In the present paper we consider a boundary value problem on a semiaxis $(0,\infty)$ for a singularly perturbed parabolic equation with the two perturbation parameters $\eps_1$ and $\eps_2$ multiplying respectively the second and first derivatives with respect to the space variable. Depending on the relation between the parameters, the differential equation can be either of reaction-diffusion type or of convection-diffusion type. Correspondingly, the boundary layer can be either parabolic or regular.

Model problems of such type appear in the mathematical modeling of heat transfer processes for flow past a flat plate. For those problems we consider the case when the boundary layer can be controlled by continuous suction of fluid. Errors of classical numerical methods applied to the problem in question can be unsatisfactorily large for small values of the parameter $\eps_1$. For the problem under consideration we construct a monotone finite difference scheme (on piecewise uniform meshes) which converges $\eps$-uniformly with the rate $\Oh{N^{-1} \ln N + N_0^{-1}}$, where $N$ and $N_0$ define the number of nodes respectively in the space mesh on a unit interval and in the time mesh.