Thermal Non-Equilibrium Similarity Solution for Nanofluid Boundary Layer in a Porous Medium

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Abstract

In the present study , we have investigated the external free convection of a nanofluid near a vertical heated surface embedded in a saturated porous medium using the thermal non - equilibrium assumption. The vertical surface has a linear temperature distribution with a uniform mass suction or injection. Assuming the Brownian motion and thermophoresis as the primary driving mechanisms of free convection of the nanofluid , suitable volume averaged equations are employed. We have also followed similarity solution method for transforming the governing equations in to the ordinary differential equations. The new set of ordinary equations is solved numerically by the Shooting method and the flow and temperature fields are determined completely. The obtained numerical results are employed for calculating the Nusselt numbers for both the solid and liquid phases in the physical domain. Moreover , the Sherwood number for the nanoparticles is determined over a wide range of parameters.

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References

[1] Tamayol, A., McGregor, F., Bahrami, M., 2012.“Thermal assessment of naturally cooled electronic enclosures with rectangular fins”, J. ElectronicPackaging 134, 034501- 6.
[2] Khan, WA., Aziz, A., 2011. “Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux”, Int. J. Thermal Sci 50,1207- 1214.
[3] Abdul-Kahar, R., Kandasamy, R., Muhaimin., 2011.“Scaling group transformation for boundary-layer flow of a nanofluid past a porous vertical stretching surface in the presence of chemical reaction with heat radiation”, Computers & Fluids 52, 15- 21.
[4] Khan, WA., Aziz, A., 2011. “Double-diffusive natural convective boundary layer flow in a porous medium
saturated with a nanofluid over a vertical plate:Prescribed surface heat, solute and nanoparticle fluxes”, Int. J. Thermal Sci 50, 2154- 2160.
[5] Kuznetsov, AV., Nield, DA., 2010. “Natural convective boundary-layer flow of a nanofluid past a vertical plate”, Int. J. Thermal Sci. 49, 243- 247.
[6] Nield, DA., Kuznetsov, AV., 2011. “The Cheng–Minkowycz problem for the double-diffusive natural
convective boundary layer flow in a porous medium saturated by a nanofluid”, Int. J. Heat Mass Transfer 54, 374- 378.
[7] Nield, DA., Kuznetsov, AV., 2009. “The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid”, Int. J. Heat Mass Transfer 52, 5792-5795.
[8] Kuznetsov, AV., Nield, DA., 2010. “Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: Brinkman Model”, Transport Porous Media 81, 409- 422.
[9] Kuznetsov, AV., Nield, DA., 2010. “The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium”, Transport Porous Media 85, 941- 951.
[10] Ahmad, S., Pop, I., 2010. “Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids”,Int. Commun. Heat Mass Transfer 37, 987- 991.
[11] Kuznetsov, AV., 1998. “Thermal nonequilibrium forced convection in porous media”, Transport Phenomena in Porous Media (D.B. Ingham and I.Pop, eds.) Pergamon, Oxford, U.K.
[12] Rees, DAS., Pop, I., 2005. “Local thermal nonequilibrium in porous medium convection”,Transport Phenomena in Porous Media III (D.B.Ingham and I. Pop, eds.) Pergamon, Oxford, U.K,147- 173.
[13] Rees, DAS., 2010. “Microscopic modelling of the two-temperature model for conduction in heterogeneous media”, J. Porous Media 13, 125- 143.
[14] Rees, DAS., “Microscopic modelling of the twotemperature model for conduction in heterogeneous media: three-dimensional media”, Proceedings of the 4th International Conference on Applications of Porous Media, Istanbul, Turkey, Paper 15.
[15] Gupta, PS., Gupta, AS., 1977. “Heat and mass transfer on a stretching sheet with suction or blowing”, Canad. J. Chem. Eng. 55, 744- 746.
[16] Magyari, E., Keller, B., 2000. “Exact analytical solutions for free convection boundary layers on a heated vertical plate with lateral mass flux embedded in a saturated porous medium”, Heat Mass Transfer 36, 109- 116.[17] Cheng, P., 1977. “The influence of lateral mass flux on free convection boundary layers in a saturated porous medium”, Int. J. Heat Mass Transfer 20, 201-206.
[18] Ali, ME., 2007. “The effect of lateral mass flux on the natural convection boundary layers induced by a heated vertical plate embedded in a saturated porous medium with internal heat generation”, Int. J.Thermal Sci. 46, 157- 63.
Amirkabir Journal of Mechanical Engineering
Volume 48, Issue 3
September 2016
Pages 281-290

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