Stanton Number and Arbitrary Surface Temperature
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_inT_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_inT_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 
Re: Stanton Number and Arbitrary Surface Temperatu
In my case, St number is St = q_w(x)/(rho*u*dH), where dH= H_inH_w, H is total enthaphy=h + q^2/2. Unless singificantly heating from interior, dH always >0.

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