Magnetohydrodynamic Boundary Layer Flow of Nanofluid over an Exponentially Stretching Permeable Sheet

Abstract

A mathematical model of the steady boundary layer flow of nanofluid due to an exponentially permeable stretching sheet with external magnetic field is presented. In the model, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, the wall mass transfer parameter, the Prandtl number, the Lewis number, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction. The magnetic field makes enhancement in temperature and nanoparticle volume fraction, whereas the wall mass transfer through the porous sheet causes reduction of both. For the Brownian motion, the temperature increases and the nanoparticle volume fraction decreases. Heat transfer rate becomes low with increase of Lewis number. For thermophoresis effect, the thermal boundary layer thickness becomes larger.

A numerical study of magnetohydrodynamic transport of nanofluids over a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects

“…This elevates thermal boundary layer thickness. This pattern has been computed by many other researchers for both nanofluid magnetohydrodynamics [51] and also classical viscous Newtonian magnetohydrodynamics [52]. Figs.…”

Does mathematics contribute to the nanofluid debate?

“…They have a high number of citations and consequently a plethora of papers follow employing similar reductions and the same basic form of heat and nanoparticle concentration equation. These extensions and modifications include magnetohydrodynamic effects; radiative heat flux in the heat equation; permeable substrates; heat generation/absorption; non-Newtonian fluids; flow in a cylindrical geometry; flow in a cylindrical geometry embedded in a porous medium; a permeable cone in a porous media; various far-field flow configurations; nanofluids with micro-organisms, see [8,22,25,52,55,56,59,65]. Simply for the stretching sheet model there are studies with sheets moving at a constant rate, with velocity proportional to distance x; proportional to x n ; proportional to x/t (and then with a substrate temperature proportional to x/t 2 ); exponentially increasing [8,12,23,54,57].…”

Homogeneous-heterogeneous reactions in the stagnation point flow of carbon nanotubes with Newtonian heating

“…Behavior of magnetohydrodynamic flow of nanofluid over a permeable exponentially stretching sheet was presented by Bhattacharyya and Layek. 4 Turkyilmazoglu 5 examined unsteady boundary layer flow of nanofluid over vertical flat plate. Mustafa et al 6 investigated the boundary layer unsteady flow of nanofluid past an impulsively stretching sheet.…”