GENERALIZED THERMODYNAMIC ANALYSIS OF STIRLING ENGINES

Schmidt's classical thermodynamic analysis of closed, regenerative gas cycles assumed isothermal phases, which implies infinite heat transfer through cylinder walls on zero speed. The more general case of limited heat transfer coefficient and variable exposed surface area for the cylinder is treated in this paper and expressions for the cyclic pressure and temperature variations of the working fluid are derived. These are based on a pair of simultaneous first-order differential equations which do not have closed solutions, so that stepwise numerical integration methods must be used. A complete heat balance is obtained so that actual efficiencies or coefficients of performance can be calculated instead of assuming them to be equal to the ideal values of a Carnot cycle, as was general practice up to now. Numerical examples covering the whole range of operation for a typical machine between adiabatic conditions (zero heat transfer) and isothermal operation (infinite heat transfer) are included.