Buongiorno’s model for double-diffusive mixed convective stagnation-point flow of a nanofluid considering diffusiophoresis effect of binary base fluid

Abstract The development of double-diffusive mixed convective boundary layer flow of a nanofluid near stagnation point region over a vertical surface has been investigated. Buongiorno’s model is used to incorporate the effects of Brownian motion and thermophoresis for the nanofluid, when the base fluid of the nanofluid is itself a binary fluid such as salty water. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. Using the local similarity method, it is shown that a set of suitable similarity transformations reduces the non-linear coupled PDEs governing on the problem into a set of non-linear coupled ODEs. The analysis shows that velocity, temperature, solutal concentration and nanoparticle concentration profiles in the respective boundary layers depend on ten dimensionless physical parameters, namely the mixed convection parameter λ , the regular double-diffusive buoyancy parameter Nc , the nanofluid buoyancy ratio Nr , the Brownian motion parameter Nb , the thermophoresis parameter Nt , the modified Dufour parameter Nd , the regular Schmidt number Sc , the nanofluid Schmidt number Sc n , Prandtl number Pr , and the Dufour-solutal Lewis number Ld . The results are presented in graphical form illustrating the effects of these parameters on boundary layer behavior. A sensitivity analysis of model is tabulated where the difference in each graph can be quantified in terms of root mean square deviation (RMSD) with respect to that with the default parameters. These results are supplemented with the data for the reduced Nusselt number and the two reduced Sherwood numbers, one for the solute and the other for the nanoparticles. It is found that for assisting flow regime the reduced Nusselt number is a decreasing function of each of Nr , Nb and Nt , and an increasing function of each of λ , Nc and Nd . The results demonstrate that the highest heat transfer rate is obtained for the situation that the thermophoresis effects are negligible. Moreover, a reduction in the reduced Sherwood number of nanoparticle is observed with increase in each of Nc and Nt , while this quantity increases with Nb .

[1]  Y. Xuan,et al.  Investigation on Convective Heat Transfer and Flow Features of Nanofluids , 2003 .

[2]  Ioan Pop,et al.  Boundary-layer flow of nanofluids over a moving surface in a flowing fluid , 2010 .

[3]  I. Pop,et al.  Dual Solutions in Magnetohydrodynamic Mixed Convection Flow Near a Stagnation-Point on a Vertical Surface , 2007 .

[4]  I. Pop,et al.  Unsteady convective heat and mass transfer of a nanofluid in Howarth’s stagnation point by Buongiorno’s model , 2015 .

[5]  I. Pop,et al.  Mixed Convection on the Stagnation Point Flow Toward a Vertical, Continuously Stretching Sheet , 2007 .

[6]  I. Pop,et al.  MHD mixed convection stagnation-point flow of a nanofluid over a vertical permeable surface: a comprehensive report of dual solutions , 2014 .

[7]  M. J. Uddin,et al.  Scaling group transformation for MHD boundary layer free convective heat and mass transfer flow past a convectively heated nonlinear radiating stretching sheet , 2013 .

[8]  P. Bradshaw,et al.  Physical and Computational Aspects of Convective Heat Transfer , 1984 .

[9]  I. Pop,et al.  Magnetohydrodynamic stagnation point flow toward stretching/shrinking permeable plate in porous medium filled with a nanofluid , 2014 .

[10]  Puneet Rana,et al.  Numerical solution for mixed convection boundary layer flow of a nanofluid along an inclined plate embedded in a porous medium , 2012, Comput. Math. Appl..

[11]  I. Pop,et al.  Double-diffusive convection from a permeable vertical surface under convective boundary condition , 2011 .

[12]  Ioan Pop,et al.  Steady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface , 2005 .

[13]  Abdul Aziz,et al.  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 , 2011 .

[14]  Seyed Mostafa Hosseinalipour,et al.  Prediction of convective heat transfer of Al2O3-water nanofluid considering particle migration using neural network , 2014 .

[15]  I. Pop,et al.  Free Convection Boundary Layer Flow Past a Horizontal Flat Plate Embedded in a Porous Medium Filled With a Nanofluid , 2011 .

[16]  B. Armaly,et al.  Mixed Convection in Stagnation Flows Adjacent to Vertical Surfaces , 1988 .

[17]  I. Pop,et al.  HOMOTOPY ANALYSIS METHOD FOR MIXED CONVECTIVE BOUNDARY LAYER FLOW OF A NANOFLUID OVER A VERTICAL CIRCULAR CYLINDER , 2012 .

[18]  A. Mahdy.  Unsteady mixed convection boundary layer flow and heat transfer of nanofluids due to stretching sheet , 2012 .

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

[20]  I. Pop,et al.  MHD mixed convection flow near the stagnation-point on a vertical permeable surface , 2010 .

[21]  A. Mahdy,et al.  Soret and Dufour effect on double diffusion mixed convection from a vertical surface in a porous medium saturated with a non-Newtonian fluid , 2010 .

[22]  I. Pop,et al.  Unsteady mixed convection flow of a nanofluid near orthogonal stagnation point on a vertical permeable surface , 2014 .

[23]  H. B. Keller.  A New Difference Scheme for Parabolic Problems , 1971 .

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

[25]  A. Kuznetsov,et al.  The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid , 2011 .

[26]  I. Pop,et al.  Post-stagnation-point boundary layer flow and mixed convection heat transfer over a vertical, linearly stretching sheet , 2008 .

[27]  Mohammad Ferdows,et al.  FINITE DIFFERENCE SOLUTION OF MHD RADIATIVE BOUNDARY LAYER FLOW OF A NANOFLUID PAST A STRETCHING SHEET , 2010 .

[28]  Amir Malvandi,et al.  The Unsteady Flow of a Nanofluid in the Stagnation Point Region of a Time-dependent Rotating Sphere , 2013 .

[29]  Mehdi Bahiraei,et al.  Laminar Forced Convection of a Water-TiO2 Nanofluid in Annuli Considering Mass Conservation for Particles , 2013 .

[30]  Oluwole Daniel Makinde,et al.  Buoyancy effects on {MHD} stagnation point flow and heat transfer of a nanofluid past a convectively , 2013 .

[31]  G. Nath,et al.  Unsteady mixed convection flow in stagnation region adjacent to a vertical surface , 1991 .

[32]  Donald A. Nield,et al.  Natural convective boundary-layer flow of a nanofluid past a vertical plate , 2010 .

[33]  Donald A. Nield,et al.  Natural convective boundary-layer flow of a nanofluid past a vertical plate: A revised model , 2014 .

[34]  Mehdi Bahiraei,et al.  A Comprehensive Review on Different Numerical Approaches for Simulation in Nanofluids: Traditional and Novel Techniques , 2014 .

[35]  Mehdi Bahiraei,et al.  Flow and heat transfer characteristics of magnetic nanofluids: A review , 2014 .