On the calculation of the external temperature of a flat-wall heat-conducting wall
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Our factory has a furnace that uses graphite electrodes for heating. The furnace is lined with three layers of insulating refractory bricks, each layer being 650 mm thick. These refractory bricks have circular holes, through which the graphite electrodes can extend into the furnace to provide heat. The cross-sectional area of these electrodes is 63.6 square centimeters. The temperature inside the furnace is around 1400°C. I would like to calculate the temperature of the graphite electrodes at the outer wall of the furnace; I’ve carried out the calculations as follows, but I feel there might be something wrong with them. I would appreciate some guidance from everyone. It is known that the thermal conductivity of the graphite electrode is 121 W/k·m, the heating power of the electrode is 64 kW, and the power factor is 0.7. The calculation process is as follows: 64*10^3*0.7 = KA; (1400 – T) = 121/0.65*63.6*10^-4*(1400 – T). This results in 3.78*10^4 = (1400 – T), and the temperature calculated in this way is negative. I would like to know what went wrong – please provide some guidance. Thank you
Just my personal opinion: This problem seems to require the use of heat conduction formulas for calculation, but the formula applied by the original poster is one for convective heat transfer. I’ll just wait patiently for an expert to appear and provide an answer!
The area was used incorrectly; the original poster should have calculated it based on the external surface area of the electrode, rather than its cross-sectional area. The reason is simple: heat transfer by radiation occurs not only through the cross-sectional area but also across the entire external surface of the electrode. The temperature of the electrode is likely around 100°C, and it should be lower than the temperature of the steel casing. . Calculate it yourself. Radiation also has a heat transfer coefficient. For heat transfer in electrode furnaces, it is recommended that the original poster refer to more specialized books; materials from chemical engineering fields are generally not used for such calculations. It is advisable to consult manuals and resources related to steelmaking, especially those related to electric arc furnace steelmaking.