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Mitigation of fluid flow and thermal non-uniformity of nanofluids in microfluidic systems applied to processor chip: a comparative analysis of mass versus thermal mitigation

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Abstract

The present research article focuses on the mitigation of fluid flow and thermal non-uniformity in the microfluidic system resulting in hot spot mitigation in microelectronic devices. A concept of variable size microchannels is extended by implementing the mass and thermal mitigation methods. In the present study, 3-D numerical simulation is carried out to study the problem of fluid flow and thermal non-uniformity of \( \mathrm {Al_{2}O_{3}}\)/water nanofluid with three different nanoparticle concentrations (1–3 vol.%) in the microfluidic system. The computational domain is considered the entire microfluidic system, including parallel microchannels, inlet/outlet manifolds, and ports. Results are analysed and compared for flow and thermal field as well as pressure drop penalty. Results indicate that mass and thermal mitigation are effective methods of obtaining uniform mass distribution and thermal field among all the microchannels. The same brings pumping power penalty due to non-uniform size of the microchannels. It is observed that equalization of fluid velocity among all the microchannels leads to uniform thermal field of the MCHS. If the development of uneven thermal stresses cannot be tolerated in the specific application, the MCHS with thermal mitigation using variable size microchannels is the best design as applied to real-world applications, but at the cost of pumping power penalty.

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Abbreviations

A :

Area of microchannel (\( \text{m}^{2} \))

\(C_{p}\) :

Specific heat (J/kg K)

D :

Diameter of microchannel (m)

d :

Nanoparticle size (nm)

\(D_{f}\) :

Fractal index (1.6–2.5)

f :

Friction factor

g :

Different grid schemes

H :

Height of MCHS (m)

h :

Heat transfer coefficient (\( {\text{W/m}}^{{\text{2}}} {\text{K}} \))

i :

Microchannel number (\( 1\le \; i \;\le \; N \))

j :

Iteration number (\( 0\le \; j \;\le \; M \))

k :

Thermal conductivity (W/m K)

L :

Length of MCHS (m)

\(\dot{m} \) :

Mass flow rate (Kg/s)

NMFR:

Normalized mass flow rate (\(\dot{m}_{{{\text{ch}} - i}} /\dot{m}_{{ch - {\text{avg}}}}\))

NHTR :

Normalized heat transfer rate (\( \dot{Q}_{{{\text{ch}} - i}} /\dot{Q}_{{ch - {\text{avg}}}}\))

N :

Total number of microchannel

p :

Pressure (Pa)

\( \dot{Q} \) :

Heat transfer rate (W)

\(q^{''}\) :

Wall heat flux (\({\text{W/m}}^{{\text{2}}}\))

r :

Nanoparticle radius (nm)

S :

Spacing between microchannels (m)

T:

Temperature (\(^{\circ }\mathrm {C}\))

v :

Flow velocity (m/s)

W :

Width of MCHS (m)

x :

Local axial length of microchannel (m)

\(x^{+}\) :

Dimensionless hydrodynamically developed length (\( \frac{L/D_{i}}{Re} \))

\(x^{*}\) :

Dimensionless thermally developing length (\( \frac{x/D_{i}}{Re\;Pr} \))

\(\alpha \) :

Nanoparticle Biot number

\(\varepsilon \) :

Grid convergence index (\( \% \))

\(\mu \) :

Dynamic viscosity (Pa s)

\(\rho \) :

Density (\({\text{kg/m}}^{{\text{3}}}\))

\(\phi \) :

Nanoparticle concentration (%)

\(\varphi \) :

Non-uniformity factor

Re:

Reynolds number \( (\frac{\rho \;v\;D}{\mu }) \)

Pr:

Prandtl number \( (\frac{\mu \;C_{p}}{k}) \)

Nu:

Local Nusselt number

a :

Aggregates

avg:

Average

B :

Brownian motion

bf:

Base fluid

cr:

Critical

f:

Fluid

ch:

Channel

in:

Inlet

\( \dot{Q} \) :

Heat transfer rate

\(\dot{m}\) :

Mass flow rate

M:

Manifold

max:

Maximum

min:

Minimum

nf:

Nanofluid

np:

Nanoparticle

p:

Port

out:

Outlet

s:

Solid

\(\infty \) :

Ambient condition

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Acknowledgements

The authors would like to acknowledge PDPM Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur (MP), to provide financial support and the computational facility.

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Authors and Affiliations

  1. Mechanical Engineering Discipline, PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, Madhya Pradesh, 482005, India

    Mangal Singh Lodhi & Tanuja Sheorey

  2. Department of Mechanical Engineering, Indian Institute of Technology, Jammu, Jammu and Kashmir, 181221, India

    Goutam Dutta

Authors
  1. Mangal Singh Lodhi
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  2. Tanuja Sheorey
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  3. Goutam Dutta
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Correspondence to Tanuja Sheorey.

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Lodhi, M.S., Sheorey, T. & Dutta, G. Mitigation of fluid flow and thermal non-uniformity of nanofluids in microfluidic systems applied to processor chip: a comparative analysis of mass versus thermal mitigation. Microsyst Technol 27, 1877–1893 (2021). https://doi.org/10.1007/s00542-020-05112-0

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  • DOI: https://doi.org/10.1007/s00542-020-05112-0

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