Modeling and numerical simulation of micropolar fluid over a curved surface: Keller box method

BACKGROUND This paper examines the flow behavior of micropolar liquid over a curved surface. MHD fluid is considered. The surface inducing the fluid motion has a prescribed temperature different from the ambient fluid moreover the heat transfer mechanism is investigated. Curvilinear coordinates are used for the mathematical formulation of the flow equation. Similarity variables are derived and are utilized to alter the governing expressions for the flow of momentum and heat transfer characteristic. METHOD The resulting non-linear ODEs are resolved systematically by two numerically approaches namely; the Keller box method and the shooting method. RESULTS The numerical results for the temperature and velocity fields has been presented through tables and graphs against the independent parameters and non-dimensional numbers i.e., material parameter, power law index, radius of curvature, magnetic parameter, Prandtl and Eckert numbers, skin friction (drag force) and Nusselt number. Physical explanation of the graph presented is given to understand the performance of fluid flow and heat transport phenomena in different emerging situation. CONCLUSION The main outcomes in the presence of various flow variables on the skin friction velocity, Nusselt number, temperature are highlighted via graphical sketch and Tables. Velocity field displays a decreasing trend with magnetic parameter, power law index and radius of curvature of the stretching velocity whereas, opposite behavior observed for the material parameter. Near the surface curvature and magnetic parameter shows an enhancement in microrotation profile whereas, it shows reverse behavior when it is far away. Material parameter increases for large values of microrotation profile on the other hand power-law index decreases for large values. For higher values magnetic parameter, radius of curvature and Eckert number temperature profile increases. But temperature reduces subject to material parameter and Prandtl number.

[1]  M. Waqas,et al.  Simulation of revised nanofluid model in the stagnation region of cross fluid by expanding-contracting cylinder , 2019, International Journal of Numerical Methods for Heat & Fluid Flow.

[2]  S. S. Chawla.  Boundary layer growth of a micropolar fluid , 1972 .

[3]  P. Siddheshwar,et al.  Magnetoconvection in a micropolar fluid , 1998 .

[4]  Tasawar Hayat,et al.  MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface , 2009 .

[5]  Tasawar Hayat,et al.  Entropy generation for flow of Sisko fluid due to rotating disk , 2018, Journal of Molecular Liquids.

[6]  R. Gorla,et al.  Flow and heat transfer from a continuous surface in a parallel free stream of micropolar fluid , 1987 .

[7]  N. Ali,et al.  Flow of a micropolar fluid over a curved stretching surface , 2011 .

[8]  Mustafa Turkyilmazoglu,et al.  Fully developed slip flow in a concentric annuli via single and dual phase nanofluids models , 2019, Comput. Methods Programs Biomed..

[9]  S. Asghar,et al.  Flow of viscous fluid along an exponentially stretching curved surface , 2017 .

[10]  Tasawar Hayat,et al.  Optimization of entropy generation and dissipative nonlinear radiative Von Karman's swirling flow with Soret and Dufour effects , 2018 .

[11]  Satyaranjan Mishra,et al.  Numerical investigation on heat and mass transfer effect of micropolar fluid over a stretching sheet through porous media , 2015 .

[12]  R. Gorla,et al.  Effects of transverse magnetic field on mixed convection in a micropolar fluid on a horizontal plate with vectored mass transfer , 1996 .

[13]  Ahmed Alsaedi,et al.  A comparative study of Casson fluid with homogeneous-heterogeneous reactions. , 2017, Journal of colloid and interface science.

[14]  M. Waqas,et al.  A mathematical and computational framework for heat transfer analysis of ferromagnetic non-Newtonian liquid subjected to heterogeneous and homogeneous reactions , 2020 .

[15]  M. Rahman,et al.  Heat Transfer in a Micropolar Fluid along a Non-linear Stretching Sheet with a Temperature-Dependent Viscosity and Variable Surface Temperature , 2009 .

[16]  Ioan Pop,et al.  Unsteady boundary layer flow over a permeable curved stretching/shrinking surface , 2015 .

[17]  Siti Hidayah Muhad Saleh,et al.  Unsteady Micropolar Fluid over a Permeable Curved Stretching Shrinking Surface , 2017 .

[18]  Ahmed Alsaedi,et al.  Homogeneous-heterogeneous reactions in MHD flow of micropolar fluid by a curved stretching surface , 2017, Journal of Molecular Liquids.

[19]  D. Pal,et al.  HEAT AND MASS TRANSFER IN MHD NON-DARCIAN FLOW OF A MICROPOLAR FLUID OVER A STRETCHING SHEET EMBEDDED IN A POROUS MEDIA WITH NON-UNIFORM HEAT SOURCE AND THERMAL RADIATION , 2010 .

[20]  Muhammad Sajid,et al.  MHD FLOW OF MICRO POLAR FLUID DUE TO A CURVED STRETCHING SHEET WITH THERMAL RADIATION , 2016 .

[21]  M. Turkyilmazoglu.  A note on micropolar fluid flow and heat transfer over a porous shrinking sheet , 2014 .

[22]  F. Ebert.  A similarity solution for the boundary layer flow of a polar fluid , 1973 .

[23]  I. Pop,et al.  Heat transfer over a stretching surface with variable heat flux in micropolar fluids , 2008 .

[24]  A. A. Bakr.  Effects of chemical reaction on MHD free convection and mass transfer flow of a micropolar fluid with oscillatory plate velocity and constant heat source in a rotating frame of reference , 2011 .

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

[26]  Ioan Pop,et al.  Stagnation point flow of a micropolar fluid towards a stretching sheet , 2004 .

[27]  Kai-Long Hsiao,et al.  To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-Nanofluid with parameters control method , 2017 .

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

[29]  Sharidan Shafie,et al.  Unsteady MHD mixed convection flow of a micropolar fluid along an inclined stretching plate , 2013 .

[30]  Flow and heat transfer in the boundary layer of a micropolar fluid on a continuous moving surface , 1999 .

[31]  S. Asghar,et al.  Flow of viscous fluid along a nonlinearly stretching curved surface , 2017 .

[32]  Kai-Long Hsiao,et al.  Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects , 2017 .

[33]  Ahmed Alsaedi,et al.  Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition , 2016 .

[34]  M. Turkyilmazoglu.  A Note on the Correspondence Between Certain Nanofluid Flows and Standard Fluid Flows , 2015 .

[35]  A. Alsaedi,et al.  Entropy optimization and quartic autocatalysis in MHD chemically reactive stagnation point flow of Sisko nanomaterial , 2018, International Journal of Heat and Mass Transfer.

[36]  Nabil T. Eldabe,et al.  Chebyshev finite difference method for heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation , 2006, Appl. Math. Comput..

[37]  H. Takhar,et al.  Flow of micropolar fluid past a continuously moving plate , 1983 .

[38]  Nasir Ali,et al.  Stretching a Curved Surface in a Viscous Fluid , 2010 .

[39]  Grzegorz Lukaszewicz,et al.  Micropolar Fluids: Theory and Applications , 1998 .