A transient formulation of Newton's cooling law for spherical bodies

Newton 's law of cooling is shown to underestimate the heat flux between a spherical body (droplet) and a homogeneous gas after this body is suddenly immersed into the gas. This problem is rectified by replacing the gas therm al conductivity by the effective thermal conductivity. The latter reduces t o the gas thermal conductivity in the limit of t --> infinity, but can be s ubstantially higher in the limit of t --> 0. In the case of fuel droplet he ating in a medium duty truck Diesel engine the gas thermal conductivity may need to be increased by more than 100 percent at the initial stage of calc ulations to account for transient effects during the process of droplet hea ting.