Expansion of a Rarefield Gas Cloud into a Vacuum

Analytical solutions are obtained describing the expansion into a vacuum of gas clouds having simple initial configurations. The assumptions employed are free molecular flow and local Maxwellian distribution of velocities initially. By means of a simple transformation in time, equivalence is shown between these solutions and the solutions of some elementary problems in transient heat flow. The initially uniform spherical gas cloud expanding into a vacuum is solved by two methods: (1) by the assumption of free molecular flow; and (2) by programming the conventional equations of gas dynamics. Good agreement is observed between the solutions resulting from the two treatments.