Application of CNT-based micropolar hybrid nanofluid flow in the presence of Newtonian heating


This research addresses the effects of Hall and ion slip in micropolar hybrid nanofluid in the presence of Newtonian heating. Furthermore, the influence of thermal radiation, Darcy–Forchheimer, viscous dissipation, and variable viscosity is discussed. Total entropy generation rate is calculated. Two distinct nanoparticles such as (SWCNT, MWCNT) used as a hybrid nanofluid. Built-in function bvp4c integrates the solution of simulated hydrodynamic boundary value problems. The effects on axial velocity, angular velocity, temperature field, concentration field, Bejan number, and entropy optimization of different flow field variables are displayed graphically. The nanoparticle fraction boosts the temperature field, Bejan number, and entropy generation, while the axial velocity and microrotation field reduces. Furthermore, the entropy generation enhances with higher the Brinkman number and variable viscosity parameter.

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\({\text{Be}}\) :

Bejan number

\({C_{f}, C_{g}}\) :

Surface drag forces

\(D_{f}\) :

Diffusion coefficient

\(E_{c}\) :

Eckert number

f :

Dimensionless stream function

\(F^{**}\) :

Non-uniform inertia coefficient

\(F_{r}\) :

Inertia coefficient

\({\text{Ha}}\) :

Hartmann number

\(K\) :

Material parameter

\(K^{**}\) :

Permeability of porous medium

\(k^{*}\) :

Mean absorption coefficient

\(\Pr\) :

Prandtl number

\(N_{s} (\eta )\) :

Entropy generation

\(P_{m}\) :

Porosity parameter

\({\mathbf{q}}_{r}\) :

Thermal radiation flux

\({\text{Re}}\) :

Local Reynolds number

\(R_{d}\) :

Radiation parameter

\(\tilde{u}\) :

Along x-axis velocity component

\(\tilde{v}\) :

Along y-axis velocity component

\(\alpha\) :

Velocity ratio parameter

\(\beta_{e} ,\beta_{i}\) :

Hall and ion slip parameter

\(\gamma^{*}\) :

Conjugate parameter

\(\rho_{{{\text{hnf}}}} ,\rho_{f}\) :


\(\phi_{1} ,\phi_{2}\) :

Nanofluid volume fraction

\(\sigma^{*}\) :

Stefan-Boltzmann constant

\(\sigma_{{{\text{nf}}}} ,\sigma_{f}\) :

Electric conductivity

\(\mu_{{{\text{nf}}}} ,\mu_{f}\) :


\(\alpha_{{{\text{hnf}}}}\) :

Nanofluid thermal diffusivity

\(\theta_{w}\) :

Temperature difference

\(\tau_{w}\) :

Shear stress

\((\rho C_{p} )_{{{\text{hnf}}}}\) :

Heat capacity of nanofluid


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Correspondence to Shafiq Ahmad.

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Ahmad, S., Nadeem, S. Application of CNT-based micropolar hybrid nanofluid flow in the presence of Newtonian heating. Appl Nanosci 10, 5265–5277 (2020).

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  • Darcy–Forchheimer
  • Micropolar hybrid nanofluid
  • Hall and ion slip currents
  • Newtonian heating
  • Partially ionized
  • Entropy generation