Impinging Howarth stagnation-point flows

The flow of one Howarth stagnation-point flow impinging directly on another Howarth stagnation-point flow is studied, and an exact similarity solution to the Navier-Stokes equations is found. The upper layer fluid has density rho(1) and kinematic viscosity nu(1) while the lower layer fluid has density rho(2) and kinematic viscosity nu(2) and the two fluids are assumed to be immiscible. This problem has potentially five independent parameters to investigate, but application of the continuity of the normal stresses at the interface imposes restrictions which reduces the problem to one with three independent parameters, namely a ratio sigma of strain rates and the fluid parameter ratios rho = rho(1)/rho(2) and nu = nu(1)/nu(2). Numerical results are presented for selected values of rho and nu for a range of sigma and show that stable results exist for all values of sigma > 0, and for a range of negative sigma values. Sample stable velocity profiles are also presented. (C) 2018 Elsevier Masson SAS. All rights reserved.