CodeCogs

Computes the radiative heat flow between an enclosing surface and a body found inside it.

Interface

#include <codecogs/engineering/thermodynamics/radiation/flow_enclosed.h>

using namespace Engineering::Thermodynamics::Radiation;

inline double flow_enclosed(double A1, double A2, double T1, double T2, double e1, double e2)

This module calculates the radiative heat flow per unit surface between an enclosing surface and a body found in its interior.

On account of the Stefan-Boltzmann law, the unit radiative heat flow between the two surfaces is given by

$q = e_{1-2} \,\, C_0 \left[\left(\frac{T_2}{100}\right)^4 - \left(\frac{T_1}{100}\right)^4\right] \qquad \left[\frac{W}{m^2}\right]$

(1)

where

$e_{1-2} = \left[\frac{1}{e_1} + \frac{A_1}{A_2}\left(\frac{1}{e_2} - 1\right)\right]^{-1}$

(2)

with $e_1$ , $e_2$ the emissivity factors of the enclosed and enclosing surfaces $(0 < e_1, e_2 \leq 1)$ , $A_1$ , $A_2$ the areas of the enclosed and enclosing surfaces, $C_0$ the emissivity constant of the black body $\displaystyle \left(C_0 \approx 5.669 \left[\frac{W}{m^2 K^4}\right]\right)$ and $T_1$ , $T_2$ the corresponding absolute temperatures of the two surfaces.

In the diagram below is shown the radiative heat transfer between a body of temperature $T_2$ which encloses a body of temperature $T_1 < T_2$ .

Example 1

The example below computes the unit radiative heat flow between an enclosing fire brick surface at 1373.16 degrees Kelvin and a spherical oxidated steel body at 873.16 degrees Kelvin, found in its interior.

#include <codecogs/engineering/heat_transfer/radiation/flow_enclosed.h>
#include <stdio.h>

int main()
{

  // the temperature of the oxidated steel body
  double T1 = 873.16;

  // the temperature of the fire brick surface
  double T2 = 1373.16;

  // the emission factor of the steel body
  double e1 = 0.79;

  // the emission factor of the fire brick surface
  double e2 = 0.75;

  // the area of the spherical steel body
  double A1 = 3.1416;

  // the area of the fire brick enclosing surface
  double A2 = 20;

  // display radiative heat flow between the two enclosed surfaces
  printf("Radiative heat flow = %.5lf W per sq. meter\n",
  Engineering::Heat_Transfer::Radiation::flow_enclosed
  (A1, A2, T1, T2, e1, e2));

  return 0;
}

Output

Radiative heat flow = 127904.73453 W per sq. meter

Parameters

the area of the enclosed body (square meter)

the area of the enclosing surface (square meter)

the absolute temperature of the enclosed body (Kelvin)

the absolute temperature of the enclosing surface (Kelvin)

the emissivity factor of the enclosed body

the emissivity factor of the enclosing surface

Returns

the radiative heat flow between the enclosing surface and the body found in its interior

A table with the emissivity factors of various materials at different temperatures can be found at the following link http://www.monarchserver.com/TableofEmissivity.pdf

References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

Interactive Calculator

Result –