An analytic solution of Navier–Stokes flow past a sphere in the region of intermediate Reynolds number

We study an analytical solution of steady, laminar, and incompressible flow past a sphere in the region of intermediate Reynolds number. The flow is governed by the Navier–Stokes (N–S) equation and the continuity equation. By applying a simple perturbation method to solve the equations, a second-order approximation cannot be obtained, as well-known (Whitehead’s paradox). Many analytical studies, such as Oseen approximation, matching technique, the homotopy analysis method, etc, have been conducted to resolve the paradox. The drag coefficients of these solutions are valid in the region of Reynolds number Rd<30 (R d is the diameter-based Reynolds number) However, the solution cannot express the flow separation behind a sphere observed in experiments. We also develop a perturbation technique to construct a solution of the N–S equation asymptotically to solve the paradox. The solution consists of power series of Rdh , where h is an arbitrary constant (0