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Show simple models using the "shape factor" can predict the "skid mark" accurately. The radiative heat transfer model is based on the R E A D (Radiative Energy Absorption Distribution) method! ll. Several numerical analysis have been performed concerning the relations between the temperature distribution of slab and the conditions of the skids and gas using the present model. 2. Mathematical model It is most important for solving heat conduction equation numerically how to give boundary conditions. The essential feature of the present model is that the boundary conditions is determined by the detail geometry of the furnace and the local temperature in the furnace; the layout of the skids and the local temperature of gas, surfaces of walls and surfaces of skid beams. Here, convection heat transfer on slabs are not considered because the convection heat transfer is much less than the radiative heat transfer. 2.1 Radiative heat transfer • • • • • • - • Figure 1 shows radiative heat transfer phenomena Wa I I on the lower surface of a slab schematically. A slab surface element j receives radiative heat from the gas, surfaces of walls, the surfaces of skid beams and the surfaces of the slab according to each Slab ; , ^ element j ,j§j temperature of these heat sources. In the upper f\ a \^^j/)\ n ""[) zone, radiative heat from surfaces of the skids is zero. S k i d ^ V / / S k . O n the other hand, the slab surface element j losses '" JI A C\^Q '" ' ^ • - y ^ ^ \ Gas radiative heat proportional to its absolute / Q. _, \ Wall / temperature to the power of four. As a result, net '*^5;^^S^5^^S5P»^SSS5SSS5K35MS^^ radiative energy into a slab surface element j is Figure x Schematic of radiative expressed in equation (1). heat transfer on a slab surface Qj = Qr+j + G~> + Q„j + Q^j - QT d) In the READ method, the READ, Rd and the self absorption ratio, a are introduced to calculate radiative heat exchange from a heat source / to a slab surface element j . The READ, Rdi_¥, is defined as the ratio of the absorbed radiative heat from / to j to the net radiative heat emitted from j . The self absorption ratio, a( is defined as the ratio of the absorbed radiative heat from i to / to the total radiative heat emitted from / . The first to fourth terms in the right side of equation (1) are expressed in equation (2) using |
