Finite element simulation of unsteady magneto-hydrodynamic transport phenomena on a stretching sheet in a rotating nanofluid

Abstract

This study examines theoretically and computationally the transient magneto-hydrodynamic boundary layer flow and heat transfer in an incompressible rotating nanofluid over a stretching continuous sheet, with a transverse magnetic field applied normal to the sheet plane. The three-dimensional conservation equations for mass, momentum, energy and species (nanoparticle) diffusion, are normalized into a system of two-dimensional dimensionless boundary layer equations, using appropriate scaling transformations. The resulting nanofluid transport model incorporates a Brownian motion parameter, thermophoresis parameter, rotation parameter, unsteady parameter, Prandtl number, Hartmann magnetic parameter and Lewis number, and physically realistic boundary conditions at the sheet surface and in the free stream. The nonlinear two-point boundary value problem is solved using a robust, efficient finite element method based on the variational formulation. A detailed evaluation of the effects of the governing physical parameters on the velocity components, temperature and nanoparticle concentration via graphical plots is conducted. Primary velocity is strongly retarded with increasing Hartmann number and there is also a reduction in secondary velocity magnitude. Both temperature and nanoparticle concentration are positively affected by the Hartmann number. Increasing rotational parameter decreases both primary and secondary velocity, and also depresses temperature and nanoparticle concentration. Unsteadiness parameter is generally found to enhance primary velocity and temperatures but exhibits a varied influence on secondary velocity and nanoparticle concentration. The reduced Nusselt number (wall temperature gradient) is observed to be depressed with both Brownian motion and thermophoresis effects, whereas the contrary behaviour is computed for the reduced Sherwood number (wall mass transfer gradient). The reduced Nusselt number and the Sherwood number also show a steady decrease with increasing rotational parameter. The present finite element method solutions have been validated extensively with the previously published results, demonstrating excellent correlation. The study has important applications in the manufacture and electromagnetic control of complex magnetic nanofluid materials of relevance to biomedical, energy systems and aerospace systems technologies.

Group analysis and numerical computation of magneto-convective non-Newtonian nanofluid slip flow from a permeable stretching sheet

“…With greater injection, the momentum boost results in a reduction in momentum boundary layer thickness. These computations concur with many previous studies in transpiring boundary layer flows of nanofluids (Rashidi et al 2013;Goyal and Bhargava 2013;Rana et al 2013b;Ferdows et al 2013;Hamad et al 2011). The case of the impervious sheet, i.e., solid wall (fw = 0) naturally falls between the injection and suction cases.…”

“…Clearly for the non-conducting case, temperatures will be minimized as magnetic field will vanish. Moreover for the pseudoplastic nanofluid case, temperatures are the highest achieved with the infliction of a magnetic field, and evidently this is beneficial in the synthesis of electro-conductive nanopolymers, as highlighted in the recent theoretical studies by Rana et al (2013b), Ferdows et al (2013), and further emphasized in the experimental study of Crainic et al (2003). Figure 4a-c depict the evolution of temperature fields with a variation in thermophoresis number (Nt), Brownian motion parameter (Nb) and Prandtl number (Pr), respectively, in all cases for both Newtonian and pseudoplastic nanofluids.…”

“…Such fluids offer many rich problems for mathematical modeling since they amalgamate nanofluid dynamics with the established field of magnetohydrodynamics (MHD). Finite element simulations of the heat and mass transfer characteristics of transient magneto-nanofluid flows in rotating manufacturing processes were reported by Rana et al (2013b). Ferdows et al (2013) used Maple software to study the effects of radiative heat transfer on unsteady MHD nanofluid transport from a stretching surface in high-temperature materials processing.…”

Explicit numerical study of unsteady hydromagnetic mixed convective nanofluid flow from an exponentially stretching sheet in porous media

“…analyzed numerically the thermal radiative flux effects on hydromagnetic nanofluid boundary layer flow from a stretching surface. Recently Rana et al (2013) studied using a finite element technique, the transient magnetohydrodynamic boundary layer flow in an incompressible rotating nanofluid over a stretching continuous sheet, showing that both Brownian motion and thermophoresis enhance wall mass transfer rates (Sherwood number). Very recently Abbasbandy and Ghehsareh (2012) used the Hankel-Padé expansion method to study nanofluid hydromagnetic boundary-layer flows.…”

Homotopy Simulation of Nonlinear Unsteady Rotating Nanofluid Flow from a Spinning Body

“…Computational rotating nanofluid dynamics has recently attracted some interest, since the deployment of nanofluids in revolving chemical engineering devices offers significant improvements over existing designs. Rana et al [35] used a variational finite element algorithm to study unsteady magnetonanofluid transport from a rotating stretching continuous sheet. They showed that greater rotational parameter reduces primary and secondary velocities, temperature, and nanoparticle concentration.…”