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Engineering › Thermodynamics › Radiation ›

flow noshield

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

Controller: CodeCogs

Contents

Interface
Flow Noshield
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Interface

C++

Excel

Flow Noshield

doubleflow_noshield(	double	`T1`
	double	`T2`
	double	`e1`
	double	`e2`	)[inline]

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

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

(2)

where

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

(3)

with $\inline e_1$ , $\inline e_2$ the emissivity factors of the first and second surface $\inline (0 < e_1, e_2 \leq 1)$ , $\inline C_0$ the emissivity constant of the black body $\inline \displaystyle \left(C_0 \approx 5.669 \left[\frac{W}{m^2 K^4}\right]\right)$ and $\inline T_1$ , $\inline T_2$ 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 $\inline E_1$ is the radiative energy emitted by the first surface, $\inline E_2$ is the radiative energy emitted by the second surface, $\inline A_1$ is the energy emitted by the first surface and absorbed by the second, $\inline A_2$ is the energy emitted by the second surface and absorbed by the first, $\inline R_1$ is the radiative energy emitted by the first surface and reflected by the second and $\inline R_2$ is the radiative energy emitted by the second surface and reflected by the first.

MISSING IMAGE!

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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

Note

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"

Parameters

T1	the absolute temperature of the first surface (Kelvin)
T2	the absolute temperature of the second surface (Kelvin)
e1	the emissivity factor of the first surface
e2	the emissivity factor of the second surface

Returns

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

Authors

Grigore Bentea, Lucian Bentea (November 2006)

Source Code

Source code is available when you buy a Commercial licence.

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