Abstract
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 <i>ρ</i>1 and kinematic viscosity <i>ʋ</i>1 while the lower layer fluid has density <i>ρ</i>2 and kinematic viscosity <i>ʋ</i>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 <i>σ</i> of strain rates and the fluid parameter ratios <i>ρ</i> = <i>ρ</i>1/<i>ρ</i>2 and <i>ʋ</i> = <i>ʋ</i>1/<i>ʋ</i>2. Numerical results are presented for selected values of <i>ρ</i> and <i>ʋ</i> for a range of <i>σ</i> and show that stable results exist for all values of <i>σ</i> > 0, and for a range of negative <i>σ</i> values. Sample stable velocity profiles are also presented.