# A Reynolds--uniform numerical method for Prandtl's boundary layer
problem for flow past a plate with mass transfer

**Source**: https://www.maths.tcd.ie/report_series/abstracts/tcdm0306.html
**Parent**: https://www.maths.tcd.ie/research/papers/

**A Reynolds--uniform numerical method for Prandtl's boundary layer
problem for flow past a plate with mass transfer**

In this paper we consider Prandtl's boundary layer
problem for incompressible laminar flow past a
plate with transfer of fluid through the surface of the plate.
When the Reynolds number is large the solution of this
problem has a parabolic boundary layer. In a neighbourhood of
the plate the solution of the problem has an additional
singularity which is caused by the absence of the
compartability conditions. To solve this problem outside nearest
neighbourhood of the leading edge, we construct a direct
numerical method for computing approximations to the solution
of the problem using a piecewise uniform mesh appropriately
fitted to the parabolic boundary layer.
To validate this numerical method, the model Prandtl problem with
self-similar solution was examined, for which a {\it reference\/}
solution can be computed using the Blasius problem for a nonlinear
ordinary differential equation. For the model problem,
suction/blowing of the flow rate density is
$v\_{0}(x)=-v\_i2^{-1/2}Re^{1/2}x^{-1/2}$,
where the Reynolds number $Re$ can be arbitrarily large and
$v\_i$ is the intensity of the mass transfer with arbitrary
values in the segment $[-.3,.3]$.
We considered the Prandtl problem
in a finite rectangle excluding the leading edge of the plate
for various values of $Re$
which can be arbitrary large and for some values of
$v\_{i}$, when meshes with different
number of mesh points were used. To find reference solutions for the
the velocity components and their derivatives with required accuracy,
we solved the Blasius problem using a semi--analytical
numerical method. By extensive numerical experiments we showed
that the direct numerical method constructed in this paper allows
us to approximate both the solution and its derivatives
$Re$--uniformly for different values of $v\_{i}$.