On dual solutions of the three‐dimensional Hiemenz flow over a stretching/shrinking sheet

Abstract

AbstractThe steady three‐dimensional Hiemenz flow over a stretching/shrinking sheet of a viscous incompressible fluid is studied. In a very recent paper, Weidman in 2020 has modified the two‐dimensional Hiemenz flow by adding some periodic terms onto the outer potential flow and made it three‐dimensional Hiemenz flow over a rigid plate. Suppose we replace the rigid plate with a stretching sheet that gives a new family of three‐dimensional viscous stagnation‐point flows depending on the shear‐to‐strain rate parameter γ and stretching parameter λ. The similarity equations are solved numerically with the shooting technique. Numerical solutions for the sheet shear stress parameters and displacement thicknesses are reported and compared with asymptotic solutions behaviors. Dual solutions of the similarity equations are found numerically in both the stretching and shrinking cases. A linear temporal stability analysis is conducted to determine the physically reliable solution, revealing that the “First solution” is stable. Sample similarity velocity profiles are also presented for both the solutions and discussed in detail.