Dual solutions of a micropolar nanofluid flow with radiative heat mass transfer over stretching/shrinking sheet using spectral quasilinearization method

Purpose The purpose of this paper is to focus on the application of Chebyshev spectral collocation methodology with Gauss Lobatto grid points to micropolar fluid over a stretching or shrinking surface. Radiation, thermophoresis and nanoparticle Brownian motion are considered. The results have attainable scientific and technological applications in systems involving stretchable materials. Design/methodology/approach The model equations governing the flow are transformed into non-linear ordinary differential equations which are then reworked into linear form using the Newton-based quasilinearization method (SQLM). Spectral collocation is then used to solve the resulting linearised system of equations. Findings The validity of the model is established using error analysis. The velocity, temperature, micro-rotation, skin friction and couple stress parameters are conferred diagrammatically and analysed in detail. Originality/value The study obtains numerical explanations for rapidly convergent solutions using the spectral quasilinearization method. Convergence of the numerical solutions was monitored using the residual error analysis. The influence of radiation, heat and mass parameters on the flow are depicted graphically and analysed. The study is an extension on the work by Zheng et al. (2012) and therefore the novelty is that the authors tend to take into account nanoparticles, Brownian motion and thermophoresis in the flow of a micropolar fluid.

[1]  Kai-Long Hsiao,et al.  Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature , 2017 .

[2]  I. Pop,et al.  Dual solutions in mixed convection boundary layer flow of micropolar fluids , 2009 .

[3]  Precious Sibanda,et al.  Dual solutions for three-dimensional magnetohydrodynamic nanofluid flow with entropy generation , 2019, J. Comput. Des. Eng..

[4]  Aurangzaib,et al.  Micropolar fluid flow and heat transfer over an exponentially permeable shrinking sheet , 2016 .

[5]  Sandile Sydney Motsa,et al.  Numerical simulation of couple stress nanofluid flow in magneto-porous medium with thermal radiation and a chemical reaction , 2018, Appl. Math. Comput..

[6]  Ioan Pop,et al.  Dual solutions in a thermal diffusive flow over a stretching sheet with variable thickness , 2013 .

[7]  O. Bég,et al.  Heat and Mass Transfer of Nanofluid from Horizontal Cylinder to Micropolar Fluid , 2015 .

[8]  Chunlei Liang,et al.  Theory and simulation of micropolar fluid dynamics , 2010 .

[9]  M. Ali,et al.  On thermal boundary layer on a power-law stretched surface with suction or injection , 1995 .

[10]  Sandile S. Motsa,et al.  Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems , 2014 .

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

[12]  G. N. Sekhar,et al.  MHD Flow and Heat Transfer of an Exponential Stretching Sheet in a Boussinesq-Stokes Suspension , 2014 .

[13]  S. Liao.  A new branch of solutions of boundary-layer flows over an impermeable stretched plate , 2005 .

[14]  Sujata Mishra,et al.  Chemical reaction and Soret effects on hydromagnetic micropolar fluid along a stretching sheet , 2016 .

[15]  Hashim,et al.  Thermal radiation effects on Williamson fluid flow due to an expanding/contracting cylinder with nanomaterials: Dual solutions , 2018, Physics Letters A.

[16]  N. Sandeep,et al.  Transpiration effect on stagnation-point flow of a Carreau nanofluid in the presence of thermophoresis and Brownian motion , 2016 .

[17]  A. Raptis.  Flow of a micropolar fluid past a continuously moving plate by the presence of radiation , 1998 .

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

[19]  Nazar Roslinda,et al.  Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation , 2009 .

[20]  S Nadeem,et al.  Boundary Layer Flow of Second Grade Fluid in a Cylinder with Heat Transfer , 2012 .

[21]  Shijun Liao,et al.  A new branch of solutions of boundary-layer flows over a permeable stretching plate , 2007 .

[22]  MHD effects on micropolar nanofluid flow over a radiative stretching surface with thermal conductivity , 2016 .

[23]  S Nadeem,et al.  Axisymmetric Stagnation Flow of a Micropolar Nanofluid in a Moving Cylinder , 2012 .

[24]  Hiranmoy Mondal,et al.  Effects of Soret Dufour, chemical reaction and thermal radiation on MHD non-Darcy unsteady mixed convective heat and mass transfer over a stretching sheet , 2011 .

[25]  S Nadeem,et al.  Model-based analysis of micropolar nanofluid flow over a stretching surface , 2014 .

[26]  Jiajia Niu,et al.  Dual solutions for flow and radiative heat transfer of a micropolar fluid over stretching/shrinking sheet , 2012 .

[27]  Poulomi De,et al.  Dual solutions of heat and mass transfer of nanofluid over a stretching/shrinking sheet with thermal radiation , 2016 .

[28]  Anuar Mohd Ishak,et al.  MHD boundary layer flow due to an exponentially stretching sheet with radiation effect , 2011 .

[29]  S. Motsa,et al.  An Unsteady Magnetohydrodynamic Jeffery Nanofluid Flow Over a Shrinking Sheet with Thermal Radiation and Convective Boundary Condition Using Spectral Quasilinearisation Method , 2016 .

[30]  D. Srinivasacharya,et al.  Numerical study of mixed convection flow of a micropolar fluid towards permeable vertical plate with convective boundary condition , 2015 .

[31]  P. Rana,et al.  Multiple solutions of MHD boundary layer flow and heat transfer behavior of nanofluids induced by a power-law stretching/shrinking permeable sheet with viscous dissipation , 2015 .

[32]  P. K. Kameswaran,et al.  Dual solutions of Casson fluid flow over a stretching or shrinking sheet , 2014 .

[33]  Stanford Shateyi,et al.  On a new quasi‐linearization method for systems of nonlinear boundary value problems , 2011 .

[34]  S. Nadeem,et al.  Mixed Convection Heat Transfer in Micropolar Nanofluid over a Vertical Slender Cylinder , 2012 .

[35]  S. Liao,et al.  A new branch of the temperature distribution of boundary-layer flows over an impermeable stretching plate , 2008 .

[36]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow , 1961 .