MHD flow of water-based Brinkman type nanofluid over a vertical plate embedded in a porous medium with variable surface velocity, temperature and concentration

Abstract The aim of this paper is to investigate the unsteady magnetohydrodynamic (MHD) flow of Brinkman type nanofluid over a vertical plate embedded in a porous medium with variable surface velocity, temperature and concentration. The thermal radiation effect in the energy equation and chemical reaction in the concentration are also considered. Four different types of nanoparticles of spherical shape namely Silver (Ag), Copper (Cu), Titanium oxide (TiO 2 ) and Aluminum oxide (Al 2 O 3 ) are suspended in water taken as conventional base fluid. The problem is modeled in terms of partial differential equations with physical boundary conditions. Closed form solutions are obtained for velocity, temperature and concentration, using the Laplace transform technique. Graphical results for different physical parameters such as Brinkman parameter, volume fraction and radiation parameter are presented. Corresponding expressions for skin-friction, Nusselt number and Sherwood number are also evaluated. The present solutions are reduced to some well-known results in the published literature and are found in an excellent agreement.

[1]  Ilyas Khan,et al.  Exact solutions for free convection flow of nanofluids with ramped wall temperature , 2015 .

[2]  Lawrence E. Payne,et al.  Structural stability for a Brinkman fluid , 2007 .

[3]  Y. Hwang,et al.  Photoluminescence characteristics of Cd1-xMnxTe single crystals grown by the vertical Bridgman method , 2012, Nanoscale Research Letters.

[4]  M Muskat,et al.  THE FLOW OF HOMOGENEOUS FLUIDS THROUGH POROUS MEDIA: ANALOGIES WITH OTHER PHYSICAL PROBLEMS , 1937 .

[5]  H. Brinkman,et al.  On the permeability of media consisting of closely packed porous particles , 1949 .

[6]  S. Kakaç,et al.  Review of convective heat transfer enhancement with nanofluids , 2009 .

[7]  Stephen U. S. Choi.  Enhancing thermal conductivity of fluids with nano-particles , 1995 .

[8]  P. Loganathan,et al.  RADIATION EFFECTS ON AN UNSTEADY NATURAL CONVECTIVE FLOW OF A NANOFLUID PAST AN INFINITE VERTICAL PLATE , 2013 .

[9]  S. M. AbdEl-Gaied,et al.  Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet , 2012, Nanoscale Research Letters.

[10]  I. Khan,et al.  The Effects of Radiation on Free Convection Flow with Ramped Wall Temperature in Brinkman Type Fluid , 2013 .

[11]  Mark E. Davis,et al.  Fundamentals of Chemical Reaction Engineering , 2002 .

[12]  Sohail Nadeem,et al.  MHD squeezed flow of water functionalized metallic nanoparticles over a sensor surface , 2015 .

[13]  J. Lasheras,et al.  Atomization of viscous and Non-Newtonean liquids by a co-axial high-speed gas jet: Experiments and droplet size modelling , 2008 .

[14]  Tasawar Hayat,et al.  Heat and mass transfer analysis on the flow of a second grade fluid in the presence of chemical reaction , 2008 .

[15]  Sohail Nadeem,et al.  Water driven flow of carbon nanotubes in a rotating channel , 2016 .

[16]  A. A. Hill.  Convection induced by the selective absorption of radiation for the Brinkman model , 2004 .

[17]  Ilyas Khan,et al.  A Note on New Exact Solutions for Some Unsteady Flows of Brinkman- Type Fluids over a Plane Wall , 2012 .

[18]  I. Khan,et al.  Conjugate effects of heat and mass transfer of nanofluids over a nonlinear stretching sheet , 2012 .

[19]  M. Ismoen,et al.  Impact of chemical reaction on Cu, Al2O3 and SWCNTs–nanofluid flow under slip conditions , 2016 .

[20]  Zafar Hayat Khan,et al.  Entropy generation analysis for non-Newtonian nanofluid with zero normal flux of nanoparticles at the stretching surface , 2016 .

[21]  Rizwan Ul Haq,et al.  Numerical simulation of water based magnetite nanoparticles between two parallel disks , 2016 .

[22]  Adriano Tiribocchi,et al.  Spontaneous flow in polar active fluids: the effect of a phenomenological self propulsion-like term , 2016, The European Physical Journal E : Soft matter.

[23]  Rizwan Ul Haq,et al.  Thermophysical effects of water driven copper nanoparticles on MHD axisymmetric permeable shrinking sheet: Dual-nature study , 2016, The European physical journal. E, Soft matter.

[24]  E. Ozturk,et al.  Nonlinear intersubband absorption and refractive index change in n-type δ-doped GaAs for different donor distributions , 2015 .

[25]  G. Neale,et al.  Practical significance of brinkman's extension of darcy's law: Coupled parallel flows within a channel and a bounding porous medium , 1974 .

[26]  Sohail Nadeem,et al.  Radiation effects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition , 2013 .

[27]  Md. S. Ansari,et al.  Effects of Thermal Radiation and Rotation on Unsteady Hydromagnetic Free Convection Flow past an Impulsively Moving Vertical Plate with Ramped Temperature in a Porous Medium , 2013 .

[28]  Francine Luppé,et al.  Experimental verification of nanofluid shear-wave reconversion in ultrasonic fields. , 2016, Nanoscale.

[29]  Zafar Hayat Khan,et al.  Flow and heat transfer analysis of water and ethylene glycol based Cu nanoparticles between two parallel disks with suction/injection effects , 2016 .

[30]  Ali J. Chamkha,et al.  Effect of chemical reaction on heat and mass transfer by mixed convection flow about a sphere in a saturated porous media , 2011 .

[31]  Davood Domiri Ganji,et al.  Three dimensional heat and mass transfer in a rotating system using nanofluid , 2014 .