Scholar 

  23. G Domairry and M Fazeli, Commun. Nonlin. Sci. Numer. Simul. 14(2), 489 (2009)

    Article  Google Scholar 

  24. M N Bouaziz and A Aziz, Energy Convers. Manage. 51(12), 2776 (2010)

    Article  Google Scholar 

  25. M Torabi and Q B Zhang, Energy Convers. Manage. 66, 199 (2013)

    Article  Google Scholar 

  26. M Anbarloei and E Shivanian, J. Heat Transfer 138(11), 114501 (2016)

    Article  Google Scholar 

  27. E Shivanian and S J H Ghoncheh, Eur. Phys. J. Plus 132(2), 97 (2017)

    Article  Google Scholar 

  28. E Shivanian, M R Ansari and M Shaban, Can. J. Phys. 97(1), 23 (2019)

    Article  ADS  Google Scholar 

  29. M Mierzwiczak, W Chen and Z J Fu, Int. J. Heat Mass Transfer 91, 205 (2015)

    Article  Google Scholar 

  30. R J Moitsheki, T Hayat and M Y Malik, Nonlinear Anal. 11(5), 3287 (2010)

    Article  MathSciNet  Google Scholar 

  31. S Abbasbandy and E Shivanian, Int. J. Therm. Sci. 116, 45 (2017)

    Article  Google Scholar 

  32. S W Sun and X F Li, Can. J. Phys.https://doi.org/10.1139/cjp-2019-0435 (2020)

  33. M Pakdemirli and A Z Sahin, Int. J. Eng. Sci. 42(17–18), 1875 (2004)

    Article  Google Scholar 

  34. S I Abu-Eishah, Int. J. Thermophys. 22(6), 1855 (2001)

    Article  Google Scholar 

  35. John H Lienhard IV and John H Lienhard V, A heat transfer textbook (Cambridge University Press, 2011)

  36. Y Huang and X F Li, Int. J. Heat Mass Transfer 150, 119303 (2020)

    Article  Google Scholar 

  37. M Torabi, A Aziz and K Zhang, Energy 51, 243 (2013)

    Article  Google Scholar 

  38. M Torabi and A Aziz, Int. Commun. Heat Mass Transfer 39(8), 1018 (2012)

    Article  Google Scholar 

  39. A Aziz and M Torabi, Heat Tran.-Asian Res. 41(2), 99 (2012)

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11872379).

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Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410075, China

    Sheng-Wei Sun & Xian-Fang Li

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  1. Sheng-Wei Sun
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  2. Xian-Fang Li
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Correspondence to Xian-Fang Li.

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Sun, SW., Li, XF. Exact solution of the nonlinear fin problem with exponentially temperature-dependent thermal conductivity and heat transfer coefficient. Pramana - J Phys 94, 94 (2020). https://doi.org/10.1007/s12043-020-01971-4

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  • DOI: https://doi.org/10.1007/s12043-020-01971-4

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