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 thermal conductivity by the effective thermal conductivity. The latter reduces to the gas thermal conductivity in the limit of but can be substantially higher in the limit of In the case of fuel droplet heating 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 calculations to account for transient effects during the process of droplet heating.
A Transient Formulation of Newton's Cooling Law for Spherical Bodies
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division September 23, 1999; revision received June 21, 2000. Associate Editor: J. P. Gore.
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Sazhin, S. S., Gol'dshtein, V. A., and Heikal, M. R. (June 21, 2000). "A Transient Formulation of Newton's Cooling Law for Spherical Bodies ." ASME. J. Heat Transfer. February 2001; 123(1): 63–64. https://doi.org/10.1115/1.1337650
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