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Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature

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Abstract

This paper discusses the natural convection boundary layer flow of a micropolar nanofluid over a vertical permeable cone with variable wall temperatures. Non-similar solutions are obtained. The nonlinearly coupled differential equations under the boundary layer approximations governing the flow are solved numerically using an efficient, iterative, tri-diagonal, implicit finite difference method. Different experimental correlations for both nanofluid effective viscosity and nanofluid thermal conductivity are considered. It is found that as the vortex-viscosity parameter increases, both the velocity profiles and the local Nusselt number decrease. Also, among all the nanoparticles considered in this investigation, Cu gives a good convection.

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References

  1. Choi, S. U. S. Enhancing thermal conductivity of fluids with nanoparticles. ASME Fluids Engineering Division, 231, 99–105 (1995)

    Google Scholar 

  2. Makinde, O. D. and Aziz, A. Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. International Journal of Thermal Sciences, 50, 1326–1332 (2011)

    Article  Google Scholar 

  3. Cheng, C. Y. Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid. International Communications in Heat and Mass Transfer, 39, 931–936 (2012)

    Article  Google Scholar 

  4. Mansour, M. A., Mohamed, R. A., Abd-Elaziz, M. M., and Ahmed, S. E. Numerical simulation of mixed convection flows in a square lid-driven cavity partially heated from below using nanofluid. International Communications in Heat and Mass Transfer, 37, 1504–1512 (2010)

    Article  Google Scholar 

  5. Mahdy, A. and Ahmed, S. E. Laminar free convection over a vertical wavy surface embedded in a porous medium saturated with a nanofluid. Transport in Porous Media, 91, 423–435 (2012)

    Article  MathSciNet  Google Scholar 

  6. Mansour, M. A. and Ahmed, S. E. Mixed convection flows in a square lid-driven cavity with heat source at the bottom utilizing nanofluid. The Canadian Journal of Chemical Engineering, 90, 100–110 (2012)

    Article  Google Scholar 

  7. Li, Y. Q., Wang, F. C., Liu, H., and Wu, H. A. Nanoparticle-tuned spreading behavior of nanofluid droplets on the solid substrate. Microfluid Nanofluid, 18, 111–120 (2015)

    Article  Google Scholar 

  8. Wang, F. C. and Wu, H. A. Enhanced oil droplet detachment from solid surfaces in charged nanoparticle suspensions. Soft Matter, 9(33), 7974–7980 (2013)

    Article  Google Scholar 

  9. Li, Y. Q., Wu, H. A., and Wang, F. C. Effect of a single nanoparticle on the contact line motion. Langmuir, 32(48), 12676–12685 (2016)

    Article  Google Scholar 

  10. Eringen, A. Theory of micropolar fluids. Journal of Mathematics and Mechanics, 16, 1–18 (1966)

    MathSciNet  Google Scholar 

  11. El-Aziz, A. M. Mixed convection flow of a micropolar fluid from an unsteady stretching surface with viscous dissipation. Journal of the Egyptian Mathematical Society, 21, 385–394 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Olajuwon, B. I., Oahimire, J. I., and Ferdow, M. Effect of thermal radiation and Hall current on heat and mass transfer of unsteady MHD flow of a viscoelastic micropolar fluid through a porous medium. Engineering Science and Technology, An International Journal, 17, 185–193 (2014)

    Article  Google Scholar 

  13. Mansour, M. A., Mohamed, R. A., El-Aziz, A. M., and Ahmed, S. E. Steady axisymmetric flow and heat transfer of micropolar fluid over a vertical permeable slender cylinder in the presence of thermal radiation. International Journal of Applied Mechanics and Engineering, 15, 1185–1203 (2010)

    Google Scholar 

  14. Mansour, M. A., Mohamed, R. A., El-Aziz, A. M., and Ahmed, S. E. Thermal stratification and suction/injection effects on flow and heat transfer of micropolar fluid due to stretching cylinder. International Journal for Numerical Methods in Biomedical Engineering, 27, 1951–1963 (2011)

