Heat transfer during compression and expansion can be out of phase with bulk gas-wall temperature difference. An ordinary convective heat transfer model is incapable of predicting this phenomenon. Expressions for compression/expansion heat transfer developed from simple conduction models use a complex heat transfer coefficient. Thus, heat flux consists of one part proportional to temperature difference plus a second part proportional to rate of change of temperature. Surface-averaged heat flux was calculated from experimental pressure-volume data for piston-cylinder gas springs over a range of speeds, pressures, gases, and geometries. The complex Nusselt number model proved capable of correlating both magnitude and phase of the measured heat transfer as functions of an oscillation Peclet number.
Application of a Complex Nusselt Number to Heat Transfer During Compression and Expansion
Kornhauser, A. A., and Smith, J. L., Jr. (August 1, 1994). "Application of a Complex Nusselt Number to Heat Transfer During Compression and Expansion." ASME. J. Heat Transfer. August 1994; 116(3): 536–542. https://doi.org/10.1115/1.2910904
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