Analysis predicting the burning rate

In a one-dimensional, spherically symmetrical system, the overall continuity equation, equation (1-23), can be written as 

Employing the expression for the divergence in spherical coordinates, we find that equations (1-45) and (1-49) give 

The coupling between the temperature and oxidizer concentration profiles is determined by the function 

Equations (1-61) and (1-62) provide conditions on T and Yq that must be satisfied at the surface of the droplet. If the subscripts -h and — refer to conditions outside and inside the droplet, respectively, then equations (1-37) and (1-62) give 

The explicit derivation of the interface condition on T from equation (1-61) is somewhat more lengthy. It is clear on physical grounds that when the temperature of the droplet is constant and uniform, the amount of heat conducted into the droplet must be just sufficient to vaporize the fuel leaving the droplet that is. 

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