An Approximate Solution to the Shuttle Heat-Transfer Losses in a Reciprocating Machine

Abstract

The axial heat transfer due to the oscillatory motion of a long displacer in a cylinder with an axial temperature gradient is treated. The effect of the resistance to heat transfer due to the radial clearance between the displacer and the cylinder is considered, as well as the effect of a limited thermal diffusivity in the walls. A method for the estimation of the effect of the gas flow in the clearance volume is presented. A simple approximate solution is obtained by linearization and application of Fourier series. The effect of radial clearance, material properties, length, and wall thickness on the net heat transfer rate is discussed.