Linear Model of Convective Heat Transfer in a Spray
The relative motion between dropets in a spray and the ambient gas is represented in an idealized fashion (Oseen-type approximation) that allows for a linear analysis of gas-phase unsteadiness and transient heating of the droplets.
One-dimensional, unsteady solutions for the gas temperature and droplet temperature are obtained. In addition to the general solution, asymptotic solutions for large liquid thermal inertia and small liquid thermal inertia are obtained and consistency is demonstrated. The solutions are expressed as combinations of exponential terms and convergent Taylor series; the solutions are piecewise analytic and a domain of independence of boundary values is obtained. In general, two characteristic times (and their associated space scales) appear in the solutions, namely a gas residence time and a droplet heating time.
KeywordsNusselt Number Convective Heat Transfer Droplet Vaporization Droplet Temperature Fuel Droplet
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