Skip to main content
SpringerLink
Log in

Investigation of nanofluids on heat transfer enhancement in a louvered microchannel with lattice Boltzmann method

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

Numerical studies of laminar forced convective heat transfer and fluid flow in a 2D louvered microchannel with Al2O3/water nanofluids are performed by the lattice Boltzmann method (LBM). Eight louvers are arranged in tandem within the single-pass microchannel. The Reynolds number based on channel hydraulic diameter and bulk mean velocity ranges from 100 to 400, where the Al2O3 fraction varies from 0 to 4%. A double distribution function approach is adopted for modeling fluid flow and heat transfer. Code validations are performed by comparing the streamwise Nusselt number (Nu) profiles and Fanning friction factors of the present LBM and those of the analytical solutions. Good agreements are obtained. Simulated results show that the louver microstructure can disturb the core flow and guide coolant toward the heated walls, thus enhancing the heat transfer significantly. Furthermore, the addition of nanoparticles in microchannels can also augment the heat transfer, but it creates an unnoticeable pressure loss. With both the louver microstructure and nanofluid, a maximum overall Nu enhancement of 7.06 is found relative to that of the fully developed smooth channel.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Abbreviations

\(\varvec{c}_{\text{k}}\) :

Discrete lattice velocity vectors

c p :

Specific heat capacity (J kg−1 K−1)

c s :

Dimensionless speed of sound

d :

Particle diameter (m)

D h :

Hydraulic diameter, 2H (m)

f :

Fanning friction factor

\(\bar{f}\) :

Average Fanning friction factor

f 0 :

Fanning friction factor for the fully developed laminar flow in two-dimensional smooth channel

f k :

Distribution function for velocity

f eq :

Equilibrium distribution function for velocity

g k :

Distribution function for energy

g eqk :

Equilibrium distribution function for velocity

H :

Height of channel (m)

H s :

Height of louver microstructures (m)

k :

Thermal conductivity (W m−1 K−1)

L :

Length of channel (m)

Nu :

Nusselt number

\(\overline{Nu}\) :

Average Nusselt number

\(Nu_{0}\) :

Nusselt number for the fully developed laminar flow in two-dimensional smooth channel

\(P\) :

Pressure (Pa)

Pr :

Prandtl number = ν/α

Re :

Reynolds number = ρfumDh/μf

T :

Temperature (K)

TPF:

Thermal performance factor

\(\varvec{u}\) :

Velocity vector (m s−1)

u :

Streamwise velocity component (m s−1)

v :

Transverse velocity component (m s−1)

w k :

Weighting factors

\(\varvec{x}\) :

Position lattice vectors (m)

x :

Streamwise coordinate (m)

y :

Transverse coordinate (m)

\(X^{*}\) :

Dimensionless coordinates (x/Dh)

\(Y^{*}\) :

Dimensionless coordinates (y/Dh)

α :

Thermal diffusion coefficient (m2 s−1)

μ :

Dynamic viscosity (kg m−1 s−1)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

τ ν :

Dimensionless relaxation time for fk

τ c :

Dimensionless relaxation time for gk

ϕ :

Particle volume fraction

bf:

Base fluid

in:

Inlet

m:

Mean

nf:

Nanofluid

out:

Outlet

p:

Particle

w:

Wall

References

  1. Tuckerman DB, Pease RFW. High-performance heat sinking for VLSI. IEEE Electron Device Lett. 1981;2(5):126–9.

    Article  Google Scholar 

  2. Webb BW, Ramadhyani S. Conjugate heat transfer in a channel with staggered ribs. Int J Heat Mass Transf. 1985;28(9):1679–87.

    Article  Google Scholar 

  3. Croce G, D’agaro P, Nonino C. Three-dimensional roughness effect on microchannel heat transfer and pressure drop. Int J Heat Mass Transf. 2007;50(25):5249–59.

    Article  CAS  Google Scholar 

  4. Desrues T, Marty P, Fourmigué JF. Numerical prediction of heat transfer and pressure drop in three-dimensional channels with alternated opposed ribs. Appl Therm Eng. 2012;45:52–63.

    Article  Google Scholar 

  5. Rahman MM, Injeti P. Heat transfer in microtube or microchannel with protrusions. Front Heat Mass Transf. 2011;2(1):013003.

