You're right, in compressible boundary layers, increasing the Prandtl number (Pr) generally leads to a decrease in shear stress (skin friction) and Stanton number. Here's why:
Prandtl Number (Pr):
Pr is the ratio of momentum diffusivity (ν) to thermal diffusivity (α). It represents the relative ease with which momentum and heat diffuse within a fluid.
- Low Pr: When Pr is low (typical for gases), momentum diffuses more readily than heat. This means velocity gradients (shear) are higher near the wall, resulting in higher skin friction.
- High Pr: As Pr increases (typical for liquids), thermal diffusivity becomes more dominant. Heat diffuses faster, reducing the temperature gradients near the wall. This, in turn, affects the viscosity (which is temperature-dependent) and reduces the shear stress at the wall.