Linear model of convective heat transfer in a spray

The relative motion between spray droplets and an ambient gas is presently treated in an idealized, Oseen-type approximation which allows a linear analysis of gas phase unsteadiness and droplet transient heating to be conducted. One-dimensional, unsteady solutions are obtained for gas and droplet temperatures; in addition to the general solution, asymptotic solutions for large and small liquid thermal inertia are obtained and consistency is demonstrated. The solutions, which are expressed as combinations of exponential terms and convergent Taylor series, are piecewise-analytic. A domain of independent boundary values is obtained. In general, two characteristic times and their associated space scales, namely a gas residence time and a droplet heating time, appear in the solutions.