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An efficient multi-component fuel droplet vaporization model has been developed in this work using discrete approach. The precise modeling of droplet vaporization process is divided into two parts: vapor-phase and liquid-phase sub-models. Temporal evolution of flow inside the droplet is considered to describe the transient behavior introduced by the slow diffusion process. In order to account for the internal circulation motion, surface regression and finite diffusion without actually resolving the spatial governing equations within the liquid phase, a set of ordinary differential equations is applied to describe the evolution of the non-uniform distributions of universal diffusional variables, i.e. temperature and species mass fraction. The differences between the droplet surface and bulk mean states are modeled by constructing a quasi-1D frame; the effect of the internal circulations is taken into consideration by using the effective diffusivity rather than physical diffusivity.

In developing new products and improving existing products, engineers make numerous trade-offs between the cost of a new or modified feature and its value to the customer. One method for estimating value is to ask potential customers their willingness to pay (WTP) for the product change. Their stated WTP may, however, depend upon how the question is framed. Mail survey techniques based upon simulated choice experiments were used for estimating value to the customer. The main objective was to explore how the framing of the survey questions affected the WTP response and if one or more of the methods provided simulated responses in reasonable agreement with actual buyer behavior. It was found that the best way to frame the questions was to give respondents multiple choices for price of the alternative versus the baseline product as opposed to having a choice of only one price or having to write in a price representing their WTP.