Water-based ferrofluid flow and heat transfer over a stretchable rotating disk under the influence of an alternating magnetic field

Abstract

Flow and heat transfer of water-based nanofluid over a stretchable rotating disk under the influence of an alternating magnetic field is investigated. The external magnetic field creates a hindrance in the flow and depends on the frequency of the alternating magnetic field. The frequency of an alternating magnetic field can increase or decrease the viscosity of the magnetic fluid in the flow. A set of nonlinear differential equations in the present theoretical model is solved numerically using the finite element method. Volume concentration, frequency of the alternating magnetic field, magnetic polarization force, and Prandtl number play an important role in the velocity and temperature distributions of iron/water nanofluid. A comparative study for velocity and heat transfer is presented for iron/water, nickel/water, and cobalt/water ferromagnetic nanofluid. The rotational viscosity enhances the heat transfer in nanofluid provided the magnetic field should be stationary.

Heat transfer and hybrid ferrofluid flow over a nonlinearly stretchable rotating disk under the influence of an alternating magnetic field

“…is the root mean square value of the H 0 cos ω 0 t and α 0 is the magnetic field's phase angle with the magnetization. Taking into account the hydrodynamical vortex � = (0, 0, �) and the spinning magnetic field, magnetization's tangential components are as follow 75 :…”

“…The tangential component of magnetization is: if the field becomes linearly polarized along the radial direction Along the z-axis, the magnetic torque operates on the fluid as follows 75 :…”

“…In the limiting case ω 0 τ B → ∞ , the impact of rotating viscosity vanishes due to the nanoparticles in the fluid no longer sensing the magnetic field. The applied magnetic field has a scalar potential 75 The magnetic field components in radial and tangential directions can be written as 75 The intensity of the entire magnetic field can be calculated as follows 75 (12)…”

Unsteady ferrohydrodynamic flow and heat transfer over a rotating and vertical moving disc embedded in a porous medium with entropy generation

“…Magnetic fields are uniformly directed in radial and tangential directions. The following is the physical model for ferrohydrodynamic flow 31–33 where bold-italicW denotes the velocity, ρ denotes density, t denotes time, μ denotes the dynamic viscosity, k0 denotes the permeability of the porous medium, bold-italicfbold-italicm denotes the forces due to magnetic field, I Sum of the particles moment of inertia, bold-italicωbold-italicp denotes the angular velocity of particles, μ0 denotes the magnetic permeability of free space, bold-italicM denotes the magnetization, bold-italicH denotes the magnetic field intensity, τs denotes the rotational relaxation time, cp denotes the specific heat at constant pressure, T denotes the temperatur...…”

“…Magnetic fields are uniformly directed in radial and tangential directions. The following is the physical model for ferrohydrodynamic flow [31][32][33] = Á W ¼ 0…”