Variable order modeling of diffusive-convective effects in the oscillatory flow past a sphere

Abstract This work advances our understanding of the drag force acting on a particle due to the oscillatory flow of a viscous fluid at finite Reynolds and Strouhal numbers. The drag force is is determined by using the novel concept of Variable-Order (VO) Calculus, where the order of derivative can vary with the parameters and variables according to the dynamics of the flow. With the VO formulation we determine: (i) the region of validity of Tchen's equation for oscillatory flow, (ii) the region where the order of the derivative is fractional, but constant and (iii) the region where the strong non-linearity of the flow requires a variable order derivative to account for the increased complexity of the flow.