The Temperature Distribution in Powder Reactants

Setting the temperature of the coldest layer (To or T ), one can determine the temperature of an adjacent layer using determined Eqs. 6.11 and 6.12. The temperatures of all the other layers can be then sequentially using Eq. 6.8. The (n + l)-th layer temperature is set to be the same as the furnace temperature. To achieve that, the magnitude of To or T is varied with all the other conditions kept constant. 

The initial temperature for each succeeding layer Tj i is taken to be equal to the preceding layer temperature, p. When the calculations are finished, the (n- - l)-th layer temperature is compared with the furnace temperature. If the condition Tf — T +i 0.01 is met, the calculation is considered finished. Otherwise the first-layer temperature is either decreased (if Tf T +i), or increased (if Tf T +i) and the calculation is repeated. If the calculation is performed for different pressures of water vapour (Pgtart P Pend), the above described procedure is repeated for each new value, which is varied from -Pstart = 10 bar to Pend = 10 bar. The results are displayed in the form of graphs and/or tables. 

For an example of the application of the software described above, the temperature distribution in a powder sample of Mg(OH)2 in a high vacuum (in the absence of foreign gas and water vapour), is considered below. The temperature distribution is presented in Fig. 6.2 as a function of the number of layers 

Parameter He An underestimation of the temperature non-uniformity in powder samples will obviously be a source of errors in estimations of their kinetic parameters. To make allowance for this factor L vov et al. [4] suggested introducing the following parameter into the calculation procedure  

This quantity represents an effective number of powder sample layers, which decompose with the same rate as the surface layer. (This value can be determined simultaneously with calculations of the temperature distribution.) As the calculation results show, the rig magnitude decreases quickly with the furnace temperature rise. At the same time the magnitude is essentially independent of the total number of layers n (for n 100) and is defined by the furnace temperature only. 

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