Modelling unsteady convective heat transfer for fuel droplets

Unsteady laminar thermal boundary layer flow about an impulsively started isothermal sphere is considered. The stream function and temperature are expanded in series in powers of time. The leading order solutions for stream function and temperature are obtained analytically. Results are applied to a fuel droplet injected into a cylinder of a Diesel engine for small initial time period prior to the time of evaporation. Effective thermal conductivity of the gas surrounding the droplet is obtained in terms of the Reynolds and Prandtl number. Results show that the effective thermal conductivity of the gas is substantially larger than its thermal conductivity.