Two-Phase Couette Flow of Couple Stress Fluid with Temperature Dependent Viscosity Thermally Affected by Magnetized Moving Surface

The Couette–Poiseuille flow of couple stress fluid with magnetic field between two parallel plates was investigated. The flow was driven due to axial pressure gradient and uniform motion of the upper plate. The influence of heating at the wall in the presence of spherical and homogeneous Hafnium particles was taken into account. The temperature dependent viscosity model, namely, Reynolds’ model was utilized. The Runge–Kutta scheme with shooting was used to tackle a non-linear system of equations. It was observed that the velocity decreased by increasing the values of the Hartman number, as heating of the wall reduced the effects of viscous forces, therefore, resistance of magnetic force reduced the velocity of fluid. However, due to shear thinning effects, the velocity was increased by increasing the values of the viscosity parameter, and as a result the temperature profile also declined. The suspension of inertial particles in an incompressible turbulent flow with Newtonian and non-Newtonian base fluids can be used to analyze the biphase flows through diverse geometries that could possibly be future perspectives of proposed model.

[1]  Rahmat Ellahi,et al.  Series solutions of non-Newtonian nanofluids with Reynolds' model and Vogel's model by means of the homotopy analysis method , 2012, Math. Comput. Model..

[2]  Stanley E. Charm,et al.  Blood flow and microcirculation , 1974 .

[3]  Rahmat Ellahi,et al.  Effects of Heat Transfer and Nonlinear Slip on the Steady Flow of Couette Fluid by Means of Chebyshev Spectral Method , 2014 .

[4]  Ahmed Zeeshan,et al.  Peristaltic Blood Flow of Couple Stress Fluid Suspended with Nanoparticles under the Influence of Chemical Reaction and Activation Energy , 2019, Symmetry.

[5]  Christopher K. W. Tam,et al.  The drag on a cloud of spherical particles in low Reynolds number flow , 1969, Journal of Fluid Mechanics.

[6]  M. Mahmoud.  Chemical reaction and variable viscosity effects on flow and mass transfer of a non-Newtonian visco-elastic fluid past a stretching surface embedded in a porous medium , 2010 .

[7]  Najeeb Alam Khan,et al.  Exact solutions for MHD flow of couple stress fluid with heat transfer , 2016 .

[8]  E. Ashmawy,et al.  Unsteady Plane Couette Flow of an Incompressible Couple Stress Fluid with Slip Boundary Conditions , 2016 .

[9]  R. Ellahi,et al.  Thermally Charged MHD Bi-Phase Flow Coatings with Non-Newtonian Nanofluid and Hafnium Particles along Slippery Walls , 2019, Coatings.

[10]  Saman Rashidi,et al.  Convective Heat Transfer and Particle Motion in an Obstructed Duct with Two Side by Side Obstacles by Means of DPM Model , 2017 .

[11]  Oluwole Daniel Makinde,et al.  Laminar falling liquid film with variable viscosity along an inclined heated plate , 2006, Appl. Math. Comput..

[12]  M. T. Rahim,et al.  Steady Poiseuille flow and heat transfer of couple stress fluids between two parallel inclined plates with variable viscosity , 2013 .

[13]  Phool Singh,et al.  A Study of Temperature-dependent Fluid Properties on MHD Free Stream Flow and Heat Transfer over a Non-Linearly Stretching Sheet , 2015 .

[14]  K. Vafai,et al.  Modelling study on heated couple stress fluid peristaltically conveying gold nanoparticles through coaxial tubes: A remedy for gland tumors and arthritis , 2018, Journal of Molecular Liquids.

[15]  Mohammad Reza Safaei,et al.  A smoothed particle hydrodynamics approach for numerical simulation of nano-fluid flows , 2018, Journal of Thermal Analysis and Calorimetry.

[16]  Rahmat Ellahi,et al.  Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions , 2018 .

