Casson nanoliquid film flow over an unsteady moving surface with time-varying stretching velocity

Abstract

AbstractPresent study explains about unsteady Casson nanoliquid film flow over a surface moving with velocity $$U_w=\lambda x/t$$ U w = λ x / t . The governing momentum equation is reduced to ODE by using corresponding similarity transformation, which is then tackled by employing numerical technique. The problem is analysed for both two-dimensional film flow and axisymmetric film flow. The exact solution is derived which satisfies the governing equation. It is noted that solution exists only for a specified scale of the moving surface parameter $$\lambda$$ λ . ie., $$\lambda \ge -1/2$$ λ ≥ - 1 / 2 for two-dimensional flow and $$\lambda \le -1/4$$ λ ≤ - 1 / 4 for axisymmetric flow. The velocity increases first and reaches the maximum velocity and then decreases to the boundary condition. Streamlines are also analysed for both axisymmetric and two-dimensional flow patterns by considering the stretching ($$\lambda >0$$ λ > 0 ) and shrinking wall conditions ($$\lambda <0$$ λ < 0 ). Study has been made for large values of wall moving parameter $$\lambda$$ λ . The aim of this investigation is to analyse the Casson nanoliquid film flow which finds applications in industries like coating of sheet or wire, laboratories, painting, many more.