Spherical conducting droplet model

Heat Transfer by Conduction. In the theoretical analysis of steady state, heterogeneous combustion as encountered in the burning of a liquid droplet, a spherically symmetric model is employed with a finite cold boundary as a flame holder corresponding to the liquid vapor interface. To permit a detailed analysis of the combustion process the following assumptions are made in the definition of the mathematical model ... 

The use of a wetted spherical model affords the opportunity of studying combustion under steady-state conditions. Forced convection of the ambient gas may be employed without distortion of the object. Sufficiently large models may be employed when it is desired to probe the gas zones surrounding the burning sphere. It is apparent that the method is restricted to conditions where polymerization products and carbonaceous residues are not formed. In the application of such models, the conditions of internal circulation, radiant heat transmission, and thermal conductivity of the interior are somewhat altered from those encountered in a liquid droplet. Thus the problem of breakup of the droplet as a result of internal temperature rise cannot be investigated by this method. 

Experimental Observations. Whereas many experiments have been performed on single-droplet vaporization (21,22), most of them are conducted under the influence of either natural and/or forced convection, which not only distorts spherical symmetry, but also produces unwanted temporally varying convective effects on the vaporization process as the droplet size diminishes. The observations on the droplet surface area variations, however, do agree qualitatively with the predicted behavior of the transient models shown in Figure 4. 

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