    Article  CAS  Google Scholar 

  6. Chai L, Xia GD, Wang HS. Numerical study of laminar flow and heat transfer in microchannel heat sink with offset ribs on sidewalls. Appl Therm Eng. 2016;92:32–41.

    Article  Google Scholar 

  7. Liu Y, Cui J, Li W, Zhang N. Effect of surface microstructure on microchannel heat transfer performance. J Heat Transf. 2011;133:124501.

    Article  Google Scholar 

  8. Gong L, Kota K, Tao W, Joshi Y. Parametric numerical study of flow and heat transfer in microchannels with wavy walls. J. Heat Transf. 2011;133(5):051702-1–-10.

    Article  Google Scholar 

  9. Ghaedamini H, Lee PS, Teo CJ. Developing forced convection in converging–diverging microchannels. Int J Heat Mass Transf. 2013;65:491–9.

    Article  Google Scholar 

  10. Patankar SV, Liu CH, Sparrow EM. Fully developed flow and heat transfer in ducts having streamwise-periodic variations of cross-sectional area. J Heat Transf. 1977;99(2):180–6.

    Article  Google Scholar 

  11. Kelkar KM, Patankar SV. Numerical prediction of flow and heat transfer in a parallel plate channel with staggered fins. J Heat Transf. 1987;109(1):25–30.

    Article  CAS  Google Scholar 

  12. Cheng CH, Hung WH. Numerical prediction for laminar forced convection in parallel-plate channels with transverse fin arrays. Int J Heat Mass Transf. 1991;34(11):2739–49.

    Article  CAS  Google Scholar 

  13. Mousavi SS, Hooman K. Heat and fluid flow in entrance region of a channel with staggered baffles. Energy Convers Manag. 2006;47(15):2011–9.

    Article  Google Scholar 

  14. Liu C, Teng JT, Chu JC, Chiu YL, Huang S, Jin S, Pan HH. Experimental investigations on liquid flow and heat transfer in rectangular microchannel with longitudinal vortex generators. Int J Heat Mass Transf. 2011;54(13):3069–80.

    Article  Google Scholar 

  15. Ebrahimi A, Roohi E, Kheradmand S. Numerical study of liquid flow and heat transfer in rectangular microchannel with longitudinal vortex generators. Appl Therm Eng. 2015;78:576–83.

    Article  Google Scholar 

  16. Sripattanapipat S, Promvonge P. Numerical analysis of laminar heat transfer in a channel with diamond-shaped baffles. Int Commun Heat Mass Transf. 2009;36(1):32–8.

    Article  CAS  Google Scholar 

  17. Saidur R, Leong KY, Mohammad H. A review on applications and challenges of nanofluids. Renew Sustain Energy Rev. 2011;15(3):1646–68.

    Article  CAS  Google Scholar 

  18. Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. In: International Mechanical Engineering Congress and Exhibition; 1995. p. 99–106.

  19. Wang XQ, Mujumdar AS. Heat transfer characteristics of nanofluids: a review. Int J Therm Sci. 2007;46(1):1–19.

    Article  Google Scholar 

  20. Li J, Li Z, Wang B. Experimental viscosity measurements for copper oxide nanoparticle suspensions. Tsinghua Sci Technol. 2002;7(2):198–201.

    CAS  Google Scholar 

  21. Mintsa HA, Roy G, Nguyen CT, Doucet D. New temperature dependent thermal conductivity data for water-based nanofluids. Int J Therm Sci. 2009;48(2):363–71.

    Article  CAS  Google Scholar 

  22. Chon CH, Kihm KD, Lee SP, Choi SU. Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement. Appl Phys Lett. 2005;87(15):153107.

    Article  CAS  Google Scholar 

  23. Nguyen CT, Desgranges F, Roy G, Galanis N, Maré T, Boucher S, Mintsa HA. Temperature and particle-size dependent viscosity data for water-based nanofluids–hysteresis phenomenon. Int J Heat Fluid Flow. 2007;28(6):1492–506.

    Article  CAS  Google Scholar 

  24. Maiga SEB, Palm SJ, Nguyen CT, Roy G, Galanis N. Heat transfer enhancement by using nanofluids in forced convection flows. Int J Heat Fluid Flow. 2005;26(4):530–46.

