Natural-Convection Flow of Nanofluids Over Vertical Cone Embedded in Non-Darcy Porous Media

In this paper, non-Darcy flow and natural convection over a vertical cone embedded in a porous medium saturated with a nanofluid is studied using the Forchheimer-extended Darcy law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. An analytical technique, similarity solution method, is used to convert the governing equations into a set of ordinary differential equations, and then numerically solved using the finite difference method. The effect of non-Darcy parameter and nanofluid parameters on the velocity, temperature, and nanoparticles volume fraction profiles, as well as on the two important parameters of heat and mass transfer, i.e., reduced Nusselt and Sherwood numbers, are discussed. The results show that an increase in the non-Darcy parameter decreases the velocity profiles, whereas it would increase the temperature and concentration profiles. Simulation results also show that an increase in the non-Darcy parameter would decrease the reduced Nusselt ...

[1]  Ali J. Chamkha,et al.  Mixed convective boundary layer flow over a vertical wedge embedded in a porous medium saturated with a nanofluid: Natural Convection Dominated Regime , 2011, 2010 3rd International Conference on Thermal Issues in Emerging Technologies Theory and Applications.

[2]  A. Nakayama,et al.  An integral treatment for non-Darcy free convection over a vertical flat plate and cone embedded in a fluid-saturated porous medium , 1988 .

[3]  K. Yih.  The effect of uniform lateral mass flux on free convection about a vertical cone embedded in a saturated porous medium , 1997 .

[4]  I. Pop,et al.  A unified similarity transformation for free, forced and mixed convection in Darcy and non-Darcy porous media , 1991 .

[5]  Ali J. Chamkha,et al.  Effects of nanoparticles diameter and concentration on natural convection of the Al2O3–water nanofluids considering variable thermal conductivity around a vertical cone in porous media , 2015 .

[6]  M. Ghalambaz,et al.  Natural convection of nanofluid over vertical plate embedded in porous medium: prescribed surface heat flux , 2013 .

[7]  I. Pop,et al.  Natural convection of a Darcian fluid about a cone , 1985 .

[8]  A. R. Sohouli,et al.  Analytical solution of natural convection of Darcian fluid about a vertical full cone embedded in porous media prescribed wall temperature by means of HAM , 2008 .

[9]  K. Yih.  Radiation effect on mixed convection over an isothermal cone in porous media , 2001 .

[10]  F. Zheng.  Thermophoresis of spherical and non-spherical particles: a review of theories and experiments. , 2002, Advances in colloid and interface science.

[11]  Wenhua Yu,et al.  Nanofluids: Science and Technology , 2007 .

[12]  M. Ghalambaz,et al.  Natural-convection heat and mass transfer from a vertical cone in porous media filled with nanofluids using the practical ranges of nanofluids thermo-physical properties , 2014 .

[13]  Alok K. Verma,et al.  An experimental study of non-Darcian effects in free convection in a saturated porous medium , 1981 .

[14]  Ching-Yang Cheng,et al.  Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium , 2009 .

[15]  I. Pop,et al.  Free Convection Boundary Layer over a Vertical Cone in a Non- Newtonian Fluid Saturated Porous Medium with Internal Heat Generation , 2004 .

[16]  Ali J. Chamkha,et al.  Free convection flow over a truncated cone embedded in a porous medium saturated with pure or saline water at low temperatures , 2006 .

[17]  G. Ramanaiah,et al.  Free convection about a wedge and a cone subjected to mixed thermal boundary conditions , 1992 .

[18]  Ali J. Chamkha,et al.  Non-similar Solution for Natural Convective Boundary Layer Flow Over a Sphere Embedded in a Porous Medium Saturated with a Nanofluid , 2011 .

[19]  J. Buongiorno.  Convective Transport in Nanofluids , 2006 .

[20]  Ioan Pop,et al.  Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids , 2010 .

[21]  Ching-Yang Cheng,et al.  Non-Darcy natural convection heat and mass transfer from a vertical wavy surface in saturated porous media , 2006, Appl. Math. Comput..

[22]  Donald A. Nield,et al.  The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid , 2009 .

[23]  L. Shampine,et al.  A collocation method for boundary value problems , 1972 .

[24]  Ching-Yang Cheng.  Natural convection heat and mass transfer from a vertical truncated cone in a porous medium saturated with a non-Newtonian fluid with variable wall temperature and concentration , 2009 .

[25]  Ahmed Mohammed Rashad,et al.  Natural convection boundary layer of a non-Newtonian fluid about a permeable vertical cone embedded in a porous medium saturated with a nanofluid , 2011, Comput. Math. Appl..

[26]  Ali J. Chamkha,et al.  Natural Convective Boundary Layer Flow over a Horizontal Plate Embedded in a Porous Medium Saturated with a Nanofluid , 2011 .

[27]  K. Abdella.  Numerical Solution of two-point boundary value problems using Sinc interpolation , 2012 .

[28]  A. Noghrehabadi,et al.  Flow and heat transfer affected by variable properties of nanofluids in natural-convection over a vertical cone in porous media , 2013 .

[29]  S. M. AbdEl-Gaied,et al.  Effect of heat generation/absorption on natural convective boundary-layer flow from a vertical cone embedded in a porous medium filled with a non-Newtonian nanofluid , 2011 .

[30]  Non-darcy natural convection over a slender vertical frustum of a cone in a saturated porous medium , 1986 .

[31]  O. Mahian,et al.  Nanofluids Flow Between Two Rotating Cylinders: Effects of Thermophoresis and Brownian Motion , 2013 .

[32]  A. Bejan,et al.  Convection in Porous Media , 1992 .