[17]  M. M. Bhatti,et al.  A comparative study on magnetic and non-magnetic particles in nanofluid propagating over a wedge , 2019, Canadian Journal of Physics.

[18]  Zahir Shah,et al.  Impact of Nonlinear Thermal Radiation and the Viscous Dissipation Effect on the Unsteady Three-Dimensional Rotating Flow of Single-Wall Carbon Nanotubes with Aqueous Suspensions , 2019, Symmetry.

[19]  O. Makinde,et al.  A numerical study of MHD generalized Couette flow and heat transfer with variable viscosity and electrical conductivity , 2011 .

[20]  Goodarz Ahmadi,et al.  Heat Transfer and Pressure Drop in Fully Developed Turbulent Flows of Graphene Nanoplatelets-Silver/Water Nanofluids , 2016 .

[21]  Saman Rashidi,et al.  Modelling Study on Internal Energy Loss Due to Entropy Generation for Non-Darcy Poiseuille Flow of Silver-Water Nanofluid: An Application of Purification , 2018, Entropy.

[22]  Adetayo Samuel Eegunjobi,et al.  Irreversibility analysis of unsteady couette flow with variable viscosity , 2015 .

[23]  S Nadeem,et al.  Analytical solutions for pipe flow of a fourth grade fluid with Reynold and Vogel's models of viscosities , 2009 .

[24]  R. Khayat,et al.  A low-dimensional approach to nonlinear plane-Poiseuille flow of viscoelastic fluids , 2000 .

[25]  P. M. Coelho,et al.  On the Generalized Brinkman Number Definition and Its Importance for Bingham Fluids , 2011 .

[26]  B. V. Swarnalathamma,et al.  Peristaltic hemodynamic flow of couple stress fluid through a porous medium under the influence of magnetic field with slip effect , 2016 .

[27]  Saleem Asghar,et al.  Unsteady Couette flow of viscous fluid under a non-uniform magnetic field , 2012, Appl. Math. Lett..

[28]  Arash Karimipour,et al.  The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump , 2017 .

[29]  Ahmed Zeeshan,et al.  Effects of Radiative Electro-Magnetohydrodynamics Diminishing Internal Energy of Pressure-Driven Flow of Titanium Dioxide-Water Nanofluid due to Entropy Generation , 2019, Entropy.

[30]  S. Abbasbandy,et al.  Numerical study of magnetohydrodynamics generalized Couette flow of Eyring-Powell fluid with heat transfer and slip condition , 2016 .

[31]  R. Ellahi,et al.  Electroosmotic Flow of MHD Power Law Al2O3-PVC Nanouid in a Horizontal Channel: Couette-Poiseuille Flow Model , 2018, Communications in Theoretical Physics.

[32]  R. Ellahi.  The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions , 2013 .

[33]  M. Dada,et al.  Reynold’s model viscosity on radiative MHD flow in a porous medium between two vertical wavy walls , 2017 .

[34]  Muhammad Adil Sadiq,et al.  MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip , 2019, Symmetry.

[35]  I. Pop,et al.  An MHD couple stress fluid due to a perforated sheet undergoing linear stretching with heat transfer , 2017 .

[36]  A. Al-Rashed,et al.  New temperature, interfacial shell dependent dimensionless model for thermal conductivity of nanofluids , 2017 .

[37]  M. M. Bhatti,et al.  Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls , 2016 .

[38]  Nehad Ali Shah,et al.  Exact solutions for some unsteady flows of a couple stress fluid between parallel plates , 2018, Ain Shams Engineering Journal.

[39]  L M Srivastava,et al.  Peristaltic transport of a particle-fluid suspension. , 1989, Journal of biomechanical engineering.

[40]  R. Gorla,et al.  Natural convection flow of non‐Newtonian power‐law fluid from a slotted vertical isothermal surface , 2009 .

[41]  W. Shaowei,et al.  Exact solution on unsteady Couette flow of generalized Maxwell fluid with fractional derivative , 2006 .