    Article  CAS  Google Scholar 

  25. Yang YT, Lai FH. Numerical study of flow and heat transfer characteristics of alumina-water nanofluids in a microchannel using the lattice Boltzmann method. Int Commun Heat Mass Transf. 2011;38(5):607–14.

    Article  CAS  Google Scholar 

  26. Akbari OA, Toghraie D, Karimipour A, Safaei MR, Goodarzi M, Alipour H, Dahari M. Investigation of rib’s height effect on heat transfer and flow parameters of laminar water–Al2O3 nanofluid in a rib-microchannel. Appl Math Comput. 2016;290:135–53.

    Google Scholar 

  27. Ghale ZY, Haghshenasfard M, Esfahany MN. Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models. Int Commun Heat Mass Transf. 2015;68:122–9.

    Article  Google Scholar 

  28. Liou TM, Wang CS. Large eddy simulation of rotating turbulent flows and heat transfer by the lattice Boltzmann method. Phys Fluids. 2018;30(1):015106.

    Article  CAS  Google Scholar 

  29. Raghuraman DRS, Raj RTK, Nagarajan PK, Rao BVA. Influence of aspect ratio on the thermal performance of rectangular shaped micro channel heat sink using CFD code. Alexandria Eng J. 2017;56(1):43–54.

    Article  Google Scholar 

  30. Aparecido JB, Cotta RM. Thermally developing laminar flow inside rectangular ducts. Int J Heat Mass Transf. 1990;33(2):341–7.

    Article  CAS  Google Scholar 

  31. Qian YH, D’Humières D, Lallemand P. Lattice BGK models for Navier–Stokes equation. Europhys Lett. 1992;17(6):479.

    Article  Google Scholar 

  32. Zou Q, He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids. 1997;9(6):1591–8.

    Article  CAS  Google Scholar 

  33. Incropera FP. Liquid cooling of electronic devices by single-phase convection. Hoboken: Wiley-Interscience; 1999.

    Google Scholar 

  34. Gherasim I, Roy G, Nguyen CT, Vo-Ngoc D. Experimental investigation of nanofluids in confined laminar radial flows. Int J Therm Sci. 2009;48(8):1486–93.

    Article  CAS  Google Scholar 

  35. Bergman TL, Incropera FP. Fundamentals of heat and mass transfer. Hoboken: Wiley; 2011.

    Google Scholar 

  36. Bejan A. Convection heat transfer. Hoboken: Wiley; 2013.

    Book  Google Scholar 

Download references

Acknowledgements

The present study is sponsored by the Ministry of Science and Technology of Taiwan under Contract: MOST105-2221-E-007-058-MY3. The National Center for High-performance Computing is also acknowledged for providing computer resources.

Author information

Authors and Affiliations

  1. Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, 30013, Taiwan, ROC

    Tong-Miin Liou, Tzu-Chiao Wei & Chun-Sheng Wang

Authors
  1. Tong-Miin Liou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tzu-Chiao Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chun-Sheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tong-Miin Liou.

Appendix: boundary conditions for D2Q9 lattice model

Appendix: boundary conditions for D2Q9 lattice model

For LBM, the macroscopic boundary conditions have to be reformulated in the kinetic form. At the inlet, the Zou and He boundary conditions [32] for velocity distribution functions are adopted as

$$\begin{aligned} f_{1} (\varvec{x},t) = f_{3} (\varvec{x},t) + \frac{2}{3}\rho u_{\text{in}} , \hfill \\ f_{5} (\varvec{x},t) = f_{7} (\varvec{x},t) - \frac{1}{2}\left[ {f_{2} (\varvec{x},t) - f_{4} (\varvec{x},t)} \right] + \frac{1}{6}\rho u_{\text{in}} , \hfill \\ f_{8} (\varvec{x},t) = f_{6} (\varvec{x},t) + \frac{1}{2}\left[ {f_{2} (\varvec{x},t) - f_{4} (\varvec{x},t)} \right] + \frac{1}{6}\rho u_{\text{in}} . \hfill \\ \end{aligned}$$
(33)

Similarly, unknown inlet temperature distribution functions are given by

$$\begin{aligned} g_{1} (\varvec{x},t) = - g_{3} (\varvec{x},t), \hfill \\ g_{5} (\varvec{x},t) = - g_{7} (\varvec{x},t), \hfill \\ g_{8} (\varvec{x},t) = - g_{6} (\varvec{x},t). \hfill \\ \end{aligned}$$
(34)

