flow — Convection

Calculates the convective heat flow per unit area of a fluid.

Interface

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

using namespace Engineering::Thermodynamics::Convection;

double flow(double lambda, double L, double dT, double Nu)

This module computes the convective heat flow per unit area of a fluid either going over a flat surface, over the exterior surface of a pipe or going through a pipe. It is recommended that one uses this module in combination with either one of the following components: Nusselt_flat, Nusselt_extpipe or Nusselt_intpipe.

Generally speaking the convective heat flow per unit area is given by the formula

$$q = \frac{\lambda}{L}{\rm Nu} \Delta T \qquad \left[\frac{W}{m^2}\right]$$

(1)

where ${\rm Nu}$ is the Nusselt number of the fluid, $\lambda$ is its thermal conductivity, $L$ is the characteristic length and $\Delta T$ is the temperature difference between the fluid and the wall.

Example 1

The following example calculates the convective unit heat flow for air at 25 degrees Celsius going through a pipe at 15 degrees Celsius with a diameter of 0.1 meters. First the Nusselt number is calculated using the Nusselt_intpipe module, then the heat flow is determined based on this value.

#include <codecogs/engineering/thermodynamics/convection/nusselt_intpipe.h>
#include <codecogs/engineering/thermodynamics/convection/flow.h>
#include <stdio.h>
 
int main()
{
  // constants of the problem
  double Pr = 0.71465, Gr = 1356596.6005, 
  lambda = 0.025969, L = 0.1, dT = 10;
 
  printf("\nAir at 25 deg. Celsius\n");
  printf("flowing through a pipe at 15 deg. Celsius\n\n");
 
  double Re1 = 800;
  printf("  Re = %.2lf (laminar flow)\n", Re1);

  // compute Nusselt number in the case Re = 800
  double Nu1 = 
  Engineering::Thermodynamics::Convection::Nusselt_intpipe(Pr, Gr, Re1);
  printf("  Nu = %.4lf\n", Nu1);

  // display the unit heat flow
  printf("Flow = %.4lf (W/sq. meters)\n\n",
  Engineering::Thermodynamics::Convection::flow(lambda, L, dT, Nu1));
 
  double Re2 = 5100;
  printf("  Re = %.2lf (turbulent flow)\n", Re2);

  // compute Nusselt number in the case Re = 5100
  double Nu2 =
  Engineering::Thermodynamics::Convection::Nusselt_intpipe(Pr, Gr, Re2);
  printf("  Nu = %.4lf\n", Nu2);

  // display the unit heat flow
  printf("Flow = %.4lf (W/sq. meters)\n\n",
  Engineering::Thermodynamics::Convection::flow(lambda, L, dT, Nu2));
 
  return 0;
}

Output

Air at 25 deg. Celsius
going through a pipe at 15 deg. Celsius

  Re = 800.00 (laminar flow)
  Nu = 4.8374
Flow = 12.5624 (W/sq. meters)

  Re = 5100.00 (turbulent flow)
  Nu = 16.8088
Flow = 43.6507 (W/sq. meters)

Parameters

lambda

the thermal conductivity of the fluid (Watt per meters Kelvin)

the characteristic length (meters)

the temperature difference (Kelvin)

the Nusselt number of the fluid

Returns

the convective heat flow per unit area of a fluid with given parameters (Watt per square meters)

References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

Interactive Calculator

lambda

Result –