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Stanton Number and Arbitrary Surface Temperature

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Old   March 8, 2006, 22:36
Default Stanton Number and Arbitrary Surface Temperature
  #1
Boris Vaisman
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Hello everyone,

-- problem --

Please advise, how would you calculate the Stanton Number (St) on flat plate with an arbitrary surface temperature? Per se, if air inlet temperature (T_in) is 1000 and the plate surface (T_w) goes from 500 to 1000.

What is the proper way to calculate St?

-- details --

In general St = q_w(x)/(rho*c_p*u*dT), where: - rho, c_p, and u are evaluated at free stream values - q_w(x) is evaluated at the wall - dT is either a reference value or T_in-T_w(x)

My dilemma is a follows.

(1) If dT is a constant reference value, St would change sign, as T_w changes from T_w<T_in to T_w>T_in. This seems to contradict all definitions of the Reynolds Analogy Factor (R). Consider von Karman or Spalding and Chi, R is always positive and constant or almost constant.

(2) On the other hand, if dT(x)= T_in-T_w(x), there will be a point where q_w(x) changes sign (for the above scenario), but dT(x) has not changed sign yet (for a short distance). This will cause St to explode. This is also problematic.

What is the proper way to calculate St?

----

Thank you very much for your time and help.

Boris Vaisman
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Old   March 9, 2006, 05:43
Default Re: Stanton Number and Arbitrary Surface Temperatu
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versi
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In my case, St number is St = q_w(x)/(rho*u*dH), where dH= H_in-H_w, H is total enthaphy=h + q^2/2. Unless singificantly heating from interior, dH always >0.

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