The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer

In the current work, the boundary layers of an unsteady incompressible stagnation-point flow with mass transfer were further investigated. Similarity transformation technique was used and the similarity equation group was solved using numerical methods. Interesting observation is that there are multiple solutions seen for negative unsteadiness parameters, β. The influences of mass transfer, unsteadiness parameter, and Prandtl numbers on velocity and temperature profiles, wall drag, and wall heat fluxes were investigated and analyzed. The asymptotic behaviors for the similarity equations in limiting situations were theoretically analyzed. It is found that solutions exist for all mass transfer parameters for β≥−1. For a certain mass transfer parameter, there are two solutions when βc<β<0; there is one solution for (β=βc)∪(β≥0); there is no solution for β<βc, where βc is a critical unsteadiness parameter dependent on mass transfer parameter.

► Numerical solutions for unsteady stagnation flow with mass transfer.
► Numerical solutions for heat transfer with specified wall temperatures.
► Multiple solutions are found for certain control parameters.
► The results are exact solutions of the Navier–Stokes equations.