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Magnetohydrodynamic Micropolar Nanofluid Flow in a Shrinking Channel with Second-Order Velocity Slip and Thermal Radiation

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Abstract

Magnetohydrodynamic (MHD) micropolar nanofluid flow in a shrinking channel is important due to its use in metallurgical processes, manufacturing industries and industrial applications. In this study, the flow and heat transfer of an electrically conducting micropolar nanofluid passing through a shrinking channel is investigated with the effects of second-order velocity slip conditions and thermal radiation. Using the similarity transformations, the governing dimensional equations were transformed into ordinary differential equations, which have been solved by the finite difference method. The results for skin friction coefficient (Rex1/2Cfx), couple stress (mx), and local Nusselt number (Rex−1/2Nufx), as well as flow profiles were presented graphically with variations of material constant (K), volume fraction of alumina nanoparticles (φ), micro-rotation parameter (n), second-order slip parameter (B), first-order slip parameter (A), magnetic parameter (M), suction parameter (S), and radiation parameter (R). The influences of φ, K, n, A, M, and S were significant. With higher K, A, n, and M, Rex1/2Cfx and Rex−1/2Nufx increased. On the other hand, an increase in S caused a decrease in Rex1/2Cfx and an increase in Rex−1/2Nufx. In the case of higher A and M, velocity increased, but angular velocity decreased. However, the converse was observed for the increase in φ and S. It is worth noting that the boundary layer separation was delayed for increasing values of K, n, A, and M, but accelerated for higher φ, B, and S.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

a :

Positive constant

A :

First-order velocity slip parameter

B :

Second-order velocity slip parameter

B 0 :

Strength of magnetic field (kg s−2 A−1)

c p :

Heat capacity (J Kg−1 K−1)

C fx :

Skin friction coefficient

h :

Distance between bottom and top wall (m)

j :

Micro-inertia density

k :

Thermal conductivity (W m−1 K−1)

K :

Material parameter

M :

Magnetic field parameter

MHD:

Magnetohydrodynamic

n :

Micro-rotation parameter

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{N}\) :

Micro-rotation component

Pr:

Prandtl number

S :

Suction parameter

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{T}\) :

Temperature (K)

T c :

Top wall temperature (K)

T h :

Bottom wall temperature (K)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{u} ,\,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{v}\) :

Velocity component (m s−1)

u e :

Local edge velocity (m s−1)

u w :

Stretched velocity (m s−1)

v w :

Mass flux through the wall

ν 0 :

Constant mass flux velocity (m s−1)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{x}\), \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{y}\) :

Cartesian coordinates (m)

α :

Thermal diffusivity (m2 s−1)

β :

Coefficient of thermal expansion (K–1)

Γ:

Micro-inertia parameter

∆:

Surface temperature parameter

θ :

Dimensionless temperature

κ :

Vortex viscosity

μ :

Absolute viscosity (Ns m−2)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

σ :

Electrical conductivity (A2 s3 kg−1 m−2)

σ c :

Stefan–Boltzmann constant

φ :

Volume fraction

(′):

Differentiation with respect to η

f :

Base fluid

nf :

Nanofluid

s :

Nanoparticles

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Authors and Affiliations

  1. Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

    Nepal Chandra Roy & Ayantika Ghosh

  2. Department of Applied Mathematics, Babeş-Bolyai University, Cluj-Napoca, Romania

    Ioan Pop

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Roy, N.C., Ghosh, A. & Pop, I. Magnetohydrodynamic Micropolar Nanofluid Flow in a Shrinking Channel with Second-Order Velocity Slip and Thermal Radiation. Arab J Sci Eng 49, 1955–1967 (2024). https://doi.org/10.1007/s13369-023-08011-4

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