OCR Text |
Show 2.2 Two-dimensional unsteady heat conduction equation Temperature distribution in a slab is obtained solving the following governing equation, a two-dimensional unsteady heat conduction equation. «^*)-*l*-*J+*lA-*J (12) Eq.(ll) is discretized in FVM (Finite Volume Method). Implicit method is employed to use large time steps, and the matrix is solved with T D M A (Tri-Diagonal Matrix Algorithm). The specific enthalpy and the thermal conductivity of a slab are the function of the temperature at each grid. A slab is a low carbon steel called Aluminum killed steel. 3. Computational conditions x=0m x=2m 3.1 Two-dimensional computational domain ^ In order to investigate temperature distribution of the slab near the skids, the small region between two walking beams is adopted for the computational domain. Figure 2 sketches the computational domain. The width of the domain is 2m, the height of Specular lower zone is 2m, the height of upper zone is 2.2m un ry and the thickness of the slab is 240mm. To simplify the calculation, it is assumed that shapes of the l"«u'ytad boundary skids and riders are rectangular. However, the incident angle of radiation into the contact region is equal to the practical skid. Figure 2 Computational domain 3.2 Unsteady boundary conditions Figure 3 shows the schematic of the reheating furnace. The total length of the reheating furnace is 40m, which is divided longitudinally into four zones, 10m each, the non-firing zone, the preheating zone, the reheating zone and the soaking zone. The initial temperature of the slab is 303K. The slab is heated for 180 minutes and discharged at about 1473K. Mean gas temperature of the each control zone is described in Figure 3. Gas temperature of the lower zone is equal to the upper one. Wall surfaces temperature in each control zones are assumed to be equal to the gas temperature. Skid surfaces temperature in each control zones are assumed to be 150K lower than the gas temperature. Heat transfer coefficient at the contact area between the slab and the skids |