Second law analysis of convective droplet burning

The entropy generation due to burning particles in a gaseous stream is considered and the contributions to it compared. A second law analysis is undertaken in order to minimize the entropy generation and, therefore, the lost available work. The optimum flow conditions from this thermodynamically advantageous perspective are determined for a burning droplet at low Reynolds number and an optimum transfer number obtained. The transfer number so obtained depends directly on the square of the relative velocity, and inversely on the net enthalpy rise due to burning and the ratio of ambient to flame temperature. In realistic flows, where the transfer number and net heat release are fixed, these quantities are related to the relative velocity and ambient to flame temperature ratio in order to operate at optimum conditions. The square of the relative velocity in such flows is a small fraction of the net heat release so that, to operate at optimum thermodynamic conditions, it is determined that the droplet Reynolds number must be large suggesting a large droplet size and low gas viscosity. Circumstances pertaining to engineering practice are also considered and it is concluded that within constraints practice is consistent with the implications of the second law analysis.