A model has been developed for regenerative thermal devices such as Stirling engines and refrigerators, in which while the heat exchangers are modeled as fully isothermal, the flow in the cylinders and dead spaces. is modeled as adiabatic, one-dimensional, and stratified Pressure is assumed to be spatially uniform, so that the two remaining conservation laws refer to mass and energy. Tt is shown that under the proposed assumptions, the conservation laws can be integrated in closed form with respect to the space variable, leaving only time integration to be performed numerically. As a result, the numerical integration is very cost-effective, sufficiently so that the resulting program can be used to chart large portions of the parameter space relatively quickly on widely available engineering workstations.