Heat losses in crucible reactions

An upper limit of die heat losses tluough the reaction container wall, usually in the form of a cylindrical ciiicible with an increasing diameter from bottom to top, by assuming that die whole reaction mixture achieves the hnal reaction teiiiperamre immediately, and heat losses occur dirough the ciiicible refractory walls by conduction. The solution of Fourier s equation 

The total heat loss over 30 minutes, tf, per unit area where k is the drermal conductivity of the container, is given by 

If tire crucible is assumed to be a cylinder, 1 m high by 1 m diameter, the total surface area for heat loss is 4 x 10 cm, and hence tire reactor loses 54 MJ during the reaction time. 

Assuming that the reactor contains about 500 moles of products, which should have generated about 350 MJ, it can be seen that the upper limit of the heat loss is 15% of the heat generated by the reaction. 

The Kroll process for tire reduction of tire halides of refractory metals by magnesium is exemplified by the reduction of zirconium tetrachloride to produce an impure metal which is subsequently refined with the van Arkel process to produce metal of nuclear reactor grade. After the chlorination of the impure oxide in the presence of carbon 

---