Laminar air flow in a 2D channel
Hello dears,
I have a problem, I am doing simulation of a laminar airflow in a 2D channel which is from an article but I cannot reach the desired results. I don't know where the problem exists. could anybody help me as it's urgent. Thank you channel: 20mm (H) x 40mm (L) 100<Re<600 Dh (hydraulic diameter)= 40mm T inlet=300K T wall=330K (const.) the Nu number obtained in the article is around 7.54 from Re=100 to Re=600 the friction factor in the article would decrease with the increase in Re number it is written in the article that the flow is a constant mass flow rate but it has not talked about the 3rd dimension of the channel in order to obtain mass flow rate. also it has not talked about the entrance length which causes the flow to be fully developed. 
Hi Adel,
Be more specific, What is the problem exactly? What boundary conditions do you use? About the mass flow rates; You can calculate the velocity entering channel by the values of the total pressure and mass flow rates. Then setup your boundary conditions as pressure inlet and outlet ( regarding to have a friction loss in your case, you will be able to calculate the pressure drop). By initializing the solution, the solver will calculate the inlet and outlet velocity as desired. Regards. 
Hi vicarious,
Thank you for your concern my case consists of 2 parts: 1st: laminar 2D airflow in a smooth channel in which the upper and lower walls are at constant temperatures (330 K) and the inlet temperature is 300 K. I can use Re= (ρuD_h)/μ to find the inlet velocity or use mdot=ρuA_c to obtain mass flow rate. but to obtain the mass flow rate with this formula, the crosssection area should be known which is the area normal to the flow direction but it is not mentioned in the article. I decided to use velocity inlet. but the entrance length should be known for a flow to be fully developed. with the formula, l=0.05*Re*D_h=1200mm but the results of the FLUENT software is totally different with the ones from the article. (in the article for smooth channel: Nu≈7.54 for Re=100 to 600 and f decreases from around 0.1 at Re=100 to around 0.14 at Re=600 
None of your dimensions are determined in your article? height and depth? In that case mass flow or velocity do not help. You have to have at least one of the dimensions, otherwise you need to have the inlet total and static pressure and outlet static pressure so you do not need velocity in this case. Maybe somewhere in the article, the operating pressure and pressure drop are mentioned. I also suppose the entrance correlation is proximate formula for calculating the hydraulic diameter, that's why it does not give the correct answer.

it has given the dimensions as I wrote above: 20mm (H) x 40mm (L)
The operating pressure is atmospheric pressure(101Kpa) the gauge pressure at the outlet is 0 
Since you have airflow through the channel and D_h is determined, so you can calculate the velocity by the same Re formula, then calculate the dynamic pressure (P_v=0.5*ρ*u*u). then you will have the static pressure (P_s=P_total  P_v). Enter these parameters as pressure inlet and outlet and you do not need the velocity and mass flow anymore, the solver will calculate it itself.

Thank you very much
but I can use VELOCITY INLET for the inlet boundary condition, can't I? another problem is the ENTRANCE LENGTH. it is not mentioned in the article and using the formula 0.05*Re*D will not give a good result in fluent. May I have your Email? Thank You 
You are quite welcome.
Velocity boundary is also accessible but the inlet pressure will be unknown, therefore the outlet pressure would be a problem and may cause in reversed flow. You need to put constraints as pressure so the solver will handle it. Regarding to the entrance length, If the article uses the theoretical correlations for boundary layer approach, then all of them are weak solutions. Since the correlation you mentioned is not exact, you can determine it numerically. The boundary layer thickness is where the u(y)=0.99u_freestream. So you can extract the values of your u(y) from simulation and look up for the location where y reaches to the h/2 (h:height). Here is my email : pedram.mojtabavi@gmail.com Best Regards. 
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