Abstract
This article deals with the numerical simulation of the electroosmotic flow of methanol-based aluminum oxide (Al2O3–CH3OH) nanofluid in a tapered microchannel. The shear-thickening attributes of methanol are characterized by the Sisko fluid model. The tapered microchannel walls move with peristaltic wave velocity. Buongiorno model in combination with the Corcione model for thermal conductivity and viscosity is employed to predict the heat transfer characteristics of Al2O3–methanol nanofluid. The Maxwell–Garnett model is employed to compute the effective electric conductivity of nanofluids. The effect of the porous medium in the flow field is signified by modified Darcy’s law. The salient attributes of viscous dissipation and Joule heating caused by electroosmosis are also taken into account. The approximations of the lubrication approach and the Debye–Hückel linearization are invoked in mathematical formulation for considerable simplification of the flow problem. The solutions of the acquired set of nonlinear governing equations are computed numerically through Maple 17. The graphical results for various physical quantities are also presented for physical interpretation and discussion. It is revealed that fluid becomes more viscous for enhancement in the consistency parameter. Furthermore, maintaining a larger temperature difference within microchannel produces a reduction in the concentration of nanoparticles. Temperature and velocity profiles are strongly dependent on the electroosmosis mechanism. The simulated results will be very important for designing biomicrofluidics devices dealing with rheologically complex fluids such as lubricating greases, blood, saliva or mucus.
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Abbreviations
- d 1 :
-
Half-width of the channel (M)
- m′ :
-
Non-uniformity parameter (–)
- b 1, b 2 :
-
Amplitude of waves (M)
- Λ:
-
Wavelength (M)
- \( \tilde{u},\tilde{v} \) :
-
Velocity components in the axial and transverse direction (ms−2)
- ρ nf :
-
Nanofluid density (kg m−3)
- \( \tilde{t} \) :
-
Time parameter (S)
- ̃\( \tilde{p} \) :
-
Pressure field (Nm−2)
- \( \tilde{S}_{{\tilde{x}\tilde{x}, }} \tilde{S}_{{\tilde{x}\tilde{y}}} , \tilde{S}_{{\tilde{y}\tilde{y}}} \) :
-
Shear stress components (ML−1 T−2)
- \( \rho_{\text{e}} \) :
-
Local electric charge density (cm−3)
- \( E_{{\tilde{x},}} E_{{\tilde{y}}} \) :
-
The axial and transverse electric field (MLA−1 T−3)
- \( c_{\text{nf}} , c_{\text{p}} \) :
-
Specific heat of nanofluid and nanoparticles (J kg−1 K−1)
- \( \tilde{T} \) :
-
Temperature field (K)
- \( D_{\text{B}} \) :
-
Brownian diffusion parameter (m2 s−1)
- \( \tilde{\phi } \) :
-
Concentration field (kg m−3)
- \( \tilde{T}_{0} , \tilde{T}_{1} \) :
-
The temperature at the lower and upper wall (K)
- \( \sigma_{\text{nf}} \) :
-
Electrical conductivity (S m−1)
- \( D_{\text{T}} \) :
-
Thermophoretic parameter (m2 s−1)
- \( n \) :
-
Power-law index (–)
- \( A_{1} \) :
-
Rivlin Erickson tensor (s−1)
- \( d_{\text{p}} , d_{\text{bf}} \) :
-
The diameter of nanoparticles and base fluid molecule (M)
- \( T_{\text{fr}} \) :
-
The freezing temperature of the base fluid (K)
- \( K^{*} \) :
-
Permeability parameter (m2)
- \( \tilde{E} \) :
-
Electric potential (V)
- \( \varepsilon_{0} \) :
-
The permittivity of free space (Fm−1)
- \( \varepsilon \) :
-
The relative permittivity of the solvent (–)
- \( n^{ + } ,n^{ - } \) :
-
Local density of positive and negative ions (cm−3)
- \( e \) :
-
Charge of electron (C)
- z:
-
Valency (–)
- \( p \) :
-
Dimensionless pressure parameter (–)
- \( U \) :
-
Helmholtz–Smoluchowski velocity (–)
- k:
-
The dimensionless Debye length parameter (–)
- \( {\text{Da}} \) :
-
Darcy resistance parameter (–)
- \( \psi \) :
-
Dimensionless stream function (–)
- \( \beta_{s} \) :
-
Dimensionless material parameter (–)
- \( Pr \) :
-
Prandtl number (–)
- \( N_{\text{b}} \) :
-
Dimensionless Brownian diffusion parameter (–)
- \( N_{\text{t}} \) :
-
Dimensionless thermophoretic parameter (–)
- \( Br \) :
-
Brinkmann number (–)
- \( \xi \) :
-
Dimensionless zeta potential (–)
- \( Q \) :
-
Dimensionless time-averaged flow rate (–)
- \( F \) :
-
Dimensionless volumetric flow rate (–)
- \( m \) :
-
Dimensionless non-uniformity parameter (–)
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Akram, J., Akbar, N.S. & Tripathi, D. Numerical study of the electroosmotic flow of Al2O3–CH3OH Sisko nanofluid through a tapered microchannel in a porous environment. Appl Nanosci 10, 4161–4176 (2020). https://doi.org/10.1007/s13204-020-01521-9
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DOI: https://doi.org/10.1007/s13204-020-01521-9