    Article  MATH  Google Scholar 

  15. Ahmed, S. E. and Rashad, A. M. Natural convection of micropolar nanofluids in a rectangular enclosure saturated with anisotropic porous media. Journal of Porous Media, 19(8), 737–750 (2016)

    Article  Google Scholar 

  16. Cheng, C. Y. Natural convection boundary layer flow of a micropolar fluid over a vertical permeable cone with variable wall temperature. International Communications in Heat and Mass Transfer, 38, 429–433 (2011)

    Article  Google Scholar 

  17. Hossain, M. A. and Paul, C. S. Free convection from a vertical permeable circular cone with non-uniform surface heat flux. Heat and Mass Transfer, 37, 167–173 (2001)

    Article  MATH  Google Scholar 

  18. Hossain, M. A. and Paul, C. S. Free convection from a vertical permeable circular cone with non-uniform surface temperature. Acta Mechanica, 151, 103–114 (2001)

    Article  MATH  Google Scholar 

  19. Hering, R. G. and Grosh, R. J. Laminar free convection from a non-isothermal cone. International Journal of Heat and Mass Transfer, 5, 1059–1068 (1962)

    Article  Google Scholar 

  20. Na, T. Y. and Chiou, J. P. Laminar natural convection over a frustum of a cone. Applied Scientific Research, 35, 409–421 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  21. Yih, K. A. Effect of radiation on natural convection about a truncated cone. International Journal of Heat and Mass Transfer, 42, 4299–4305 (1999)

    Article  MATH  Google Scholar 

  22. Pop, I. and Na, T. Y. Natural convection over a vertical wavy frustum of a cone. International Journal of Non-linear Mechanics, 34, 925–934 (1999)

    Article  MATH  Google Scholar 

  23. Pop, I. and Na, T. Y. Coupled heat and mass transfer by natural convection about a truncated cone in the presence of magnetic field and radiation effects. Numerical Heat Transfer, Part A: Application, 39, 511–530 (2001)

    Article  Google Scholar 

  24. Postelnicu, A. Free convection about a vertical frustum of a cone in a micropolar fluid. International Journal of Engineering Science, 44, 672–682 (2006)

    Article  MATH  Google Scholar 

  25. Blottner, F. G. Finite-difference methods of solution of the boundary-layer equation. AIAA Journal, 8, 193–205 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  26. Ahmadi, G. Self-similar solution of incompressible micropolar boundary layer flow over a semiinfinite flat plate. International Journal of Engineering Science, 14(7), 639–646 (1976)

    Article  MATH  Google Scholar 

  27. Rees, D. A. S. and Pop, I. Free convection boundary-layer flow of a micropolar fluid from a vertical flat plate. IMA Journal of Applied Mathematics, 61(2), 179–197 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  28. Pak, B. C. and Cho, Y. I. Hydrodynamic and heat transfer study of dispersed fluid with submicron metallic oxide particles. Experimental Heat Transfer, 11(2), 151–170 (1998)

    Article  Google Scholar 

  29. Godson, L., Raja, B., Lal, D. M., and Wongwises, S. Experimental investigation on the thermal conductivity and viscosity of silver-deionized water nanofluid. Experimental Heat Transfer, 23(4), 317–332 (2010)

    Article  Google Scholar 

  30. Aminossadati, S. M. and Ghasemi, B. Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure. European Journal of Mechanics B/Fluids, 28(5), 630–640 (2009)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt

    S. E. Ahmed

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  1. S. E. Ahmed
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Correspondence to S. E. Ahmed.

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Ahmed, S.E. Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature. Appl. Math. Mech.-Engl. Ed. 38, 1171–1180 (2017). https://doi.org/10.1007/s10483-017-2231-9

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  • DOI: https://doi.org/10.1007/s10483-017-2231-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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