Derivation of the Semenov equation

Let us suppose that a closed container, in which a self-heating fluid is filled, is placed in the atmosphere maintained at a 

The spatial distribution of temperature in the fluid is assumed to be uniform while the self-heating process is in the early stages. 

Assuming the temperature of the fluid to be 7, the quantity of heat generated per unit time in the whole volume, V, of the fluid, qu is expressed as 

On the other hand, assuming the cooling mode of the fluid to be Newtonian, the quantity of heat transferred per unit time from the fluid, through the whole fluid surface, across the container walls, to the atmosphere, q2, is expressed as 

When Tais varied in the range, Taj .Ta,c Ta,h, we get the response shown in Fig. 2, where are drawn one q curve with regard to the heat generation and three q2 lines, with regard to the heat transfer, corresponding each to the three values of r , respectively. 

---