The temperature field in a compressible flow

In order to explain the basic properties of compressible flow, we will look at a two-dimensional, steady, boundary layer flow of a pure fluid. In a change from the previous discussion, in addition to the density, the viscosity and thermal conductivity will also be locally variable. The continuity equation is 

The momentum equation (3.58), with the boundary layer simplifications explained in section 3.5, is transformed into 

With the boundary layer simplifications from section 3.5, the enthalpy form of the energy equation (3.83) becomes 

3 Convective heat and mass transfer. Single phase flow 

Here it is possible to replace the heat flux by the enthalpy h = h(p, T), then taking dp/dy = 0 and q = —XdT/dy into account, it holds that 

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