This paper presents a numerical scheme for the solution of unsteady velocity andtemperaturefields in an enclosedcompressible fluid tluu is subjected to thermaUy induced mechanical motion. The numerical scheme includes recisionsof earlier models as well as a scheme applied to the simplified form of the governing equations. The results are compared with previous numerical results and available analytical solutions. The fluid unsteady temperature profile is also compared with recent experimental resulJs. The suggested numerical revisions are shown to improve the results significantly, as verified by experimental data.