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Numerical simulation of three-dimensional thermo-solutal convection of micropolar multi-walled carbon nanotubes water nanofluid stabilized by lignin and sodium polycarboxylate

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Abstract

A computational analysis has been performed in this study to solve three-dimensional thermo-solutal natural convection in a differentially heated cubical enclosure filled with micropolar CNT/water nanofluid stabilized by two types of surfactants lignin and sodium polycarboxylate. The work is carried out for different pertinent parameters as Rayleigh number (104 \(\le\) Ra \(\le\) 106), micropolar parameter (0 \(\le\) K \(\le\) 10), buoyancy ratio (−1 \(\le\) N \(\le\) 0) and nanoparticles’s volume fraction (0.0055% \(\le \varphi \le\) 0.557%). It is observed that the heat and mass transfer rates are lower for a micropolar nanofluid model when compared to the pure nanofluid model. In fact, the enhancement of micropolar parameter results a decrease in average Nusselt and Sherwood numbers. The use of lignin as a surfactant ameliorates heat and mass transfer rate and nanofluid flow better than the use of sodium polycarboxylate as a surfactant. The nanoparticles volume fraction can be used as a control element for heat rate and fluid flow. Thus, for a nanoparticles volume concentration less than the critical value, the flow intensity is ameliorated and is deteriorated when it exceeds this value.

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Abbreviations

C :

Dimensionless species concentration, \(C = \frac{{C^{\prime} - C_{\text{l}}^{^{\prime}} }}{{C_{\text{H}}^{^{\prime}} - C_{\text{L}}^{^{\prime}} }}\)

C′:

Species concentration (kg m−3)

C p :

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

D :

Species diffusivity (m2 s−1)

G :

Acceleration of gravity (m s−2)

\(\mathop{H}\limits^{\rightharpoonup}\) :

Dimensionless microrotation vector

\(\vec{H}^{\prime}\) :

The microrotation vector (m s−1)

J:

Microinertia coefficient (microrotation radius)

K :

Micropolar parameter, \(K = \frac{k}{{\mu_{\text{f}} }}\)

K :

Vortex viscosity (kg m−1 s−1)

\(k\) :

Thermal conductivity (W m−1 K−1)

L:

Enclosure height (m)

Le :

Lewis number, \(Le = \frac{\alpha }{D}\)

N :

Buoyancy ratio, \(N = \frac{{\beta_{\text{Cf}} \left( { C_{\text{H}} - C_{\text{L}} } \right)}}{{\beta_{\text{Tf}} \left( { T_{\text{H}} - T_{\text{C}} } \right)}}\)

Nu :

Local Nusselt number

\(\overline{Nu}\) :

Average Nusselt number

P :

Dimensionless pressure

Pr :

Prandtl number, \(Pr = \frac{{\nu_{\text{f}} }}{{\alpha_{\text{f}} }}\),

Ra :

Thermal Rayleigh number, \(Ra = \frac{{g\beta_{{{\text{Tf}}}} \left( { T_{{\text{H}}} - T_{{\text{C}}} } \right)L^{3} }}{{\nu_{{\text{f}}} \alpha_{{\text{f}}} }}\)

Sh :

Local Sherwood number

\(\overline{Sh}\) :

Average Sherwood number

T :

Dimensionless time, \(t = \frac{\alpha t^{\prime}}{{L^{2} }}\)

T :

Dimensionless temperature, \(T = \frac{{T^{{\prime }} - T_{\text{C}}^{^{\prime}} }}{{T_{\text{H}}^{^{\prime}} - T_{\text{C}}^{^{\prime}} }}\)

T′:

Temperature (K)

\(\vec{U}\) :

Dimensionless velocity \(\vec{U} = \frac{{\overrightarrow {U^{\prime}} L}}{{\alpha_{\text{f}} }}\)

\(\vec{U}^{\prime}\) :

Velocity (m s−1)

x, y, z :

Dimensionless Cartesian coordinates, x = x′/L, y = y′/L, z = z′/L

\(\alpha\) :

Thermal diffusivity (m2 s−1)

β C :

Coefficient of compositional expansion(m3 kg−1)

β T :

Coefficient of thermal expansion (K−1)

φ :

Solid volume fraction

μ :

Dynamic viscosity (kg m−1 s−1)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

\(\vec{\omega }\) :

Dimensionless vorticity, \(\vec{\omega } = \frac{{\overrightarrow {\omega ^{\prime}} L}}{{\alpha_{\text{f}} }}\)

\(\vec{\omega }^{^{\prime}}\) :

Vorticity (s−1)

\(\vec{\psi }\) :

Dimensionless vector potential of velocity, \(\vec{\psi } = \frac{{\overrightarrow {\psi ^{\prime}} }}{{\alpha_{{\text{f}}} }}\)

\(\vec{\psi }^{^{\prime}}\) :

Vector potential of velocity (m2 s−1)

C :

Cold

f :

Fluid

H :

Hot

L:

Low

max:

Maximum

nf :

Nanofluid

P :

Particle

1 :

x-Component

2 :

y-Component

3 :

z-Component

′ :

Dimensional variables

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the General Research Project under Grant Number (G.R.P-74-42). The first author gratefully acknowledges the Tunisian Ministry of Higher Education and Scientific Research for financial support to her stay in LGCGM, France.

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Authors and Affiliations

  1. Research Laboratory of Metrology and Energy Systems LR81ES21, Energy Engineering Department, National Engineering School, Monastir University, Monastir City, Tunisia

    Nessrin Manaa, Awatef Abidi & Mohammed Naceur Borjini

  2. Physics Department, College of Sciences Abha, King Khalid University, Abha, Saudi Arabia

    Awatef Abidi

  3. Higher School of Sciences and Technology of Hammam Sousse, Sousse University, Sousse, Tunisia

    Awatef Abidi

  4. Univ Rennes, LGCGM, 35000, Rennes, France

    Patrice Estellé

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  1. Nessrin Manaa
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Correspondence to Patrice Estellé.

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Manaa, N., Abidi, A., Estellé, P. et al. Numerical simulation of three-dimensional thermo-solutal convection of micropolar multi-walled carbon nanotubes water nanofluid stabilized by lignin and sodium polycarboxylate. J Therm Anal Calorim 147, 2985–3005 (2022). https://doi.org/10.1007/s10973-021-10667-9

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