Finite element numerical technique for magneto-micropolar nanofluid flow filled with chemically reactive casson fluid between parallel plates subjected to rotatory system with electrical and Hall currents

ABSTRACT

Steady electro-magnetohydrodynamic flow of a micropolar nanofluid in the attendance of reactive Casson fluid passing through parallel plates influenced by the rotating system with the implementation of Buongiorno nanofluid model is examined in this study. The momentum transport equation is enhanced by incorporating the electric field. In addition, the influence of reactive species has a vital role that is affecting the flow phenomenon in conjunction with a transverse magnetic field. The physical flow problem is modeled in the form of partial differential equations which are then transformed into nonlinear ordinary differential equations by using appropriate similarity functions and then solved numerically by the usage of the finite element method and procured results are visualized graphically. The outcomes for flow rate, microrotation, temperature, concentration, and engineering quantities distributions are shown in terms of graphical presentation. Momentum and angular momentum transport progressively in nature as the Casson parameter grows. Opposite results of microrotational profiles are found for electric currents in comparison with Hall currents. Both thermophoresis and Brownian motion are found to be significant effects in improving heat transportation phenomena in nanofluids. The existing available literature was utilized to test for validation of the numerical findings.

KEYWORDS:

• Micropolar nanofluid
• Casson fluid
• electric field
• reactive species
• rotating parallel plates
• FEM

Nomenclature

$B_0$ magnetic field strength [Newton-meters per ampere (Nm/A), i.e. Teslas (T)]

$C$ concentration of the solute [mol m^–3]$mol{m}^{-3}$]

$C_f$ skin friction coefficient

$C_p$ specific heat at constant pressure [J kg^–1 K^–1]$JK{g}^{-1}{K}^{-1}$

$C_0$ lower plate concentration [mol m^–3]$mol{m}^{-3}$

$C_h$ upper plate concentration [mol m^–3]$mol{m}^{-3}$

$d$ distance between the plates [m]$m$

$D_B$ coefficient of Brownian diffusion

$D_T$ coefficient of thermophoresis diffusion

$E$ dimensionless electric field parameter

$E_0$ electric field intensity [NC^–1]$N{C}^{-1}$

$j$ micro inertia per unit mass [m²]$m^2$

$J_w$ mass flux

$k$vertex viscosity [m Pa]$mPa$

$k_1$ mean absorption coefficient [m^–1]$m^{-1}$

$k^{\ast }$ boundary parameter

$K_1$ coupling parameter

$K_2$ spin gradient viscosity parameter [kg ms^–1]$kgm{s}^{-1}$

$K_3$ material (micropolar) parameter

$Kr$ rotation parameter

$m$ Hall parameter

$M$ magnetic field parameter

$Nb$ Brownian motion parameter

$Nt$ thermophoresis parameter

$Nu$ Nusselt number

$Pr$ Prandtl number

$q_r$ radiative heat flux [W m^–2] $W{m}^{-2}$

$Q_w$ heat flux [W m^–2]$W{m}^{-2}$

$R$ radiation parameter

$Re$ viscosity parameter

${Re}_x$ local Reynolds number

$Sc$ Schmidt number

$Sh$ Sherwood number

$T$ temperature of the field in the boundary layer [K]$K$

$T_0$ lower plate temperature [K]$K$

$T_h$ upper plate temperature [K]$K$

$u$ velocity component in x-direction [m s^–1]$m{s}^{-1}$

$u_w$ stretching velocity [m s^–1]$m{s}^{-1}$

$v$ velocity component in y-direction [m s^–1]$m{s}^{-1}$

$x,y,z$ components

Greek symbols

$\alpha$ thermal diffusivity [m² s^–1]$m^2{s}^{-1}$

$\beta$ Casson parameter

$\mu$ dynamic viscosity [m Pa]$mPa$

${\mu }_B$ dynamic viscosity [m Pa]$mPa$

$\nu$ kinematic viscosity [m² s^–1]$m^2{s}^{-1}$

${\rho }_f$ density of base fluid [kg m^–3]$kg{m}^{-3}$

$\sigma$ electrical conductivity of the fluid [S m^–1]$S{m}^{-1}$

${\sigma }_1$ Stefan–Boltzmann constant [W m^–2 K^–4]$W{m}^{-2}{K}^{-4}$

$\theta$ dimensionless temperature

${\tau }_e$ electron collision rate

${\tau }^{\ast }$ ratio of nanoparticle and effective heat capacity

$\phi$ dimensionless concentration

$\eta$ similarity variable

$\gamma$ chemical reaction parameter

$\mathrm{\Omega }$ angular velocity [m s^–1]$m{s}^{-1}$

$\omega$ dimensionless angular velocity component

${\omega }_e$ cyclotron frequency

Acknowledgments

The authors express their sincere gratitude to the editor and reviewers for their suggestions which have improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

MD. Shamshuddin

Dr. MD. Shamshuddin has completed his Masters in Mathematics from Osmania University in the year 2002; and also completed his M. Phil from Sri Venkateswara University in the year 2010. He received his prestigious PhD degree in Applied Mathematics at GITAM Deemed to be University, Andhra Pradesh in the year 2019. He has published more than 80 International repute articles through various journals and Conferences. Currently, his research interest is in fluid mechanics, magnetofluid dynamics, micropolar fluid, nanofluid and hybrid nanofluids and heat and mass transfer with its applications. He is a seasoned researcher with strong mentality and sound analytical mind, and he has contributed tremendously in his core areas of research. He has reviewed several research articles for many journals and publishers.

W. Ibrahim

Prof. Wubshet Ibrahim has obtained his MSc. Degree from Addis Ababa university, Ethiopia in 2005 and his PhD degree from Osmania university Hyderabad, India in 2012. He has published more than 70 articles on reputable international journals. His area of research includes computational fluid dynamics, Nanofluids, heat and mass transfer, Finite difference method, finite element method. He served as academic editor for mathematical problems in engineering (Hindawi). Also, he reviewed different articles for different reputable International Journals.