Near-wall Taylor-series expansion solution for compressible Navier–Stokes–Fourier system

This paper presents the Taylor-series expansion solution of near-wall velocity and temperature for a compressible Navier–Stokes–Fourier system with a no-slip curved boundary surface. When the shear viscosity is a single-valued function of local fluid temperature, the near-wall velocity and temperature are explicitly expressed using the surface quantities including skin friction, surface pressure, surface dilatation, surface heat flux, surface temperature, surface curvature, and their relevant derivatives at the wall. In addition, the wall-normal pressure gradient at the wall is found to be contributed by three physical mechanisms including the skin friction divergence and surface dilatation effect as well as the coupled skin friction and surface heat flux with varying shear viscosity. Furthermore, without losing generality, we derive the near-wall Taylor-series expansion solution for the Lamb vector under the assumption of constant viscosities. Different physical mechanisms that are responsible for initial formation of the Lamb vector in the viscous sublayer are elucidated. The significance of the skin friction divergence and surface dilatation to the near-wall Lamb vector is highlighted.