Burning in convective atmospheres

BURNING IN CONVECTIVE ATMOSPHERES 1. The Stagnant Film Case 

The spherical-symmetric fuel droplet burning problem is the only quiescent case that is mathematically tractable. However, the equations for mass burning may be readily solved in one-dimensional form for what may be considered the stagnant film case. If the stagnant film is of thickness 5, the free-stream conditions are thought to exist at some distance 8 from the fuel surface (Fig. 6.16). 

Within the stagnant film, the energy equation can be written as 

With b defined as before, the solution of this equation and case proceeds as follows. Analogous to Eq. (6.117), for the one-dimensional case 

Substituting this boundary condition into Eq. (6.144), one obtains 

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If, indeed, Eqs. (6.171) and (6.172) adequately predict the burning rate of a droplet in laminar convective flow, the droplet will follow a d3/2 burning rate law for a given relative velocity between the gas and the droplet. In this case (3 will be a function of the relative velocity as well as B and other physical parameters of the system. This result should be compared to the d2 law [Eq. (6.172)] for droplet burning in quiescent atmospheres. In turbulent flow, droplets will appear to follow a burning rate law in which the power of the diameter is close to 1. 

In the Sun, the ON cycle occurs about 25 times less frequently than the CN cycle, but this proportion varies with stellar temperature. It is also worth noting that when matter just starts to bum hydrogen in the ON cycle, the relative slowness of the 0+ H reaction causes abundant 0 to shift into 0 thus, an enrichment of O in the atmosphere of a star is a useful signature of dredge up by convective mixing of material that experienced partial hydrogen burning from the inner part of the star to the star s surface. 

By inspection of the absorption lines in stellar spectra, it is possible to measure the contents of the stellar atmosphere. A theoretical model has to explain how many of those nuclides were inherited from the proto-cloud from which the star formed and what amount was produced in the central, nuclear burning regions of the star itself and brought up by convection. 

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