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Numerical study of the effects of nanorod aspect ratio on Poiseuille flow and convective heat transfer in a circular minichannel

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Abstract

The effects of nanorod aspect ratio on Poiseuille flow and convective heat transfer of a nanofluid were studied numerically. A coupled model was proposed that considered the non-uniformity of the nanoparticle volume fraction and the orientation distribution. The thermal properties of the base fluid varied with temperature, and the nanofluid viscosity and thermal conductivity were correlated with the particle volume fraction based on experimental data. The model was verified useful to predict nanofluid flow that contains nanorods by comparing the numerical results with experimental data. The non-uniformity of nanorod volume fraction distribution increases near the boundary when the aspect ratio is larger. The nanorods orient nearly randomly-in-space along the flow center and align around the flow direction when particles migrate towards the wall. The flow resistance increases with the augment of the nanorod aspect ratio. The radial velocity profile of the fully developed Poiseuille flow is flattened due to the non-uniformity of the apparent stress, and the effect is enhanced with the increase of the nanorod aspect ratios. The convective heat transfer and overall thermal performance of the nanofluids is enhanced with the augment of the nanorod aspect ratio, especially in the low-flow-rate region. Hence, non-spherical nanofluids can be applied to cooling applications in minichannels with low-power consumption.

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Abbreviations

a :

Primary nanoparticle size (m)

a a :

Aggregate nanoparticle size (m)

a ij :

Second-order tensor of nanoparticle orientation

a ijkl :

Fourth-order tensor of nanoparticle orientation

b :

Proportionality factor for fitting function

c :

Proportionality factor between pressure drop and flow rate

C I :

Interaction coefficient

C nf :

Thermal diffusivity of the nanofluid (m2/s)

C p :

Specific heat capacity [J/(kg K)]

d :

Particle diameter (m)

D :

Diameter of the channel (m)

D tB :

Translational diffusion coefficient that is due to Brownian motion (m2/s)

D rB :

Rotary diffusion coefficient that is due to Brownian motion (1/s)

D rI :

Rotary diffusion coefficient that is due to particle–particle interactions (1/s)

D T :

Thermophoretic diffusion coefficient of nanoparticles (m2/s)

E :

Energy consumption or pumping power (W)

f :

Friction factor

FOM:

Figure of merit

h :

Convective heat transfer coefficient [W/(m2 K)]

k :

Thermal conductivity [W/(m K)]

k b :

Boltzmann constant = 1.38 × 10−23 (J/K)

k11, k33 :

Equivalent thermal conductivities along the two spheroidal axes

l :

Half-length of a cylindrical nanoparticle (m)

L :

Length of the channel (m)

L ii :

Depolarization factors for prolate spheroids

M :

Fractal index

M k :

kth-order moment

n :

Number density of nanoparticles (#/m3)

Nu:

Nusselt number

P :

Pressure (Pa)

p :

Orientation vector of a particle

p i :

Unit vector that is parallel to the nanoparticle’s principal axis

v i :

Particle angular velocity (rad/s)

PAO:

Polyalphaolefin

Pr:

Prandtl number

q :

Heat flux (kW/m2)

Q :

Flow rate (mLPM, milliliters per minute)

R b :

Interfacial resistance (m2K/W)

Re:

Reynolds number

r :

Aspect ratio, 2 l/d

t :

Time (s)

T :

Temperature (K)

u :

Velocity (m/s)

u 0 :

Inlet velocity (m/s)

u ave :

Average velocity (m/s)

x, y, z :

Cartesian coordinates

\(\varepsilon_{ij}\) :

Rate-of-strain tensor (s−1)

λ :

A material constant that depends on the particle aspect ratio

μ :

Dynamic viscosity (N s/m2)

ν :

Kinematic viscosity (m2/s)

ρ :

Density (kg/m3)

\(\phi\) :

Particle volume fraction

\(\phi_{0}\) :

Inlet particle volume fraction

\(\phi_{\text{m}}\) :

Maximum volume fraction, which is related to the nanorod aspect ratio

Ψ :

Probability density function for particle orientation

\(\omega_{ij}\) :

Vorticity tensor (s−1)

\(\gamma_{\text{rL}}\) :

Rotational friction coefficient around the long axis (kg m2/s)

\(\gamma_{\text{rS}}\) :

Rotational friction coefficient around the short axis (kg m2/s)

\(\delta_{\text{rL}}\) :

Correction coefficient for the rotational friction coefficient around the long axis

\(\delta_{\text{rS}}\) :

Correction coefficient for the rotational friction coefficient around the short axis

\(\gamma_{\text{tL}}\) :

Translational friction coefficient around the long axis (kg/s)

\(\gamma_{\text{tS}}\) :

Translational friction coefficient around the short axis (kg/s)

\(\delta_{\text{tL}}\) :

Correction coefficient for the translational friction coefficient around the long axis

\(\delta_{\text{tS}}\) :

Correction coefficient for the translational friction coefficient around the short axis

θ :

Angle between the particle principal axis and the x-direction (rad)

a :

Apparent

ave:

Average

B:

Brownian diffusion

e:

Effective

f:

Base fluid

in:

Inlet

nf:

Nanofluid

p:

Particle

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Acknowledgements

This work has been financially supported by the National Natural Science Foundation of China (nos. 11802105, 91852102) and the Fundamental Research Funds for the Central Universities (JUSRP11825).

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Authors and Affiliations

  1. Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, School of Mechanical Engineering, Jiangnan University, Wuxi, 214122, Jiangsu, China

    Fangyang Yuan & Wei Yu

  2. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, China

    Jianzhong Lin

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  1. Fangyang Yuan
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  2. Wei Yu
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Correspondence to Fangyang Yuan.

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Yuan, F., Yu, W. & Lin, J. Numerical study of the effects of nanorod aspect ratio on Poiseuille flow and convective heat transfer in a circular minichannel. Microfluid Nanofluid 24, 62 (2020). https://doi.org/10.1007/s10404-020-02370-2

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