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energy

Computes the total energy radiated by a body with given parameters.
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C++
Excel

Energy

 doubleenergy( double T double e = 1.0 )[inline]
This module calculates the total energy radiated by a body per unit surface area in unit time.

The total radiative energy $\inline&space;E_0$ of a black body is given by the Stefan-Boltzmann law
$E_0&space;=&space;\int_0^{\infty}&space;I(\lambda)&space;{\rm&space;d}\lambda&space;\qquad&space;\left[\frac{W}{m^2}\right]$
where $\inline&space;I(\lambda)$ is the radiative intensity of the black body.

In practice, the following formula due to Kirchoff is used
$E_0&space;=&space;e&space;c_0&space;\left(\frac{T}{100}\right)^4&space;\qquad&space;\left[\frac{W}{m^2}\right]$
where $\inline&space;C_0$ is the emissivity constant of the black body $\inline&space;\displaystyle&space;\left(C_0&space;\approx&space;5.669&space;\left[\frac{W}{m^2&space;K^4}\right]\right)$, $\inline&space;e$ is the emissivity factor of the body $\inline&space;(0&space;<&space;e&space;\leq&space;1)$ and $\inline&space;T$ is its absolute temperature.

Example 1

The following example calculates the total radiative energy emitted by the Wolfram filament of an incandescent light bulb at 3573.16 degrees Kelvin.
#include <codecogs/engineering/heat_transfer/radiation/energy.h>
#include <stdio.h>

int main()
{
// the temperature of the Wolfram filament
double T = 3573.16;

// emissivity factor of the filament
double e = 0.39;

// display the total radiative energy
printf("Energy = %.5lf kW per sq. meter\n",

return 0;
}

Output

Energy = 3603.96794 kW 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

 T the absolute temperature of the body (Kelvin) e Default value = 1.0

Returns

the total radiative energy emitted by the body (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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