Apparent Emissivity in the Base of a Cone Cosmin DAN, Gilbert DE MEY University of Ghent Belgium
Overview 1.Introduction 2.Description of the problem 3.Configuration factors computation 4.Apparent emissivity computation 5.Genetic algorithms (GA) 6.Results 7.Conclusions
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
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
Description of the problem
The boundary integral equation
Description of the problem The net radiation method
Description of the problem The net radiation method –Gauss elimination method
Configuration factors computation
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
Genetic algorithms –System for function optimisation –Adaptive search – iterative procedures –Variables = structures x i, population –Vector of parameters to the objective function
Genetic algorithms
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 – and → and Mutation –Alteration of one ore more bites in parent structure – →
Genetic algorithms
Termination criteria: Acceptable approximate solution Fixed total number of evaluations
Results
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
Results
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 = for z 1 =0.01 cm
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