At the outlet, the unknown velocity and temperature distribution functions are extrapolated by

$$\begin{aligned} f_{3} (\varvec{x},t) = f_{3} (\varvec{x} - \varvec{c}_{1} \Delta t,t), \hfill \\ f_{6} (\varvec{x},t) = f_{6} (\varvec{x} - \varvec{c}_{1} \Delta t,t), \hfill \\ f_{7} (\varvec{x},t) = f_{7} (\varvec{x} - \varvec{c}_{1} \Delta t,t), \hfill \\ \end{aligned}$$
(35)

and

$$\begin{aligned} g_{3} (\varvec{x},t) = 2g_{3} (\varvec{x} - \varvec{c}_{1} \Delta t,t) - g_{3} (\varvec{x} - 2\varvec{c}_{1} \Delta t,t), \hfill \\ g_{6} (\varvec{x},t) = 2g_{6} (\varvec{x} - \varvec{c}_{1} \Delta t,t) - g_{6} (\varvec{x} - 2\varvec{c}_{1} \Delta t,t), \hfill \\ g_{7} (\varvec{x},t) = 2g_{7} (\varvec{x} - \varvec{c}_{1} \Delta t,t) - g_{7} (\varvec{x} - 2\varvec{c}_{1} \Delta t,t). \hfill \\ \end{aligned}$$
(36)

To model the solid walls and obstacles, bounce back schemes for velocity distribution functions are applied, i.e.

$$\begin{aligned} f_{2} (\varvec{x},t) = f_{4} (\varvec{x},t), \hfill \\ f_{3} (\varvec{x},t) = f_{1} (\varvec{x},t), \hfill \\ f_{5} (\varvec{x},t) = f_{7} (\varvec{x},t), \hfill \\ f_{6} (\varvec{x},t) = f_{8} (\varvec{x},t), \hfill \\ \end{aligned}$$
(37)

and

$$\begin{aligned} f_{1} (\varvec{x},t) = f_{3} (\varvec{x},t), \hfill \\ f_{4} (\varvec{x},t) = f_{2} (\varvec{x},t), \hfill \\ f_{7} (\varvec{x},t) = f_{5} (\varvec{x},t), \hfill \\ f_{8} (\varvec{x},t) = f_{6} (\varvec{x},t). \hfill \\ \end{aligned}$$
(38)

For the temperature boundary condition on the top and bottom walls, the unknown distribution functions can be written as

$$\begin{aligned} g_{1} (\varvec{x},t) = T_{w} (w_{1} + w_{3} ) - g_{3} (\varvec{x},t), \hfill \\ g_{3} (\varvec{x},t) = T_{w} (w_{1} + w_{3} ) - g_{1} (\varvec{x},t), \hfill \\ g_{4} (\varvec{x},t) = T_{w} (w_{2} + w_{4} ) - g_{2} (\varvec{x},t), \hfill \\ g_{7} (\varvec{x},t) = T_{w} (w_{5} + w_{7} ) - g_{5} (\varvec{x},t), \hfill \\ g_{8} (\varvec{x},t) = T_{w} (w_{6} + w_{8} ) - g_{6} (\varvec{x},t), \hfill \\ \end{aligned}$$
(39)

and

$$\begin{aligned} g_{1} (\varvec{x},t) = T_{w} (w_{1} + w_{3} ) - g_{3} (\varvec{x},t), \hfill \\ g_{2} (\varvec{x},t) = T_{w} (w_{2} + w_{4} ) - g_{4} (\varvec{x},t), \hfill \\ g_{3} (\varvec{x},t) = T_{w} (w_{1} + w_{3} ) - g_{1} (\varvec{x},t), \hfill \\ g_{5} (\varvec{x},t) = T_{w} (w_{5} + w_{7} ) - g_{7} (\varvec{x},t), \hfill \\ g_{6} (\varvec{x},t) = T_{w} (w_{6} + w_{8} ) - g_{8} (\varvec{x},t). \hfill \\ \end{aligned}$$
(40)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liou, TM., Wei, TC. & Wang, CS. Investigation of nanofluids on heat transfer enhancement in a louvered microchannel with lattice Boltzmann method. J Therm Anal Calorim 135, 751–762 (2019). https://doi.org/10.1007/s10973-018-7299-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-018-7299-3

Keywords

Search

Navigation