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# Nusselt intpipe

Returns the Nusselt number for a fluid going through a pipe.
Controller: CodeCogs

C++

## Nusselt Intpipe

 doubleNusselt_intpipe( double Pr double Gr double Re )[inline]
This module calculates the Nusselt number for a fluid which flows through a pipe, the flow being either laminar or turbulent. The fluid must keep its state of matter during the heat transfer process.

The formulae for each case are given by

${\rm&space;Nu}&space;=&space;0.15&space;{\rm&space;Re}^{0.33}&space;{\rm&space;Pr}^{0.33}&space;&space;({\rm&space;Gr}&space;\cdot&space;{\rm&space;Pr})^{0.1}\qquad&space;\mbox{(laminar&space;case)}$

and

${\rm&space;Nu}&space;=&space;0.021&space;{\rm&space;Re}^{0.8}&space;{\rm&space;Pr}^{0.43}&space;\qquad&space;\mbox{(turbulent&space;case)}$

where $\inline&space;{\rm&space;Re}$ is the Reynolds number, $\inline&space;{\rm&space;Pr}$ is the Prandtl number and $\inline&space;{\rm&space;Gr}$ is the Grashof number of the fluid. If the Reynolds number is less than 2000 the flow is considered laminar, while if it is greater than 4000 the flow is considered turbulent.

In the diagrams below the unit heat flow is shown in the laminar and turbulent regimes.

### Example 1

The following code calculates the Nusselt number for Air at 65 degrees Celsius flowing throug a pipe at 25 degrees with diameter of 0.5 meters. Both the laminar and turbulent cases are considered.
#include <codecogs/engineering/thermodynamics/convection/nusselt_intpipe.h>
#include <stdio.h>

int main()
{
double Pr = 0.70849, Gr = 384057065.8607, Re1 = 800, Re2 = 5100;

printf("\nAir at 65 deg. Celsius\n");
printf("flowing through a pipe at 25 deg. Celsius\n\n");

printf("Re = %.2lf (laminar flow)\n", Re1);
printf("Nu = %.4lf\n\n",
Engineering::Heat_Transfer::Convection::Nusselt_intpipe(Pr, Gr, Re1));

printf("Re = %.2lf (turbulent flow)\n", Re2);
printf("Nu = %.4lf\n\n",
Engineering::Heat_Transfer::Convection::Nusselt_intpipe(Pr, Gr, Re2));

return 0;
}

### Output

Air at 65 deg. Celsius
flowing through a pipe at 25 deg. Celsius

Re = 800.00 (laminar flow)
Nu = 8.4761

Re = 5100.00 (turbulent flow)
Nu = 16.7463

### References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

### Parameters

 Pr the Prandtl number of the fluid Gr the Grashof number of the fluid Re the Reynolds number of the fluid

### Returns

the Nusselt number of the fluid with given parameters

### Authors

Grigore Bentea, Lucian Bentea (November 2006)
##### Source Code

Source code is available when you buy a Commercial licence.

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