Optimization of 3-D Radiant Enclosures With the Objective of Uniform Thermal Conditions on 3-D Design Bodies

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.