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Fuzzy Equations for Mixed Convection in a Rectangular Cavity

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Recent Advances in Intuitionistic Fuzzy Logic Systems and Mathematics

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 395))

Abstract

In this paper, the fuzzy equations of mixed convection heat transfer has been introduced. The fuzzy boundary conditions for temperature is considered. We study the existence and uniqueness of fuzzy solutions, under some conditions. The results are presented and proved in terms of velocity, steram function and temperature profiles.

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References

  1. Bejan, A.: The boundary layer regime in a porous layer with uniform heat flux from side. Int. Heat Mass Trans. 26, 1339–1346 (1983)

    Article  Google Scholar 

  2. Buckley, J.J., Qu, Y.: On using \(\alpha \)-cuts to evaluate fuzzy equations. Fuzzy Sets Syst. 38, 309–312 (1990)

    Google Scholar 

  3. Chadli, L.S., Harir, A., Melliani, S.: Solutions of fuzzy heat-like equations by variational iterative method. Ann. Fuzzy Math. Inf. 10(1), 29–44 (2015)

    MATH  Google Scholar 

  4. Chadli, L.S., Harir, A., Melliani, S.: Solutions of fuzzy wave-like equations by variational iteration method. Int. Ann. Fuzzy Math. Inf. 8(4), 527–547 (2014)

    MathSciNet  MATH  Google Scholar 

  5. El Harfi, H., Naimi, M., Lamsaadi, M., Raji, A., Hasnaoui, M.: Mixed convection heat transfer for nanofluids in a lid-driven shallow rectangular cavity uniformly heated and cooled from the vertical sides: the cooperative case. J. Electron. Cool. Therm. Control 3(3) (2013)

    Google Scholar 

  6. Lamsaadi, M., Naimi, M., Hasnaoui, M.: Natural convection heat transfer in shallow horizontal rectangular enclosures uniformly heated from the side and filled with non-Newtonian power law fluids. En. Con. Man. 47, 2535–2551 (2006)

    Article  Google Scholar 

  7. Leite, J., Bassanezi, R.C.: Sistemas dinamicos fuzzy aplicados a processos difusivos. Biomatemtica 20, 157–166 (2010). (in Portuguese)

    Google Scholar 

  8. Kaleva, O.: Fuzzy differential equations. Fuzzy Sets Syst. 24(3), 301–317 (1987)

    Article  MathSciNet  Google Scholar 

  9. Kaleva, O.: The Cauchy problem for fuzzy differential equations. Fuzzy Sets Syst. 35, 389–396 (1990)

    Article  MathSciNet  Google Scholar 

  10. Getschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets Syst. 18, 31–43 (1986)

    Article  MathSciNet  Google Scholar 

  11. Seikkala, S.: On the fuzzy initial value problem. Fuzzy Sets Syst. 24, 319–330 (1987)

    Article  MathSciNet  Google Scholar 

  12. Diamond, P., Kloeden, P.E.: Metric Spaces of Fuzzy Sets: Theory and Applications. World Scienific, Singapore (1994)

    Book  Google Scholar 

  13. Ma, M., Friedman, M., Kandel, A.: A new fuzzy arithmetic. Fuzzy Sets Syst. 108, 83–90 (1999)

    Article  MathSciNet  Google Scholar 

  14. Jafelice, R.M., Almeida, C.G., Meyer, J.F., Vasconcelos, H.L.: Fuzzy parameter in a partial differential equation model for population dispersal of leaf-cuttingants. Nonlinear Anal. Real World Appl. 12, 3397–3412 (2011)

    Article  MathSciNet  Google Scholar 

  15. Oberguggenberger, M.: Fuzzy and weak solutions to differential equations. In: Proceedings of the 10th International IPMU Conference, pp. 517–524 (2004)

    Google Scholar 

  16. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353

    Google Scholar 

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Correspondence to Said Melliani .

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Harir, A., El Harfi, H., Melliani, S., Chadli, L.S. (2021). Fuzzy Equations for Mixed Convection in a Rectangular Cavity. In: Melliani, S., Castillo, O. (eds) Recent Advances in Intuitionistic Fuzzy Logic Systems and Mathematics. Studies in Fuzziness and Soft Computing, vol 395. Springer, Cham. https://doi.org/10.1007/978-3-030-53929-0_11

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