OCR Text |
Show 4 surface of the heater [2] and models do not yet exist for predicting combustion and heat transfer in the panels. • All surfaces of the enclosure are assumed to be diffuse emitters and reflectors of radiation. • The radiosity method [4] is employed to calculate the net radiant heat exchange within the enclosure. • The net local radiant heat flux incident on the load surface is calculated using the local load surface temperature. This heat flux is then used as the boundary condition for the solution of the temperature distribution in the load. • The furnace enclosure is usually filled with inert gases such as argon or nitrogen to prevent oxidation and decarbonization of the load. These gases are radiatively non-participating at the temperatures encountered in batch reheating furnaces. The spectral (net) radiation heat flux at any zone i, q , can be expressed as a difference between the leaving flux (radiosity), J , and the incident flux (irradiation), G , l.A. 1,/- vtf-w-'w (2) where the spectral radiation flux leaving a surface of an opaque material is a sum of the emitted and the reflected fluxes where e. and p. are the spectral emissivities and reflectivities of zone i, respectively. The spectral incident radiant flux G is composed of portions of the leaving fluxes from other elements of the enclosure and is given by [5] N N G (r.) = Y J.,(r.)dF.A ^A (r.,r.) = Y J.,(r.)K(r.,r.)dA. (4) i,Xx r *-i JA. J.X J dA.-dA.v T y *-* J\ j.X j » J J j=l J J j=i J where kernel K(r,r.) can be expressed in terms of the differential configuration factor ^dA.-dA.85 ' J K(r,r.) = dF.A ^A (r.,r.)/dA. (5) v i y dA.-dA. i j j Elimination of the spectral incident flux G. from equations (2) and (3) and solution for 1,A, the leaving flux J. yields lv A, Ju(ri> = \x ^V - KM/\x W*ix<$ (6) After substituting equation (6) into equation (4) to eliminate J. yields N p (r.) + ei.^l L {EbJTi(r i)]-EbxITj(rj>*1FdA1-dAj(r i'rj)} .M-U--N 0) |