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Computes the radiative heat flow between two plane surfaces that are separated by a non-absorptive medium.

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Interface

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

using namespace Engineering::Thermodynamics::Radiation;

inline double flow_noshield(double T1, double T2, double e1, double e2)

This module calculates the radiative heat flow per unit surface between two plane surfaces, considering the case when these are separated by a non-absorptive medium.

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

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

(1)

where

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

(2)

with $e_1$ , $e_2$ the emissivity factors of the first and second surface $(0 < e_1, e_2 \leq 1)$ , $C_0$ 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 plane surfaces.

In the diagram below is show the radiative heat transfer between two plane surfaces, in which $E_1$ is the radiative energy emitted by the first surface, $E_2$ is the radiative energy emitted by the second surface, $A_1$ is the energy emitted by the first surface and absorbed by the second, $A_2$ is the energy emitted by the second surface and absorbed by the first, $R_1$ is the radiative energy emitted by the first surface and reflected by the second and $R_2$ is the radiative energy emitted by the second surface and reflected by the first.

Example 1

The example below computes the unit radiative heat flow between an oxidated aluminium plane surface at 873.16 degrees Kelvin and an oxidated copper plane surface at 403.16 degrees Kelvin, separated by a non-absorptive medium.

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

int main()
{
  // the temperature of the oxidated aluminium surface
  double T1 = 873.16;

  // the temperature of the oxidated copper surface
  double T2 = 403.16;

  // the emission factor of the aluminium surface
  double e1 = 0.19;

  // the emission factor of the copper surface
  double e2 = 0.76;

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

  return 0;
}

Output

Radiative heat flow = 5638.04033 W per sq. meter

Parameters

the absolute temperature of the first surface (Kelvin)

the absolute temperature of the second surface (Kelvin)

the emissivity factor of the first surface

the emissivity factor of the second surface

Returns

the radiative heat flow between the two plane surfaces (Watt per square meter)

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"

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