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

doi:10.1007/s10483-017-2231-9

Abstract

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.

Key words: hyperelastic rectangular plate, finite deformation, growth of void, variational principle, micropolar nanofluid, finite difference method, cone, non-similar solution, non-uniform heating

2010 MSC Number:

76D10
76R10

S. E. AHMED. Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature. Applied Mathematics and Mechanics (English Edition), 2017, 38(8): 1171-1180.

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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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[10] Eringen, A. Theory of micropolar fluids. Journal of Mathematics and Mechanics, 16, 1-18(1966)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[20] Na, T. Y. and Chiou, J. P. Laminar natural convection over a frustum of a cone. Applied Scientific Research, 35, 409-421(1979)
[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)
[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)
[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)
[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)
[25] Blottner, F. G. Finite-difference methods of solution of the boundary-layer equation. AIAA Journal, 8, 193-205(1970)
[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)
[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)
[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)
[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)
[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)