Time-varying stretching velocity analysis for an unsteady flow of Williamson fluid by Hermite wavelet

Abstract

AbstractThis study investigates unsteady velocity $${U}_{w}=\xi x/t$$ U w = ξ x / t for a Williamson nanofluid film flowing over a moving surface. This work can be used to outline the effects of an applied angled magnetic-field on liquid film flow, which occurs in numerous real-world solicitations such as coating industries for wire or sheet, labs, painting, and several others. Analyzing williamson nanoliquid film flow over a stretching sheet is the main aim of this investigation. The leading Navier–Stokes models are reduced to third-order nonlinear ODE through similarity transformations that are then undertaken using the Hermite wavelet method (HWM). Both 2-dimensional and axisymmetric film flow circumstances have been analyzed. The moving surface parameter $$\xi$$ ξ is said to have a limited range for which the solution exists. Specifically, $$\xi \le -1/4$$ ξ ≤ - 1 / 4 for axisymmetric flow and $$\xi \ge -1/2$$ ξ ≥ - 1 / 2 for two-dimensional flow. Before decreasing to the boundary condition, the velocity climbs until it reaches its maximum. By taking into account the stretching ($$\xi >0$$ ξ > 0 ) and shrinking ($$\xi <0$$ ξ < 0 ) wall conditions, streamlines are also examined for axisymmetric and 2-dimensional flow patterns.