Average Nusselt number or heat transfer coefficient to compare better heat transfer?

Moreza7 · September 8, 2019, 16:15

I'm simulating different arrays for cylinders in a simple cross flow heat exchanger (cylindrical pipes) as shown below:

Inlet temperate(300K) is constant and the cylinders are at constant temperature(400K).

I've calculated average Nusselt on each pipe then summed all of them and finally divided it by the number of cylinders (9).

This gives me an average Nusselt number for heat exchanger. Let's call it $Nu_{av}$ .
$Nu_{av}=\frac{\sum Nu_{cylinder}}{9}$

I also calculated the heat transfer coefficient of heat exchanger using the following equation:

$\dot{m}c(T_o-T_i)=UA(T_s-T_i)$

$\dot{m}$ : Mass flow of fluid passing the heat exchanger

: Specific heat of fluid

: Average outlet temperature

: Average inlet temperature

: Heat exchanger coefficient

: Total surface of all cylinders

: Cylinders surface temperature

I've simulated a lot of arrays. In some cases, the average Nusselt number( $Nu_{av}$ ) is bigger and in some others, the average outlet temperature and so, the heat exchanger coefficient(

) is bigger.

My question is: Which one should be my criteria to compare cases? Average Nusselt number or heat exchanger coefficient?

evcelica · September 24, 2019, 15:55

Something tells me you are calculating something wrong. These values shouldn't be going back and forth, they should agree with each other. U should equal Nu*k.

How are you calculating Nusselt number?
How are you calculating outlet temperature? You would want the mass flow average of temperature, not area average, or nodal average.

How do these values compare with total heat transferred? Which should be easy to get, and the most important I would think. But they should all match performance wise.

Moreza7 · September 24, 2019, 17:02

Quote:

Originally Posted by evcelica

Something tells me you are calculating something wrong. These values shouldn't be going back and forth, they should agree with each other. U should equal Nu*k.

How are you calculating Nusselt number?
How are you calculating outlet temperature? You would want the mass flow average of temperature, not area average, or nodal average.

How do these values compare with total heat transferred? Which should be easy to get, and the most important I would think. But they should all match performance wise.

Thank you! I used area average instead of mass flow average! Now by using mass flow average outlet temperature the results are better ,but still in some cases, the problem exists!
Can you tell me how can I get total heat transfered?
Is it $\dot{m}c(T_o-T_i)$ or you mean something else?

About Nusselt calculation:

For each cylinder we have:
$Nu_\theta=\frac{hD}{k}$

Also, we have:
$-k\frac{dT}{dn}=h(T_s-T_i)$

is the direction which is normal to the curve.

Using second equation and rewriting first equation yields:
$Nu_\theta=\frac{dT}{dn}\frac{D}{T_i-T_s}$

So, the average Nusselt Number on each cylinder is: (Line average)
$\overline{Nu_\theta}=\frac{1}{\pi D}\oint{\frac{dT}{dn}\frac{D}{T_i-T_s}ds}$

evcelica · October 8, 2019, 16:15

Total Heat Transferred can be obtained many ways

= areaInt(Wall Heat Flux)@CylinderSurface
Or check the .out file, and that should give you your boundary data at the end.
Or m.dot * cp * (massFlowAve(T)@Outlet - massFlowAve(T)@Inlet)

I know the definition/derivation of Nusselt. But I still don't get how you are actually calculating it, using what CEL expression exactly?
Have you looked in the FAQ's in the wiki page?
https://www.cfd-online.com/Wiki/Ansy...ficient_in_CFX

Moreza7 · October 8, 2019, 17:20

Quote:

Originally Posted by evcelica

Total Heat Transferred can be obtained many ways

= areaInt(Wall Heat Flux)@CylinderSurface
Or check the .out file, and that should give you your boundary data at the end.
Or m.dot * cp * (massFlowAve(T)@Outlet - massFlowAve(T)@Inlet)

I know the definition/derivation of Nusselt. But I still don't get how you are actually calculating it, using what CEL expression exactly?
Have you looked in the FAQ's in the wiki page?
https://www.cfd-online.com/Wiki/Ansy...ficient_in_CFX

Thank you.
COMSOL gives derivatives at any direction + gradient magnitude!

evcelica · October 15, 2019, 08:50

Those gradients might not be best suited for your needs. Especially if you are using wall functions, and not fully integrating to the wall to calculate heat transfer. It may be giving you a nodal/cell gradient, and not a wall function gradient. I would use a different method than the gradient method.

September 8, 2019, 16:15	Average Nusselt number or heat transfer coefficient to compare better heat transfer?	#1
Moreza7 Senior Member Join Date: Jan 2018 Posts: 121 Rep Power: 8	I'm simulating different arrays for cylinders in a simple cross flow heat exchanger (cylindrical pipes) as shown below: Inlet temperate(300K) is constant and the cylinders are at constant temperature(400K). I've calculated average Nusselt on each pipe then summed all of them and finally divided it by the number of cylinders (9). This gives me an average Nusselt number for heat exchanger. Let's call it $Nu_{av}$ . $Nu_{av}=\frac{\sum Nu_{cylinder}}{9}$ I also calculated the heat transfer coefficient of heat exchanger using the following equation: $\dot{m}c(T_o-T_i)=UA(T_s-T_i)$ $\dot{m}$ : Mass flow of fluid passing the heat exchanger : Specific heat of fluid : Average outlet temperature : Average inlet temperature : Heat exchanger coefficient : Total surface of all cylinders : Cylinders surface temperature I've simulated a lot of arrays. In some cases, the average Nusselt number( $Nu_{av}$ ) is bigger and in some others, the average outlet temperature and so, the heat exchanger coefficient() is bigger. My question is: Which one should be my criteria to compare cases? Average Nusselt number or heat exchanger coefficient?

September 24, 2019, 15:55		#2
evcelica Senior Member Erik Join Date: Feb 2011 Location: Earth (Land portion) Posts: 1,167 Rep Power: 23	Something tells me you are calculating something wrong. These values shouldn't be going back and forth, they should agree with each other. U should equal Nu*k. How are you calculating Nusselt number? How are you calculating outlet temperature? You would want the mass flow average of temperature, not area average, or nodal average. How do these values compare with total heat transferred? Which should be easy to get, and the most important I would think. But they should all match performance wise. Moreza7 likes this.

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October 8, 2019, 16:15		#4
evcelica Senior Member Erik Join Date: Feb 2011 Location: Earth (Land portion) Posts: 1,167 Rep Power: 23	Total Heat Transferred can be obtained many ways = areaInt(Wall Heat Flux)@CylinderSurface Or check the .out file, and that should give you your boundary data at the end. Or m.dot * cp * (massFlowAve(T)@Outlet - massFlowAve(T)@Inlet) I know the definition/derivation of Nusselt. But I still don't get how you are actually calculating it, using what CEL expression exactly? Have you looked in the FAQ's in the wiki page? https://www.cfd-online.com/Wiki/Ansy...ficient_in_CFX

October 15, 2019, 08:50		#6
evcelica Senior Member Erik Join Date: Feb 2011 Location: Earth (Land portion) Posts: 1,167 Rep Power: 23	Those gradients might not be best suited for your needs. Especially if you are using wall functions, and not fully integrating to the wall to calculate heat transfer. It may be giving you a nodal/cell gradient, and not a wall function gradient. I would use a different method than the gradient method.