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For small values of M the thermodynamic properties of the flow will not deviate significantly from the reservoir conditions, hence Re increases linearly with U and therefore with M.
Show that for increasing expansion (i.e. increasing M) the value of Re will eventually decrease by investigating the limit behaviour for M>>1. For the temperature dependence of viscosity, employ, Sutherlands expression and the power law where w=1.5 - T_0/(T_0+S).