Sample Problem Shannon Method for Temperature-Versus-Time Curves

Sample Problem Shannon Method for Temperature-Versus-Time Curves 

Given 200 000 pounds/hoiu of 0.4% carbon steel to be heated to 2150 F 25°F for rolling. The 4.5 sq x 30 ft long billets are spaced 8 center-to-center, so the spacing-to-thickness ratio = 8 /4.5 = 1.78, on a walking hearth. 

Preliminary Decisions Walking hearth foiu-zone reheat furnace, with all zones longitudinally or side fired. Zone 1 (charge end) is to be unfired. Zones 2 and 3 are to be side fired, and zone 4 (soak) is to be fired longitudinally, using ambiet air in all burners. Fuel = natural gas. Hearth width should include 2 ft clearance on each end of 30 ft long billets = 34 ft. 

Look-up data Load density = 489 Ib/ft (reference 51, table 4.4b). Load emissivity = 0.85 (from reference 51, table 4). Estimated possible hearth loading = 83.3 Ib/ft, from figure 4.21, considering space-to-thickness ratio, number of zones, whether with bottom heating, and/or with enhanced heating. 

Procedure—Phase A—Datasheet. Table 8.1 = blank datasheet. Table 8.2 = the datasheet filled in for this problem to find heat transfer factor, H.lf H is less than 0.4 with time-lag (line 11) greater than 6 min, increase the furnace length by 10% and perform a second iteration. Continue iterations with increased furnace lengths until H is greater than 0.4. If H is greater than 0.47 with time-lag (line 11) less than 6 minutes, try an iteration with 10% less furnace length. 

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