Abstract
In this study, an optimization methodology is presented to obtain the uniform thermal conditions over the design body (DB) surfaces. The DB has an asymmetrical and irregular shape that is placed inside a 3-D radiant enclosure equipped with heaters on its top wall. The Monte Carlo ray tracing (MCRT) method and genetic algorithm (GA) are employed to find the optimal temperatures of the heaters and the best location of the DB inside the enclosure. The radiative heat transfer problem is solved on the basis of the MCRT method to calculate heat fluxes on the DB surfaces. The GA is used to minimize the objective function defined based on the calculated and desired heat fluxes. The results indicate that thermal conditions on the DB surfaces are greatly influenced by the location of the DB and temperatures of the heaters. It is concluded that the introduced method is very capable of achieving the uniform thermal conditions on the DB surfaces by finding the optimal values for temperatures of the heaters and the best location for the DB inside the radiant enclosure.
NOMENCLATURE
A | = | area of surface |
= | central processing unit | |
= | conjugate gradient method | |
Dij | = | radiation distribution factor between surfaces i and j |
DB | = | design body |
F | = | objective function |
Fij | = | radiation shape factor between surfaces i and j |
GA | = | genetic algorithm |
H | = | height of the rectangular surface |
Iα | = | probability of absorption of incident energy parcels |
= | Monte Carlo ray tracing | |
N | = | number of surfaces |
= | number of variables in GA | |
Npop | = | population size in GA |
ni | = | number of discrete energy parcels emitted from surface i |
nij | = | number of discrete energy parcels emitted from surface i and absorbed by surface j |
P | = | individual in the GA |
P* | = | offspring in the GA |
Q | = | radiant energy |
Qij | = | radiant energy exchanged between surfaces i and j |
q" | = | heat flux |
Rα, Rx, Ry, Rθ, Rφ | = | random numbers between zero and unity |
= | radiation distribution factor | |
= | radiation shape factor | |
T | = | temperature |
VMM | = | variable metric method |
W | = | width of the rectangular surface |
x, y, z | = | local coordinate system |
x0, y0 | = | coordinates of one corner of the surface |
X, Y, Z | = | global coordinate system |
Greek Symbols
α | = | absorptivity |
θ | = | azimuthal angel |
λ | = | random number between zero and unity |
ϕ | = | circumferential angel |
σ | = | Stefan–Boltzman constant |
ϵ | = | emissivity of surface |
δij | = | Kronecker delta |
Subscripts
a | = | values over adiabatic surfaces |
d | = | values over design surfaces |
e | = | values over enclosure surfaces |
H | = | heater |
Additional information
Notes on contributors
Leila Darvishvand
Leila Darvishvand received her M.Sc. degree in mechanical engineering from the School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran, in 2011. She received her B.Sc. degree in mechanical engineering from the same university in 2008. She is currently working on heat transfer and thermal systems.
Farshad Kowsary
Farshad Kowsary is a professor in the field of heat transfer at the University of Tehran, Iran. His research interests are in the area of inverse heat transfer with a focus on inverse radiation and conduction. He has a sizable number of papers in these subjects in reputable heat transfer journals. He is a major reviewer for the Journal of Quantitative Spectroscopy and Radiative Transfer and for Heat and Mass Transfer.
Pantea Hadi Jafari
Pantea Hadi Jafari received her M.Sc. degree in mechanical engineering from the School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran, in 2011. She received her B.Sc. degree in mechanical engineering from the same university in 2007. She is currently a Ph.D. student at Luleå University of Technology, Sweden.