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(trans-pseudocritical number) is introduced. The critical trans-pseudocritical number Ntpc,c first goes up and down with the increase of the inlet pressure and the reduction of the inlet temperature. The rise of the mass flow rate, the shortening of the tube length, and the enlargement of the tube diameter all induce the temperature difference along the radial direction to become large. These tendencies make the critical Ntpc,c small. Consequently, the stability boundary 
is obtained to distinguish the regions of the flow and heat transfer stability and instability.
