Calculation of Nusselt Number

Mondal131211 · October 16, 2018, 03:49

Hi Foamers,

I am working on buoyantSimpleFoam. I have got some results from my simulations. Now I need to calculate the Nusselt Number from my simulations. Can anyone tell me how to calculate Nu number from OpenFOAM simulations?

backscatter · October 16, 2018, 04:37

Hi,
Nusselt number is the ratio of convective and conductive heat transfer. It can be derived from the following two equations
$q' = Q'/A = h(T_{b}-T_{w})------(1)$
where,

heat transfer coeff.,
$T_{b}$ and $T_{w}$ are bulk and wall temperature respectively

$q' = -k(\partial T/\partial x)|_{x=wall}--------(2)$

Equation (1) is specific form of Newtons law of cooling. Equation (2) represents the heat transfer in the boundary layer, which is assumed to be governed by pure conduction.

If we set these two equations equal and reformulate in terms of the definition of Nusselt number, which is

, we get:
$Nu = hL/k = \frac{L(\partial T/\partial x)|_{x=wall}}{(T_{b}-T_{w})}---------(3)$

where

characteristic length of your problem.
Equation (3) is what you need to calculate (for Nu) from your simulation data.

RobertHB · October 16, 2018, 04:57

Quote:

Originally Posted by Mondal131211

Can anyone tell me how to calculate Nu number from OpenFOAM simulations?

I'd recommend Shah & London "Laminar Flow Forced Convection in Ducts" (Link) pg. 108 which details the calculation of the Nusselt number.

Mondal131211 · October 16, 2018, 19:21

Quote:

Originally Posted by halo

Hi,
Nusselt number is the ratio of convective and conductive heat transfer. It can be derived from the following two equations
$q' = Q'/A = h(T_{b}-T_{w})------(1)$
where,

heat transfer coeff.,
$T_{b}$ and $T_{w}$ are bulk and wall temperature respectively

$q' = -k(\partial T/\partial x)|_{x=wall}--------(2)$

Equation (1) is specific form of Newtons law of cooling. Equation (2) represents the heat transfer in the boundary layer, which is assumed to be governed by pure conduction.

If we set these two equations equal and reformulate in terms of the definition of Nusselt number, which is

, we get:
$Nu = hL/k = \frac{L(\partial T/\partial x)|_{x=wall}}{(T_{b}-T_{w})}---------(3)$

where

characteristic length of your problem.
Equation (3) is what you need to calculate (for Nu) from your simulation data.

Hi Halo,
Thank you for your response. Actually, I know the definition for a Nusselt number. I would like to know how to apply it to the OpenFOAM simulation for getting the value. I am trying to calculate the Nu value from a heated wall inside the cavity.

Mondal131211 · October 16, 2018, 19:25

Quote:

Originally Posted by RobertHB

I'd recommend Shah & London "Laminar Flow Forced Convection in Ducts" (Link) pg. 108 which details the calculation of the Nusselt number.

Hi RobertHB,

Thank you for your help to provide important material. Actually, I know the definition for a Nusselt number. I would like to know how to apply it to the OpenFOAM simulation for getting the value. I am trying to calculate the Nu value from a heated wall inside the cavity.

backscatter · October 16, 2018, 19:40

Quote:

Originally Posted by Mondal131211

Hi Halo,
Thank you for your response. Actually, I know the definition for a Nusselt number. I would like to know how to apply it to the OpenFOAM simulation for getting the value. I am trying to calculate the Nu value from a heated wall inside the cavity.

If you just calculate wall temperature gradient then you can easily proceed to compute the nusselt number. To compute the gradient of T at the wall, you can modify wallGradU utility of OpenFOAM to compute wallGradT for you by changing the U by T. Rest of the calculations can also be carried out in any post-processor like paraview.
Also, please see page 28 of this:

http://www.tfd.chalmers.se/~hani/kur...ssonReport.pdf

Mondal131211 · October 16, 2018, 20:17

Quote:

Originally Posted by halo

If you just calculate wall temperature gradient then you can easily proceed to compute the nusselt number. To compute the gradient of T at the wall, you can modify wallGradU utility of OpenFOAM to compute wallGradT for you by changing the U by T. Rest of the calculations can also be carried out in any post-processor like paraview.
Also, please see page 28 of this:

http://www.tfd.chalmers.se/~hani/kur...ssonReport.pdf

Hi Halo,

Thank you. I think this material will help me a lot. If I face any problem I will get back to you soon.

Cheers,
Razon

backscatter · October 16, 2018, 21:11

Quote:

Originally Posted by Mondal131211

Hi Halo,

Thank you. I think this material will help me a lot. If I face any problem I will get back to you soon.

Cheers,
Razon

Razon,

Here is the wallGradT utility that I have modified from wallGradU a long time back. This might help you:

Mondal131211 · November 14, 2018, 20:21

Quote:

Originally Posted by halo

Razon,

Here is the wallGradT utility that I have modified from wallGradU a long time back. This might help you:

Hi Halo,
Thank you for giving me your case file. Anyways, I did all the procedure that you told for calculating Nusselt Number. I also Used your WallGradT file. But when I run wmake then it shows the following (image) error. have you any solution for that?

amdk136 · November 21, 2018, 05:38

Quote:

Originally Posted by Mondal131211

Hi Halo,
Thank you for giving me your case file. Anyways, I did all the procedure that you told for calculating Nusselt Number. I also Used your WallGradT file. But when I run wmake then it shows the following (image) error. have you any solution for that?

I also get this error when I run wmake. I am unsure why that is too. Hoping for a solution!

October 16, 2018, 03:49	Calculation of Nusselt Number	#1
Mondal131211 Member Mondal Join Date: Sep 2018 Location: Canberra ACT Posts: 68 Rep Power: 7	Hi Foamers, I am working on buoyantSimpleFoam. I have got some results from my simulations. Now I need to calculate the Nusselt Number from my simulations. Can anyone tell me how to calculate Nu number from OpenFOAM simulations?

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
[Other] Can't Shake Erros: patch type 'patch' not constraint type 'empty'	BrendaEM	OpenFOAM Meshing & Mesh Conversion	12	April 3, 2022 18:32
decomposePar -allRegions	stru	OpenFOAM Pre-Processing	2	August 25, 2015 03:58
calculation of average nusselt number along a wall surface	abhishek.iiest	FLUENT	0	June 11, 2015 02:38
DecomposePar unequal number of shared faces	maka	OpenFOAM Pre-Processing	6	August 12, 2010 09:01
Unaligned accesses on IA64	andre	OpenFOAM	5	June 23, 2008 10:37

October 16, 2018, 04:37		#2
backscatter Member Anonymous Join Date: Aug 2016 Posts: 75 Rep Power: 9	Hi, Nusselt number is the ratio of convective and conductive heat transfer. It can be derived from the following two equations $q' = Q'/A = h(T_{b}-T_{w})------(1)$ where, heat transfer coeff., $T_{b}$ and $T_{w}$ are bulk and wall temperature respectively $q' = -k(\partial T/\partial x)\|_{x=wall}--------(2)$ Equation (1) is specific form of Newtons law of cooling. Equation (2) represents the heat transfer in the boundary layer, which is assumed to be governed by pure conduction. If we set these two equations equal and reformulate in terms of the definition of Nusselt number, which is , we get: $Nu = hL/k = \frac{L(\partial T/\partial x)\|_{x=wall}}{(T_{b}-T_{w})}---------(3)$ where characteristic length of your problem. Equation (3) is what you need to calculate (for Nu) from your simulation data.