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Thermal mixing, cooling and entropy generation in a micromixer with a porous zone by the lattice Boltzmann method

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Short transport paths with high surface to volume ratios in microfluidic devices have the potential to increase the heat transfer significantly. However, because of the very low Reynolds numbers reached in microchannel flows, it is difficult to achieve effective thermal mixing. Microfluidic mixing requires fast mixing process of low diffusivity fluids. To obtain a rapid thermal mixing in passive micromixers, a porous block may be inserted to enhance the thermal performance. A 2D lattice Boltzmann thermal model is utilized here to investigate the thermal performance of a Y-micromixer with a porous block. Different parameters of porous block including its aspect ratio, its position, its porosity and its effective thermal conductivity are considered. The thermal mixing and cooling of two miscible fluids at 50 and 25 °C entering the micromixer are investigated in detail. The results show that the porous block significantly improves the thermal mixing of both streams. Increasing the porous block aspect ratio leads to better cooling, low entropy generation and high dimensionless entropy generation. It is also observed that thermal mixing and cooling performance increase by decreasing the effective thermal conductivity and porosity of the block, which causes a low entropy generation.

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Discrete lattice velocity


Darcy number (= \( K/H^{2} \))

f :

Distribution function for flow

F :

Acceleration due to external force, (\( {\text{ms}}^{ - 2} \))

g :

Distribution function for temperature

H :

Characteristic height, (m)

K :

Permeability, (\( {\text{m}}^{2} \))

Nu :

Local Nusselt number, (\( = hx/k_{f} \)), (−)

Pr :

Prandtl number, (\( = \upsilon /\theta \)), (−)

Q :

Heat transfer to horizontal wall, (W)

Re :

Reynolds number (= \( UH/\nu \)), (−)

\( S^{'''}_{\text{gen}} \) :

Total volumetric entropy generation rate, (−)

\( S^{'''}_{\text{P}} \) :

Volumetric entropy generation rate due to friction, (−)

\( S^{'''}_{\text{T}} \) :

Volumetric entropy generation rate due to heat transfer, (−)

S :

Entropy generation, (\( {\text{Wm}}^{ - 3} {\text{K}}^{ - 1} \))

t :

Time, (s)

T :

Temperature, (K)

u :

Velocity component, (\( {\text{ms}}^{ - 1} \))

x :

Dimension, (m)

\( \varepsilon \) :

Porosity of porous media

\( \mu \) :

Dynamic viscosity, (Pa.s)

\( \rho \) :

Density, (kg/m³)

\( \sigma \) :

Conductivity ratio (= \( K_{\text{f}} /K_{\text{s}} \))

\( \upsilon \) :

Kinematic viscosity, (\( {\text{m}}^{2} {\text{s}}^{ - 1} \))

\( \tau \) :

Relaxation time

\( \omega \) :

Weighting factor




Equilibrium distribution function

i, j:

Dimension directions


Lattice model direction


Total generated


Lattice Boltzmann method


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Sébastien Poncet acknowledges Natural Sciences and Engineering Research Council of Canada for its financial support through a discovery Grant (RGPIN-2015-06512).

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Correspondence to Seyed Soheil Mousavi Ajarostaghi.

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Ajarostaghi, S.S.M., Delavar, M.A. & Poncet, S. Thermal mixing, cooling and entropy generation in a micromixer with a porous zone by the lattice Boltzmann method. J Therm Anal Calorim 140, 1321–1339 (2020).

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