How to calculate Nusselt number

SeRGeiSarov · May 4, 2009, 11:57

Hello I need to calculate the Nusselt number for liquid sodium in a pipeline. Length of the pipeline is 3 meter. Diameter of the pipeline is 0.3 meter. Heat flux through outer surface of the pipeline is equal zero. Temperature on the right side and left side of the pipeline is 573 K and 773 K, respectively. Solution of the problem is free convective heat transfer.

Nu= $\lambda_{eff}$ / $\lambda$

$\lambda$ is heat flux coefficient for liquid sodium at 673 K (average temperature)
$\lambda_{eff}$ is effective heat flux coefficient including effect of free convective heat transfer. $\lambda_{eff}$ =Q $\delta$ /S $\Delta$ T

Q is heat flux through surface
$\delta$ is the length
S is cross sectional area of the pipe
$\Delta$ T is temperature difference (200 K)

Which the surface have be used for calculation of Q? (the right side, the left side, the outer surface) How to calculate Nusselt number?

TIA

Ahmed · May 4, 2009, 14:13

The Nu number, by definition, is a non dimensional heat transfer coefficient, in your case, you stated the outer surface of the pipe is adiabatic, so there is no heat transfer there.
Could you check your problem statement

SeRGeiSarov · May 5, 2009, 01:55

Quote:

Originally Posted by Ahmed

The Nu number, by definition, is a non dimensional heat transfer coefficient, in your case, you stated the outer surface of the pipe is adiabatic, so there is no heat transfer there.
Could you check your problem statement

In problem statement it is written that Nu= $\lambda_{eff}$ / $\lambda$

Ahmed · May 5, 2009, 21:38

Quote:

Originally Posted by SeRGeiSarov

Heat flux through outer surface of the pipeline is equal zero. Temperature on the right side and left side of the pipeline is 573 K and 773 K, respectively. Solution of the problem is free convective heat transfer.

TIA

1- The sodium enters at 773K and leaves at 573K
2- Heat flux through outer surface is equal zero
This is your problem statement, so what causes this temperature drop

SeRGeiSarov · May 6, 2009, 01:57

Quote:

Originally Posted by Ahmed

1- The sodium enters at 773K and leaves at 573K
2- Heat flux through outer surface is equal zero
This is your problem statement, so what causes this temperature drop

The pipe is insulated. There is boyuancy driven flow. On the left side and the right side only heat flux is set (temperature). Problem is solved into the pipe.

May 4, 2009, 11:57	How to calculate Nusselt number	#1
SeRGeiSarov New Member Sergey Malashenko Join Date: May 2009 Posts: 5 Rep Power: 16	Hello I need to calculate the Nusselt number for liquid sodium in a pipeline. Length of the pipeline is 3 meter. Diameter of the pipeline is 0.3 meter. Heat flux through outer surface of the pipeline is equal zero. Temperature on the right side and left side of the pipeline is 573 K and 773 K, respectively. Solution of the problem is free convective heat transfer. Nu= $\lambda_{eff}$ / $\lambda$ $\lambda$ is heat flux coefficient for liquid sodium at 673 K (average temperature) $\lambda_{eff}$ is effective heat flux coefficient including effect of free convective heat transfer. $\lambda_{eff}$ =Q $\delta$ /S $\Delta$ T Q is heat flux through surface $\delta$ is the length S is cross sectional area of the pipe $\Delta$ T is temperature difference (200 K) Which the surface have be used for calculation of Q? (the right side, the left side, the outer surface) How to calculate Nusselt number? TIA

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May 4, 2009, 14:13		#2
Ahmed Senior Member Ahmed Join Date: Mar 2009 Location: NY Posts: 251 Rep Power: 18	The Nu number, by definition, is a non dimensional heat transfer coefficient, in your case, you stated the outer surface of the pipe is adiabatic, so there is no heat transfer there. Could you check your problem statement