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

Abstract

Present study explains about unsteady Casson nanoliquid film flow over a surface moving with velocity U_w=lambda 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. ie., lambda ge -1/2 for two-dimensional flow and lambda le -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) and shrinking wall conditions (lambda <0). Study has been made for large values of wall moving parameter lambda. 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.