Small Reynolds Number Flow around Flat Plate

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SUMMARY

The discussion focuses on modeling small Reynolds number flow around a semi-infinite plate using argon gas at 1100 degrees Celsius with a kinematic viscosity of 1.6 cm²/sec and a flow velocity of 10 cm/s. The user seeks an expression for the thickness of the viscous region as a function of position from the leading edge, noting that the Blasius solution is not applicable due to Reynolds numbers ranging from less than 1 to approximately 60. The conversation emphasizes the need for alternative analytical methods suitable for low Reynolds number scenarios.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically laminar flow.
  • Familiarity with Reynolds number calculations and significance.
  • Knowledge of kinematic viscosity and its impact on flow behavior.
  • Basic analytical modeling techniques in fluid mechanics.
NEXT STEPS
  • Research analytical solutions for small Reynolds number flow, such as the Stokes flow equations.
  • Explore the concept of boundary layer theory in low Reynolds number contexts.
  • Study the effects of fluid properties on flow characteristics, particularly for argon gas.
  • Investigate numerical simulation tools like ANSYS Fluent for modeling viscous flow scenarios.
USEFUL FOR

This discussion is beneficial for fluid mechanics researchers, chemical engineers, and anyone involved in modeling low Reynolds number flows, particularly in applications involving gases like argon.

uby
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Hello,

I have a problem I am trying to model analytically (please note: I am NOT a fluid mechanics expert -- I come from a chemistry background):

A semi-infinite plate is oriented axially in the direction of flow.

Please refer to the following page for an illustration of my problem:
http://www.ecourses.ou.edu/cgi-bin/eBook.cgi?doc=&topic=fl&chap_sec=09.3&page=theory

The third picture is the Blasius solution, which does not apply at small Reynolds numbers. I am looking for an expression to tell me the thickness of the shaded viscous region from the top two pictures (i.e. - for small Reynolds numbers!) as function of position from the leading edge.

Any references would be appreciated.

Thanks!
 
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What is the fluid, it's velocity and the size of the plate?
 
hi RTW:

the fluid is argon at 1100 degrees celsius (kinematic viscosity 1.6 cm^2/sec) , traveling at 10 cm/s over a square rod (0.635x0.635cm, ~10cm length)

based on these values, i expect the reynolds number to vary from < 1 near the leading edge to ~60 far from the leading edge.

the blasius solution is only valid for reynolds numbers greater than about 1000, so i feel safe in assuming that it doesn't apply.
 

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