A steel strip of thickness 8 = 12 mm is annealed by passing it through a large furnace whose walls are maintained at a temperature Tw corresponding to that of combustion gases flowing through the furnace (T_w = T_∞). The strip, whose density, specific heat, thermal conductivity, and emissivity are p = 7900 kg/m³, c p = 640 J/kg ∙ K, k = 30 W/m ∙ K, and ϵ = 0.7, respectively, is to be heated from 300°C to 600°C.

(a) For a uniform convection coefficient of h = 100 W/m² ∙ K and T_w = T_∝ = 700°C, determine the time required to heat the strip. If the strip is moving at 0.5 m/s, how long must the furnace be?

(b) The annealing process may be accelerated (the strip speed increased) by increasing the environmental temperatures. For the furnace length obtained in part (a), determine the strip speed for T_w = T_∞ = 850°C and T_w = T_∝ = 1000°C, for each set of environmental temperatures (700. 850 and 1000°C), plot the strip temperature as a function of time over the range 25°C < T < 600°C. Over this range, also plot the radiation heat transfer coefficient, h r , as a function of time.

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Furnace walls, T Combustion gases T, h T8 Combustion gases