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# Nusselt extpipe

Returns the Nusselt number for a fluid flowing over a pipe.
Controller: CodeCogs  C++

## Nusselt Extpipe

 doubleNusselt_extpipe( double Pr double Prw double Re )[inline]
This module calculates the Nusselt number of a fluid which flows over 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 Nu} = 0.5 {\rm Re}^{0.5} {\rm Pr}^{0.38} \left(\frac{\rm Pr}{\rm Pr_w}\right)\right)^{0.25} \qquad \mbox{(laminar case)}

and

{\rm Nu} = 0.25 {\rm Re}^{0.6} {\rm Pr}^{0.38} \left(\frac{\rm Pr}{\rm Pr_w}\right)\right)^{0.25} \qquad \mbox{(turbulent case)}

where is the Reynolds number, is the Prandtl number of the fluid and is the Prandtl number of the fluid at the temperature of the pipe wall. 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 Water at 50 degrees Celsius flowing over a pipe at 20 degrees Celsius, considering both the laminar and turbulent cases.
#include <codecogs/engineering/thermodynamics/convection/nusselt_extpipe.h>
#include <stdio.h>

int main()
{
double Pr = 0.71977, Prw = 6.5870, Re1 = 1300, Re2 = 6000;

printf("\nWater at 50 deg. Celsius\n");
printf("flowing over a pipe at 20 deg. Celsius\n\n");

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

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

return 0;
}

### Output

Water at 50 deg. Celsius
flowing over a pipe at 20 deg. Celsius

Re = 1300.00 (laminar flow)
Nu = 9.1475

Re = 6000.00 (turbulent flow)
Nu = 23.4526

### References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

### Parameters

 Pr the Prandtl number of the fluid Prw the Prandtl number of the fluid at the temperature of the wall 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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