Application of a Complex Nusselt Number to Heat Transfer During Compression and Expansion

Abstract

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.

Einfluß von Einlaufeffekten auf den Wärmeübergang bei laminarer oszillierender Rohrströmung

“…To calculate the wall heat flux, Newton's law of convection (which in effect is an engineering approximation rather than a law of nature) may also be written in complex notation as proposed by Kornhauser [5]. Wall heat flux then is obtained by wherein the imaginary part of the wall-to-mean temperature difference can be replaced by the real part of its derivative with respect to time, assuming sinusoidal temperature variations, and subsequently by the real part of the mean temperature's derivative, regarding a constant wall temperature.…”

Numerical simulation and performance optimization of a high capacity pulse tube cryocooler

“…We have chosen the empirical correlation for the oscillating flow which was proposed by Tanaka [14]. Heat transfer between the gas and tube wall in tube section is obtained from the Nusselt number equation under oscillating flow in complex form, as described by Kornhouser [15].…”

Effect of magnetic field on the Nusselt number of a multi-plate thermoacoustic system

“…Kornhauser and Smith [30] presented an experimental study on the complex Nusselt number for oscillating pressure and flow. They observed that Newton's law of convection is not enough to describe the convection heat transfer rate when the fluid compression or expansion is out of phase with the temperature difference between the bulk fluid and wall temperature.…”

“…The Nusselt number was maximum when these two parts were in the same phase. The complex Nusselt number can provide magnitude and phase information [30]; thus, the heat transfer between the oscillating fluid and solid wall can be calculated more accurately using the complex Nusselt number for a thermoacoustic system [30].…”