Unsteady natural convection flow of a dusty non-Newtonian Casson fluid along a vertical wavy plate: numerical approach

The present contribution provides a numerical treatment for the flow of unsteady natural convection of non-Newtonian Casson fluid model loaded with dusty particles over a vertical wavy plate. It is assumed that the fluid is incompressible and the dusty particles are considered to be spheres with the same size. Via the help of primitive variable formulation, the dimensionless boundary layer governing equations are reduced into a convenient coordinate system. The transformed resulting system of governing equations is tackled numerically employing the fully implicit finite difference method. The impact of various controlling physical parameters such as the amplitude of the wavy plate, the dimensionless time and fluid–particle interaction parameters on the velocity and temperature of both fluid and particle phase is analyzed. It is found that the magnitude of the velocity of both fluid and particle phase diminishes with increasing amplitude of the wavy plate parameter, while an opposite behavior is observed on temperature distributions as the amplitude of the wavy plate parameter rises. A significant impact is noticed for the heat transfer rate with enhancement values of fluid–particle interaction parameter. The numerical solutions are compared with the available data in the literature. Quantitative comparison illustrates good compatibility between the current and previous results.