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Heat transfer enhancement of ferrofluid flow within a wavy channel by applying a non-uniform magnetic field

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Abstract

This paper presents the effects of a non-uniform magnetic field on the hydrodynamic and thermal behavior of ferrofluid flow in a wavy channel by 3D numerical simulation. The wavy surfaces at the top and bottom of the channel are heated by constant heat fluxes. Moreover, the sidewalls are adiabatic. In the wavy section, in the perpendicular direction of the main flow, the magnetic field that linearly varies along the direction of the main flow is applied. The mathematical model that is consistent with the principles of ferrohydrodynamics and magnetohydrodynamics is used for the problem formulation. The results indicate that the wavy wall enhances the heat transfer rate on the bottom of the channel in comparison with the plain wall, while it does not have any significant effect on the top wall where the natural convection is weak. Furthermore, it can be found that the influence of the magnetic field on the flow field and heat transfer in the channel with the wavy walls is greater than one for the channel with the plain walls. This is due to the elimination of the recirculation zones in the sinusoidal cavities of the wavy walls by applying the magnetic field. The rise of the magnetic gradient value from 0 to 1.5 × 105 increases the skin-friction factors on the top and bottom wavy walls by factors of 11 and 1.6, respectively. In addition, it changes the Nusselt number 40% and 300% for the bottom and top walls, respectively.

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Abbreviations

a :

x–y Cross-section side of channel (m)

B :

Magnetic field induction (T)

C f :

Skin-friction coefficient (\(\tau_{\text{w}} /1/2\rho_{\text{nf}} W_{0}^{2}\))

c p :

Specific heat at constant pressure (J kg−1 K)

d :

Particle diameter (m)

g :

Gravitational acceleration (m s−2)

G :

Magnetic field gradient (A m−2)

Gr :

Grashof number (\(g\beta_{\text{nf}} q^{\prime \prime } \rho_{\text{nf}}^{2} a^{4} /k_{\text{nf}} \mu_{\text{nf}}^{2}\))

h :

Heat transfer coefficient (W m−2K)

H :

Magnetic field intensity (A m−1)

J :

Electric current density (A m−2)

k :

Thermal conductivity (W m−1 K)

k B :

Boltzmann constant (= 1.3806503 × 10−23 J K−1)

L :

Langevin function

m :

Particle magnetic moment (A m−2)

M :

Magnetization (A m−1)

M s :

Saturation magnetization (A m−1)

Nu :

Nusselt number (\({{ha} \mathord{\left/ {\vphantom {{ha} {k_{\text{nf}} = q^{{\prime \prime }} a/k_{\text{nf}} (T_{\text{wall}} - T_{\text{bulk}} )}}} \right. \kern-0pt} {k_{\text{nf}} = q^{{\prime \prime }} a/k_{\text{nf}} (T_{\text{wall}} - T_{\text{bulk}} )}}\))

P :

Pressure (Pa)

q″:

Heat flux (W m−2)

Re :

Reynolds number (\({{\rho_{\text{nf}} W_{0} a} \mathord{\left/ {\vphantom {{\rho_{\text{nf}} W_{0} a} {\mu_{\text{nf}} }}} \right. \kern-0pt} {\mu_{\text{nf}} }}\))

T :

Temperature (K)

T 0 :

Inlet flow temperature (K)

V = (u, v, w):

Velocity field (m s−1)

W 0 :

Inlet velocity (m s−1)

X :

Axis in Cartesian coordinates

Y :

Axis in Cartesian coordinates

Z :

Axis in Cartesian coordinates

β :

Thermal expansion coefficient (1 K−1)

μ :

Dynamic viscosity (kg m−1 s)

μ 0 :

Magnetic permeability of vacuum (= 4π × 10−7 Tm A−1)

μ B :

Bohr magneton (= 9.27 × 10−24 A m−2)

ξ :

Langevin parameter

ρ :

Density (kg m−3)

σ :

Electrical conductivity (s m−1)

τ w :

Wall shear stress (Pa)

ϕ :

Particles volume fraction

f:

Base fluid

nf:

Nanofluid

p:

Particle

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

    S. Morteza Mousavi, Mousa Farhadi & Hamid Hassanzadeh Afrouzi

  2. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Mohit Biglarian

  3. Department of Mechanical Engineering, University of Mazandaran, Babolsar, Iran

    A. Ali Rabienataj Darzi

  4. Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch, Khomeinishahr, 84175-119, Iran

    Davood Toghraie

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  1. S. Morteza Mousavi
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Mousavi, S.M., Biglarian, M., Darzi, A.A.R. et al. Heat transfer enhancement of ferrofluid flow within a wavy channel by applying a non-uniform magnetic field. J Therm Anal Calorim 139, 3331–3343 (2020). https://doi.org/10.1007/s10973-019-08650-6

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