Sieder Tate equation

ilsaggio · January 6, 2020, 10:01

Hello everyone

I am carrying out the simulation of a laminar flow within a duct of triangular section (equilateral of 12mm side) long L = 0.8m, with the walls heated from the beginning with a thermal flow of 37.5Wm2. the fluid inside the duct is air with a speed of 1 m / s. Calculating Reynolds I find that the outflow is laminar.
Now I am calculating the average Nusselt and to do this I use the Sieder Tate equation for the laminar outflow within ducts:
Nu_D =1.86* (Re_D*Pr/(L/D))^1/3*(μ/μ_p)^0,14

I don't know what μ_p is like, can someone help me?

LuckyTran · January 6, 2020, 12:16

The μ in the numerator is the viscosity at the bulk temperature. The μ in the denominator is evaluated at the wall temperature.

But why are you calculating a Nusselt number from an empirical correlation? Just for academic curiosity or comparison purposes? Because Nusselt number readily comes from the CFD simulation.

ilsaggio · January 6, 2020, 12:52

first of all thank you. Because I have to write a report and I want to verify that the nusselt number that I get with the simulation is close to that obtained with the Sieder Tate equation. I have all the data but I don't know how to calculate μ_p, is there a way to get it?

LuckyTran · January 6, 2020, 23:04

If you can evaluate μ then you can evaluate μ_p. Why are you only having trouble with μ_p and not μ?

Your equation of state for viscosity is one of the user inputs. All you need is to find the bulk temperature from the CFD and the wall temperature from the CFD. Then put these temperatures into the equation of state for viscosity using your smartphone, excel, calculator, whatever. This is trivial if the bulk temperature and wall temperature are constant. If they are locally varying, then you end up with a locally varying variant of each.

January 6, 2020, 10:01	Sieder Tate equation	#1
ilsaggio New Member marko seggio Join Date: Dec 2019 Posts: 3 Rep Power: 6	Hello everyone I am carrying out the simulation of a laminar flow within a duct of triangular section (equilateral of 12mm side) long L = 0.8m, with the walls heated from the beginning with a thermal flow of 37.5Wm2. the fluid inside the duct is air with a speed of 1 m / s. Calculating Reynolds I find that the outflow is laminar. Now I am calculating the average Nusselt and to do this I use the Sieder Tate equation for the laminar outflow within ducts: Nu_D =1.86* (Re_DPr/(L/D))^1/3(μ/μ_p)^0,14 I don't know what μ_p is like, can someone help me?

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January 6, 2020, 12:16		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,675 Rep Power: 66	The μ in the numerator is the viscosity at the bulk temperature. The μ in the denominator is evaluated at the wall temperature. But why are you calculating a Nusselt number from an empirical correlation? Just for academic curiosity or comparison purposes? Because Nusselt number readily comes from the CFD simulation.

January 6, 2020, 12:52		#3
ilsaggio New Member marko seggio Join Date: Dec 2019 Posts: 3 Rep Power: 6	first of all thank you. Because I have to write a report and I want to verify that the nusselt number that I get with the simulation is close to that obtained with the Sieder Tate equation. I have all the data but I don't know how to calculate μ_p, is there a way to get it?

January 6, 2020, 23:04		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,675 Rep Power: 66	If you can evaluate μ then you can evaluate μ_p. Why are you only having trouble with μ_p and not μ? Your equation of state for viscosity is one of the user inputs. All you need is to find the bulk temperature from the CFD and the wall temperature from the CFD. Then put these temperatures into the equation of state for viscosity using your smartphone, excel, calculator, whatever. This is trivial if the bulk temperature and wall temperature are constant. If they are locally varying, then you end up with a locally varying variant of each.