An electric furnace is to be used for batch heating a certain material (specific heat of 670 J/(kg K)) from 20 to 760?C. The material is placed on the furnace floor which is 2m x 4m in area as shown in the accompanying sketch. The side walls of the furnace are made of a refractory material. Parallel to the plane of the roof, but several inches below it, a grid of round resistor rods is installed. The resistors are 13 mm in diameter and are spaced 5 cm center to center. The resistor temperature is to be maintained at 1100?C, under which conditions the emissivity of the resistor surface is 0.6. If the top surface of the stock may be assumed to have an emissivity of 0.9, estimate the time required for heating a 6 metric ton batch. External heat losses from the furnace may be neglected, the temperature gradient through the stock may be considered negligibly small, and steady-state conditions may be assumed.

GIVENBatch heating of material in the furnace shown aboveSpecific heat of material (c) = 670 Jkg KMaterial temperaturesInitial (T1i) = 20?C = 293 KFinal (Thf) = 760?C = 1033 KFurnace dimensions: 2 m x 4 m x 1.3 m highSide walls are refractory materialResistor rod diameter (Dr) = 13 mm = 0.013 mResistor center to center distance (s) = 5 cm = 0.05 mResistor temperature (T2) = 1100?C = 1373 KEmissivity of the resistor surface (ε2) = 0.6Emissivity of the material surface (ε1) = 0.9Mass of material (m) = 6 metric tons = 6000 kgASSUMPTIONSQuasi-steady state conditionsExternal heat losses are negligibleTemperature gradient through the material is negligible (negligible internal thermal resistance)Material is grayConvective heat transfer isnegligible

4 m Az, Tz- AR A1 Stock- 1,3 m