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Variable order modeling of diffusive-convective effects on the oscillatory flow past a sphere. (English) Zbl 1229.76099
Summary: This work advances our understanding of the drag force acting on a particle due to the oscillatory flow of a viscous fluid with finite Reynolds and Strouhal numbers. The drag force is is determined 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. Using 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.
MSC:
76R99Diffusion and convection (fluid mechanics)
26A33Fractional derivatives and integrals (real functions)