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Returns the Nusselt number for a fluid flowing over a pipe.

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Interface

#include <codecogs/engineering/thermodynamics/convection/nusselt_extpipe.h>

using namespace Engineering::Thermodynamics::Convection;

inline double Nusselt_extpipe(double Pr, double Prw, double Re)

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

${\rm Nu} = 0.5 {\rm Re}^{0.5} {\rm Pr}^{0.38} \left(\frac{\rm Pr}{\rm Pr_w}\right)\right)^{0.25} \qquad \mbox{(laminar case)}$

(1)

and

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

(2)

where ${\rm Re}$ is the Reynolds number, ${\rm Pr}$ is the Prandtl number of the fluid and ${\rm Pr_w}$ 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

Parameters

the Prandtl number of the fluid

Prw

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

the Reynolds number of the fluid

Returns

the Nusselt number of the fluid with given parameters

References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

Interactive Calculator

Prw

Result –