Skip to main content
SpringerLink
Log in

Effects of Knudsen number and geometry on gaseous flow and heat transfer in a constricted microchannel

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

A flow and heat transfer numerical simulation is performed for a 2D laminar incompressible gas flow through a constricted microchannel in the slip regime with constant wall temperature. The effects of rarefaction, creeping flow, first order slip boundary conditions and hydrodynamically/thermally developing flow are assumed. The effects of Knudsen number and geometry on thermal and hydrodynamic characteristics of flow in a constricted microchannel are explored. SIMPLE algorithm in curvilinear coordinate is used to solve the governing equations including continuity, energy and momentum with the temperature jump and velocity slip conditions at the solid walls in discretized form. The resulting velocity and temperature profiles are then utilized to obtain the microchannel C f Re and Nusselt number as a function of Knudsen number and geometry. The results show that Knudsen number has declining effect on the C f Re and Nusselt number in the constricted microchannel. In addition, the temperature jump on wall and slip velocity increase with increasing Knudsen number. Moreover, by decreasing the throttle area, the fluid flow characteristics experience more intense variations in the constricted region. To verify the code a comparison is carried out with available results and good agreement is achieved.

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
Fig. 16
Fig. 17

Similar content being viewed by others

Abbreviations

a :

Amplitude of the wave (m)

k :

Thermal conductivity of air (W/m K)

h :

Local heat transfer coefficient (W/m2 K)

J :

Jacobian of the coordinate transformation

p :

Dimensionless pressure

Re :

Reynolds number (Re = ρu i L */μ)

Pr :

Prandtl number (Pr = ν/α)

Nu :

Local Nusselt number

Nu ∞ :

Fully developed Nusselt number

Kn :

Knudsen number

Ma :

Mach number

Pe :

Peclet number

Ec :

Eckert number

C f :

Skin-friction coefficient

c p :

Specific heat (J/kg K)

n :

Dimensionless normal direction to the wall

s :

Dimensionless tangential direction to the wall

q11, q22, q12:

Grid parameters

R :

Gas constant (J/kg K)

T :

Temperature (K)

q″:

Heat flux

u :

Dimensionless velocity component in x-direction

v :

Dimensionless velocity component in y-direction

L*:

Channel inlet width

x :

Dimensionless horizontal coordinate

y :

Dimensionless vertical coordinate

α :

Thermal diffusivity (m2/s)

λ :

Surface wavelength (m)

ρ :

Density of fluid (kg/m3)

μ :

Dynamic viscosity (kg/m s)

γ :

Ratio of specific heats (cp/cv)

λ :

Molecular mean free path (m)

ν :

Kinematic viscosity (m2/s)

σ T :

Energy accommodation coefficient

σ ν :

Momentum accommodation coefficient

θ :

Dimensionless temperature

ξ :

Curvilinear horizontal coordinate

η :

Curvilinear vertical coordinate

τ :

Shear stress

ave:

Mean value

w :

Surface conditions

i :

Inlet conditions

s :

Fluid property near the wall

C :

Contravariant velocities

tang:

Tangential direction

*:

Returns to dimensional parameters

References

  1. Galvis E, Jubran BA, Xi F, Behdinan K, Fawaz Z (2008) Numerical modeling of pin–fin micro heat exchangers. Heat Mass Transf 44:659–666

    Article  Google Scholar 

  2. Graur IA, Méolans JG, Zeitoun DE (2006) Analytical and numerical description for isothermal gas flows in microchannels. Microfluid Nanofluid 2:64–67

    Article  Google Scholar 

  3. Jiji LM (2008) Effect of rarefaction, dissipation, and accommodation coefficients on heat transfer in microcylindrical couette flow. ASME J Heat Transf 130:385–393

    Article  Google Scholar 

  4. Jie D, Diao X, Cheong KB, Yong LK (2000) Navier–Stokes simulations of gas flow in micro devices. J Micromech Microeng 10:372–379

    Article  Google Scholar 

  5. Chen CS, Kuo WJ (2004) Heat transfer characteristics of gaseous flow in long mini- and microtubes. Numer Heat Transf Part A Appl 46:497–514

    Article  Google Scholar 

  6. Larrode FE, Housiadas C, Dreossinos Y (2000) Slip-flow heat transfer in circular tubes. Int J Heat and Mass Transf 43:2669–2680

