1. Radiative Heat Flux Distribution inside a Highly Reflective Tube
Cosmin DAN, Gilbert DE MEY, Erik DICK

2. Overview Introduction Net radiation method and implementation
Validation of the numerical solution
Experimental measurements
Results
Conclusions

3. Introduction The heat transfer phenomena (radiative);
How well a real body radiates energy as compared with a blackbody;
Emissivity is a material property depending on: body temperature, wavelength of the emitted energy, angle of emission;
The emissivity is determined using experimental measurements;
Combined measured data with numerical computation software

4. The net radiation method and implementation
The cavity is divided in small areas in which:
The surfaces are isothermal
The surfaces are diffuse emitters and reflectors
The surfaces are gray

5. The net radiation method and implementation
Two energy balance equations
-Gaussian elimination
-configuration factors computation

6. The net radiation method and implementation

7. The net radiation method and implementation
The configuration factors:

8. The net radiation method and implementation
The configuration factors:

9. Validation of the numerical solution
R. Siegel, J. R. Howell, “Thermal Radiation Heat Transfer”, 1992
C. M. Usiskin, R. Siegel, “Thermal Radiation From a Cylindrical Enclosure With Specified Wall Heat Flux”, Journal of Heat Transfer, Vol. 82, No. 4, pp ,1960
approximate analytical solution
Kernel approximated with an exponential e-2z
Variational methods

10. Validation of the numerical solution

11. Validation of the numerical solution
Cylinder with open ends
Uniform heated q(z)=const.
L-dimensionless length
Relative difference < 3%
Approximate analytical formula:

12. Validation of the numerical solution
Cylinder with open ends
Uniform heated q(z)=const.
L-dimensionless length
Relative difference <2.5%
Results obtained with formula
using variational methods

13. Experimental measurements
Infrared scanner, from the Thermovision® 900 series
Measurements in short wavebands with a spectral response of microns
The accuracy of the measurement with the thermographic camera is ±1°C
The repeatability is ±0.5°C
The collected data with the scanner are processed by the ERIKA software
All undesired radiation quantities that appear in the measurements are compensated by the software
The result of the measurements is a temperature depending only by the radiation emitted by the object

14. Experimental measurements

15. Experimental measurements

16. Results

17. Results

18. Results

19. Results

20. Results

21. Conclusions
Software to compute the heat flux distribution and the apparent temperature along cylindrical enclosures
Measurements were carried out using a thermographic scanner
The emissivity of the inner surface of the tube has been determined in an easy way
One of the weaknesses of the proposed method is that in the simulation was assumed that no heat transfer by conduction and convection occur

22. Thank You!