1. Apparent Emissivity in the Base of a Cone Cosmin DAN, Gilbert DE MEY University of Ghent Belgium

2. Overview 1.Introduction 2.Description of the problem 3.Configuration factors computation 4.Apparent emissivity computation 5.Genetic algorithms (GA) 6.Results 7.Conclusions

3. Introduction Why to calculate the apparent emissivity? -Build a black-body -What kind of shapes has usually a black body -Find the optimal shape -Solve the radiative energy balance equations -Write a computer program for apparent emissivity computation -Use a genetic algorithm optimization method

4. Description of the problem Circular cavities –Diffuse-gray surfaces –Known distribution of the temperature –Only radiative heat transfer –Known inner walls emissivity not depending on temperature –Known geometrical dimensions –Unknown apparent emissivity

5. Description of the problem

6. The boundary integral equation

7. Description of the problem The net radiation method

8. Description of the problem The net radiation method –Gauss elimination method

9. Configuration factors computation

11. Apparent emissivity –Radiative heat flux leaving the cavity –Radiative heat flux that would leave the cavity if it were a blackbody –Computation of the total heat flux for different particular cases with specified temperature –Find the highest value for apparent emissivity Same length Same open area Different shapes for cavity

12. Genetic algorithms –System for function optimisation –Adaptive search – iterative procedures –Variables = structures x i, population –Vector of parameters to the objective function

13. Genetic algorithms

14. Two steps to create a new population –Selection of the best members for replication –Alteration of the selected members using genetic operators: Crossover –Two parents → two offspring's –100011001111 and 011100110011 → 100011000011 and 011100111111 Mutation –Alteration of one ore more bites in parent structure –100011001111 → 100010001111

15. Genetic algorithms

16. Termination criteria: Acceptable approximate solution Fixed total number of evaluations

17. Results

18. Configuration factors from each surface to the open area: –Disk-to-disk method –Monte Carlo integration method Configuration factors from each surface to all the others surfaces –Formula for differential configuration factors between two ring elements –The approximated formula e -2z

19. Results

27. L=z 3 =30 cm; 0 ≤ z 1 ≤ L; ε wall =0.9 R 1 =R 2 =15 cm ε app =0.971 for z 1 =0.91 cm R 1 =R 2 =5 cm ε app =0.975 for z 1 =0.01 cm L=z 2 =z 3 =z 4 =30 cm; 0 ≤ z 1 ≤ L; ε wall =0.9 R 1 =R 2 =10 cm; R 3 =2.5 cm ε app =0.9986 for z 1 =0.01 cm

28. Conclusions New tool for determination of the maximum value of the apparent emissivity Results for configuration factors were verified and compared Good agreement between the results A software was written for the computation of the apparent emissivity The software was combined with an optimisation genetic algorithm routine The cylindrical cavities have higher apparent emissivities than the conical cavities for the same length and the same open area