  Accurately predicting drag and heat transfer for compressible high-speed
flows is of utmost importance for a range of engineering applications. This
requires the precise knowledge of the entire velocity and temperature profiles.
A common approach is to use compressible velocity scaling laws
(transformation), that inverse transform the velocity profile of an
incompressible flow, together with a temperature-velocity relation. In this
Note, we use distinct velocity transformations for the inner and outer layers.
In the inner layer, we utilize a recently proposed scaling law that
appropriately incorporates variable property and intrinsic compressibility
effects, while the outer layer profile is inverse-transformed with the
well-known Van Driest transformation. The result is an analytical expression
for the mean shear valid in the entire boundary layer, which combined with a
temperature-velocity relationship, provides predictions of mean velocity and
temperature profiles at unprecedented accuracy. Using these profiles, drag and
heat transfer is evaluated with an accuracy of +/-4% and +/-8%, respectively,
for a wide range of compressible turbulent boundary layers up to Mach numbers
of 14.
