Abstract
Abstract A theoretical model is developed for steady magnetohydrodynamic viscous flow resulting from a moving semi-infinite flat plate in an electrically conducting nanofluid. Thermal radiation and magnetic induction effects are included in addition to thermal convective boundary conditions. Buongiorno’s two-component nanoscale model is deployed, which features Brownian motion and thermophoresis effects. The governing nonlinear boundary layer equations are converted to nonlinear ordinary differential equations by using suitable similarity transformations. The transformed system of differential equations is solved numerically, employing the spectral relaxation method (SRM) via the MATLAB R2018a software. SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation, and linearization for solving a nonlinear system of equations. Effects of embedded parameters such as sheet velocity parameter$\lambda$, magnetic field parameter$\beta$, Prandtl number$Pr$, magnetic Prandtl number$Prm$, thermal radiation parameter$Rd$, Lewis number$Le$, Brownian motion parameter$Nb$, and thermophoresis parameter$Nt$ on velocity, induced magnetic field, temperature, and nanoparticle concentration profiles are investigated. The skin-friction results, local Nusselt number, and Sherwood number are also discussed for various values of governing physical parameters. To show the convergence rate against iteration, residual error analysis has also been performed. The flow is strongly decelerated, and magnetic induction is suppressed with greater magnetic body force parameter, whereas temperature is elevated due to extra work expended as heat in dragging the magnetic nanofluid. Temperatures are also boosted with increment in nanoscale thermophoresis parameter and radiative parameter, whereas they are reduced with higher wall velocity, Brownian motion, and Prandtl numbers. Both hydrodynamic and magnetic boundary layer thicknesses are reduced with greater reciprocal values of the magnetic Prandtl number Prm. Nanoparticle (concentration) boundary layer thickness is boosted with higher values of thermophoresis and Prandtl number, whereas it is diminished with increasing wall velocity, nanoscale Brownian motion parameter, radiative parameter, and Lewis number. The simulations are relevant to electroconductive nanomaterial processing.
Highlights
Nanoscale colloidal suspensions containing solid nanoparticles and fibers are called nanofluids and were first introduced by Choi (1995). Choi et al (2001) showed that the addition of a small number of nanoparticles to conventional heat transfer liquids such as water, toluene, oil and ethylene glycol, etc. enhances the thermal conductivity of the original fluids
Extensive computations have been conducted in MATLAB, and spectral relaxation method (SRM) solutions are shown in Tables 2–4 and Figs 2–18
It is observed that the rate of heat transfers at the surface increases with more significant Prandtl number
Summary
Nanoscale colloidal suspensions containing solid nanoparticles and fibers are called nanofluids and were first introduced by Choi (1995). Choi et al (2001) showed that the addition of a small number of nanoparticles to conventional heat transfer liquids such as water, toluene, oil and ethylene glycol, etc. enhances the thermal conductivity of the original fluids. Daniel et al (2018) studied the combined effects of thermal stratification, applied magnetic field, and thermal radiation on a boundary layer flow of electrically conducting nanofluid over a nonlinear stretching sheet. A new model is presented for MHD induction convection flow of an electrically conducting nanofluid from a moving semi-infinite stretching surface with appreciable thermal radiative heat transfer. This constitutes the novelty of the present simulations, which for the first time use a spectral relaxation method (SRM) and combine properly electromagnetic induction, moving sheet velocity effects, nonlinear radiative flux. The simulations are relevant to multiphysical magnetic nanoliquid material processing (Ali et al, 2018)
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