Two-dimensional supersonic flows with heat addition from given interna
l sources and/or nonequilibrium condensation are considered. The criti
cal amount of heat necessary to thermally choke the flow is defined at
any point in the flow field, and the necessary and sufficient conditi
ons for thermal choking are identified from the singularities of the e
quations of motion along streamlines. In particular, for any practical
purposes, it is shown that the flow Mach number reaches unity at any
point where the heat added to the flow along the streamline passing th
rough that point reaches the critical value. Thermally choked flows ar
e then identified as those flows where the critical heat along streaml
ines is exceeded leading to embedded oblique shock waves with a local
subsonic Row field downstream.