Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection

The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer assumptions are taken into account to govern the mathematical model of the flow analysis. Some suitable similarity variables are introduced to transform the partial differential equations into ordinary differential systems. The Runge-Kutta-Fehlberg fourth- and fifth-order techniques with the shooting method are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the non-linear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation.

[1]  Mohsen Sheikholeslami Kandelousi.  Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition , 2014 .

[2]  T. Hayat,et al.  Three-dimensional mixed convection squeezing flow , 2015 .

[3]  Numerical Investigation of the Effect of Unsteadiness on Three-Dimensional Flow of an Oldroyb-B Fluid , 2015, PloS one.

[4]  K. Vajravelu,et al.  Nanofluid flow and heat transfer in a cavity with variable magnetic field , 2017, Appl. Math. Comput..

[5]  M. Gorji-Bandpy,et al.  Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM) , 2013 .

[6]  Mohsen Sheikholeslami Kandelousi.  KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel , 2014 .

[7]  Oluwole Daniel Makinde,et al.  Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate , 2005 .

[8]  M. Sheikholeslami.  CVFEM for magnetic nanofluid convective heat transfer in a porous curved enclosure , 2016 .

[9]  Tasawar Hayat,et al.  Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation , 2015 .

[10]  Liancun Zheng,et al.  Radiation effects on Marangoni convection flow and heat transfer in pseudo-plastic non-Newtonian nanofluids with variable thermal conductivity , 2014 .

[11]  N. Ali,et al.  Boundary layer flow of an Oldroyd-B fluid in the region of a stagnation point over a stretching sheet , 2010 .

[12]  F. Alsaadi,et al.  MHD MIXED CONVECTION FLOW OF THIXOTROPIC FLUID WITH THERMAL RADIATION , 2014 .

[13]  Davood Domiri Ganji,et al.  Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid , 2014 .

[14]  Mohsen Sheikholeslami,et al.  Numerical simulation of magnetic nanofluid natural convection in porous media , 2017 .

[15]  Tasawar Hayat,et al.  Nonlinear radiative heat transfer in the flow of nanofluid due to solar energy: A numerical study , 2014 .

[16]  K. Iramina,et al.  Numerical simulation of effect of convection-diffusion on oxygen transport in microcirculation , 2015 .

[17]  Liancun Zheng,et al.  MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction , 2015 .

[18]  Ahmed Alsaedi,et al.  Nonlinear thermal radiation in three-dimensional flow of Jeffrey nanofluid: A model for solar energy , 2014, Appl. Math. Comput..

[19]  Liancun Zheng,et al.  MHD mixed convective heat transfer over a permeable stretching wedge with thermal radiation and ohmic heating , 2012 .

[20]  B. J. Gireesha,et al.  Nonlinear radiative heat transfer in MHD three-dimensional flow of water based nanofluid over a non-linearly stretching sheet with convective boundary condition , 2016 .

[21]  F. M. Abbasi,et al.  Analytical study of Cattaneo–Christov heat flux model for a boundary layer flow of Oldroyd-B fluid , 2015 .

[22]  B. J. Gireesha,et al.  Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid , 2016 .

[23]  Tasawar Hayat,et al.  Doubly stratified mixed convection flow of Maxwell nanofluid with heat generation/absorption , 2016 .

[24]  Mohammad Mehdi Rashidi,et al.  Effect of non-uniform magnetic field on forced convection heat transfer of Fe3O4–water nanofluid , 2015 .

[25]  Qiang Sun,et al.  Three-dimensional free bio-convection of nanofluid near stagnation point on general curved isothermal surface , 2016 .

[26]  R. Cortell,et al.  Fluid flow and radiative nonlinear heat transfer over a stretching sheet , 2014 .

[27]  Ali J. Chamkha,et al.  Influence of Lorentz forces on nanofluid forced convection considering Marangoni convection , 2017 .

[28]  Mohammad Mehdi Rashidi,et al.  Buoyancy effect on MHD flow of nanofluid over a stretching sheet in the presence of thermal radiation , 2014 .

[29]  Liancun Zheng,et al.  Convection of Maxwell fluid over stretching porous surface with heat source/sink in presence of nanoparticles: Lie group analysis , 2016 .

[30]  B. J. Gireesha,et al.  Perturbation Solution for Radiating Viscoelastic Fluid Flow and Heat Transfer with Convective Boundary Condition in Nonuniform Channel with Hall Current and Chemical Reaction , 2013 .

[31]  Tasawar Hayat,et al.  A model of solar radiation and Joule heating in magnetohydrodynamic (MHD) convective flow of thixotropic nanofluid , 2016 .

[32]  T. Hayat,et al.  Three-Dimensional Flow of an Oldroyd-B Fluid with Variable Thermal Conductivity and Heat Generation/Absorption , 2013, PloS one.

[33]  P. Donald Ariel,et al.  The three-dimensional flow past a stretching sheet and the homotopy perturbation method , 2007, Comput. Math. Appl..

[34]  T. Hayat,et al.  MHD free convection of Al2O3–water nanofluid considering thermal radiation: A numerical study , 2016 .

[35]  T. Hayat,et al.  Effects of thermophoresis and thermal radiation in mixed convection three-dimensional flow of Jeffrey fluid , 2015 .

[36]  T. Hayat,et al.  Thermally Stratified Stagnation Point Flow of an Oldroyd-B Fluid , 2014 .

[37]  D. Ganji,et al.  Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method , 2012 .

[38]  Mohsen Sheikholeslami,et al.  Magnetic field influence on nanofluid thermal radiation in a cavity with tilted elliptic inner cylinder , 2017 .

[39]  Mohammad Mehdi Rashidi,et al.  Numerical investigation of magnetic field effect on mixed convection heat transfer of nanofluid in a channel with sinusoidal walls , 2016 .

[40]  Mohsen Sheikholeslami,et al.  Nanofluid two phase model analysis in existence of induced magnetic field , 2017 .