Exact analytical solution for the Sakiadis boundary layer

Abstract

It has recently been established [Naghshineh et al., IMA J. of Appl. Math., 88, 1 (2023)] that a convergent series solution may be obtained for the Sakiadis boundary layer problem once key parameters are determined iteratively using the series itself. Here, we provide exact and explicit analytical expressions for these parameters, including that associated with wall shear, thus completing the exact analytical solution. The complete exact analytical solution to the Sakiadis problem is summarized here for direct use.

Figures (2)

• Figure 1: The numerical solution of (\ref{['eq:SakIVP']}), obtained using the $4^\mathrm{th}$-order accurate Runge-Kutta scheme using a step size of $\Delta g=10^{-4}$ and taking special care to pass through removable singularities.
• Figure 2: Example usage of the exact Sakiadis solution (\ref{['eq:full']}), using 37 terms. (top) $f'(\eta)$ with gridlines indicating that $df/d\eta=u/u_w=0.1$ at $\eta\approx3.47$. (left) Contours of constant $\psi$ obtained, displayed in increments of $\Delta\psi=1$ in the $\bar{y}\equiv u_w y$ vs. $\bar{x}\equiv \nu u_w x$ plane. The dashed curve is the envelope of the boundary layer (chosen here to be the locus of points at which $u/u_w = 0.1$), and restricts the display of the streamlines for velocities where $u/u_w > 0.1$. (right) The $u$ velocity field.