MHD flow of radiative micropolar nanofluid in a porous channel: optimal and numerical solutions

The flow of a radiative and electrically conducting micropolar nanofluid inside a porous channel is investigated. After implementing the similarity transformations, the partial differential equations representing the radiative flow are reduced to a system of ordinary differential equations. The subsequent equations are solved by making use of a well-known analytical method called homotopy analysis method (HAM). The expressions concerning the velocity, microrotation, temperature, and nanoparticle concentration profiles are obtained. The radiation tends to drop the temperature profile for the fluid. The formulation for local Nusselt and Sherwood numbers is also presented. Tabular and graphical results highlighting the effects of different physical parameters are presented. Rate of heat transfer at the lower wall is seen to be increasing with higher values of the radiation parameter while a drop in heat transfer rate at the upper wall is observed. Same problem has been solved by implementing the numerical procedure called the Runge–Kutta method. A comparison between the HAM, numerical and already existing results has also been made.

[1]  Mohammad Mehdi Rashidi,et al.  A semi-analytical solution of micro polar flow in a porous channel with mass injection by using differential transform method , 2010 .

[2]  Sohail Nadeem,et al.  Mixed convection stagnation flow of a micropolar nanofluid along a vertically stretching surface with slip effects , 2015 .

[3]  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..

[4]  Shijun Liao,et al.  Advances in the homotopy analysis method , 2014 .

[5]  Arshad Riaz,et al.  Analytical solutions for MHD flow in a third-grade fluid with variable viscosity , 2010, Math. Comput. Model..

[6]  Davood Domiri Ganji,et al.  Heat transfer of Cu-water nanofluid flow between parallel plates , 2013 .

[7]  Rahmat Ellahi,et al.  Study of Natural Convection MHD Nanofluid by Means of Single and Multi-Walled Carbon Nanotubes Suspended in a Salt-Water Solution , 2015, IEEE Transactions on Nanotechnology.

[8]  Neil A. Kelson,et al.  Micropolar flow in a porous channel with high mass transfer , 2003 .

[9]  Naveed Ahmed,et al.  Heat transfer effects on carbon nanotubes suspended nanofluid flow in a channel with non-parallel walls under the effect of velocity slip boundary condition: a numerical study , 2015, Neural Computing and Applications.

[10]  Z. Ziabakhsh,et al.  Homotopy Analysis Solution of Micro-Polar Flow in a Porous Channel with High Mass Transfer , 2008 .

[11]  Saeid Abbasbandy,et al.  Heat flux performance in a porous medium embedded Maxwell fluid flow over a vertically stretched plate due to heat absorption , 2016 .

[12]  A. Eringen,et al.  THEORY OF MICROPOLAR FLUIDS , 1966 .

[13]  O. Abdulaziz,et al.  Homotopy analysis method for fully developed MHD micropolar fluid flow between vertical porous plates , 2009 .

[14]  T. Ariman,et al.  Microcontinuum fluid mechanics—A review , 1973 .

[15]  Syed Tauseef Mohyud-Din,et al.  Magnetohydrodynamic Flow and Heat Transfer of Nanofluids in Stretchable Convergent/Divergent Channels , 2015 .

[16]  E. Grulke,et al.  Anomalous thermal conductivity enhancement in nanotube suspensions , 2001 .

[17]  M. G. Reddy.  Influence of Magnetohydrodynamic and Thermal Radiation Boundary Layer Flow of a Nanofluid Past a Stretching Sheet , 2014 .

[18]  A. Cemal Eringen,et al.  Theory of thermomicrofluids , 1972 .

[19]  Oluwole Daniel Makinde,et al.  Hermite-Padé approximation approach to MHD Jeffery-Hamel flows , 2006, Appl. Math. Comput..

[20]  Rama Bhargava,et al.  Finite element solution of micropolar fluid flow and heat transfer between two porous discs , 2000 .

[21]  Naveed Ahmed,et al.  Nonlinear radiation effects on MHD flow of nanofluid over a nonlinearly stretching/shrinking wedge , 2017, Neural Computing and Applications.

[22]  Sohail Nadeem,et al.  Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet , 2015 .

[23]  Davood Domiri Ganji,et al.  Investigation of squeezing unsteady nanofluid flow using ADM , 2013 .

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

[25]  A. Cemal Eringen,et al.  NONLINEAR THEORY OF SIMPLE MICRO-ELASTIC SOLIDS-I , 1964 .

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

[27]  Zulfiqar Ali Zaidi,et al.  On heat and mass transfer analysis for the flow of a nanofluid between rotating parallel plates , 2015 .

[28]  K. S. Syed,et al.  Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel , 2009 .

[29]  Liancun Zheng,et al.  The flow of a micropolar fluid through a porous channel with expanding or contracting walls , 2011 .

[30]  Neil A. Kelson,et al.  Micropolar flow over a porous stretching sheet with strong suction or injection , 2001 .

[31]  Shijun Liao,et al.  On the homotopy analysis method for nonlinear problems , 2004, Appl. Math. Comput..

[32]  R. Ellahi,et al.  Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid , 2015 .

[33]  Mohammad Mehdi Rashidi,et al.  Heat and Mass Transfer of a Micropolar Fluid in a Porous Channel , 2014 .

[34]  Naveed Ahmed,et al.  Heat and mass transfer analysis for MHD flow of nanofluid inconvergent/divergent channels with stretchable walls using Buongiorno’s model , 2017, Neural Computing and Applications.

[35]  Zulfiqar Ali Zaidi,et al.  MHD squeezing flow between two infinite plates , 2014 .

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

[37]  D. Srinivasacharya,et al.  Unsteady stokes flow of micropolar fluid between two parallel porous plates , 2001 .