Heat and Mass Transfer

, Volume 47, Issue 2, pp 119–130 | Cite as

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

  • Hossein Shokouhmand
  • Sajjad BighamEmail author
  • Rasool Nasr Isfahani


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.


Nusselt Number Slip Velocity Knudsen Number Local Nusselt Number Temperature Jump 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Amplitude of the wave (m)


Thermal conductivity of air (W/m K)


Local heat transfer coefficient (W/m2 K)


Jacobian of the coordinate transformation


Dimensionless pressure


Reynolds number (Re = ρu i L */μ)


Prandtl number (Pr = ν/α)


Local Nusselt number


Fully developed Nusselt number


Knudsen number


Mach number


Peclet number


Eckert number


Skin-friction coefficient


Specific heat (J/kg K)


Dimensionless normal direction to the wall


Dimensionless tangential direction to the wall

q11, q22, q12

Grid parameters


Gas constant (J/kg K)


Temperature (K)


Heat flux


Dimensionless velocity component in x-direction


Dimensionless velocity component in y-direction


Channel inlet width


Dimensionless horizontal coordinate


Dimensionless vertical coordinate

Greek symbols


Thermal diffusivity (m2/s)


Surface wavelength (m)


Density of fluid (kg/m3)


Dynamic viscosity (kg/m s)


Ratio of specific heats (cp/cv)


Molecular mean free path (m)


Kinematic viscosity (m2/s)


Energy accommodation coefficient


Momentum accommodation coefficient


Dimensionless temperature


Curvilinear horizontal coordinate


Curvilinear vertical coordinate


Shear stress



Mean value


Surface conditions


Inlet conditions


Fluid property near the wall



Contravariant velocities


Tangential direction


Returns to dimensional parameters


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Hossein Shokouhmand
    • 1
  • Sajjad Bigham
    • 1
    Email author
  • Rasool Nasr Isfahani
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of TehranTehranIran

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