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EngineeringHeat TransferRadiation

energy

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

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Interface

#include <codecogs/engineering/heat_transfer/radiation/energy.h>

using namespace Engineering::Heat_Transfer::Radiation;

double energy (double T, double e = 1.0)[inline]
Computes the total energy radiated by a body with given parameters.
ExcelReal cc_energy (Real T, Real e)
This function is available as a Microsoft Excel add-in.

Function Documentation

Energy Calculator
  
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doubleenergydoubleT
doublee = 1.0 )[inline]
This module calculates the total energy radiated by a body per unit surface area in unit time.

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

In practice, the following formula due to Kirchoff is used
E_0 = e c_0 \left(\frac{T}{100}\right)^4 \qquad \left[\frac{W}{m^2}\right]
where C_0 is the emissivity constant of the black body \displaystyle \left(C_0 \approx 5.669 \left[\frac{W}{m^2 K^4}\right]\right), e is the emissivity factor of the body (0 < e \leq 1) and 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",
  Engineering::Heat_Transfer::Radiation::energy(T, e)/1000.0);
 
  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:
Tthe absolute temperature of the body (Kelvin)
eDefault 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:

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Page Comments

Conway\′s Photo
15 Dec 09, 8:45PM
Stefan-Boltzmann constant
Regarding equation 2, it is more usual to use the Stefan-Boltzmann constant \sigma = 5.670400\times 10^{-8}~\mathrm{Wm^{-2}K^{-4}} and loose the factor of 100^4 from the temperature term.
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