    Article  MATH  Google Scholar 

  7. Kavehpour HP, Faghri M, Asako Y (1997) Effects of compressibility and rarefaction on gaseous flows in microchannels. Numer Heat Transf Part A Appl 32:677–696

    Article  Google Scholar 

  8. Dennis SCR, Smith FT (1980) Steady flow through a channel with a symmetrical constriction in the form of a step. Proc R Soc Loud A 372:393–414

    Article  MATH  MathSciNet  Google Scholar 

  9. Vradis G, Zalak V, Bentson J (1992) Simultaneous, variable solutions of the incompressible steady Navier-Stokes equations in general curvilinear coordinate systems. Trans ASME I J Fluids Engng 114:299–305

    Article  Google Scholar 

  10. Wang CC, Chen CK (2004) Forced convection in a wavy-wall channel. Int J Heat Mass Transf 47:3877–3887

    Article  Google Scholar 

  11. Cheng RT-S (1972) Numerical Solution of the Navier-Stokes Equations by the Finite Element Method. Phys Fluids 15:2098–2105

    Article  MATH  Google Scholar 

  12. Deshpande MD, Giddens DP, Mabon RF (1976) Steady laminar flow through modelled vascular stenoses. J Biomech 9:165–174

    Article  Google Scholar 

  13. Ahmed SA, Giddens DP (1983) Flow disturbance measurements through a constricted tube at moderate Reynolds number. J Biomech 16:955–963

    Article  Google Scholar 

  14. Arkilic EB, Breuer KS, Schmidt MA (1994) Gaseous flow in microchannels. ASME Appl Microfabrication Fluid Mech 197:57–66

    Google Scholar 

  15. Harley JC, Huang Y, Bau HH, Zemel JN (1995) Gas flow in micro-channels. J Fluid Mech 284:257–274

    Article  Google Scholar 

  16. Beskok A, Karniadakis GE, Trimmer W (1996) Rarefaction and compressibility effects in gas microflows. ASME J Fluids Eng 118:448–456

    Article  Google Scholar 

  17. Chen CK, Cho CC (2007) Electro-kinetically-driven flow mixing in microchannels with wavy surface. J Colloid Interf Sci 312:470–480

    Article  Google Scholar 

  18. Kennard EH (1938) Kinetic theory of gasses. McGraw-Hill, New York

    Google Scholar 

  19. Gombosi TI (1994) Gas kinetic theory. Cambridge University Press, New York

    Google Scholar 

  20. Gad-el-Hak M (2002) The MEMS Handbook, CRC Press LLC, Boca Raton

  21. Karniadakis GE, Beskok A, Aluru N (2004) Micro flows and nanoflows fundamental and simulation. Springer, USA

    Google Scholar 

  22. Kandlikar S, Garimella S, Li D, Colin S, King MR (2006) Heat transfer and fluid flow in minichannels and microchannels, Elsevier, Britain

  23. Liou WW, Fang Y (2006) Microfluid mechanics principal and modeling. McGraw-Hill, New York

    Google Scholar 

  24. Morini GL, Spiga M, Tartarini P (2004) The rarefaction effect on the friction factor of gas flow in microchannels. Superlattices and microstructures 35:587–599

    Article  Google Scholar 

  25. van Rij J, Ameel T, Harman T (2009) The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer. Int J Therm Sci 48:271–281

    Article  Google Scholar 

  26. Patankar SV (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transf 15:1787–1806

    Article  MATH  Google Scholar 

  27. Spalding DB (1972) A novel finite difference formulation for differential expressions involving both first and second derivatives. Int J Numer Methods Eng 4:551–559

    Article  Google Scholar 

  28. Hoffman KA (1989) Computational fluid dynamics for engineers. Eng Educ Sys, Austin

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Tehran, Tehran, Iran

    Hossein Shokouhmand, Sajjad Bigham & Rasool Nasr Isfahani

Authors
  1. Hossein Shokouhmand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sajjad Bigham
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rasool Nasr Isfahani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sajjad Bigham.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shokouhmand, H., Bigham, S. & Nasr Isfahani, R. Effects of Knudsen number and geometry on gaseous flow and heat transfer in a constricted microchannel. Heat Mass Transfer 47, 119–130 (2011). https://doi.org/10.1007/s00231-010-0674-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-010-0674-7

Keywords

Search

Navigation