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- W4282032023 abstract "A century-old scientific conundrum is solved in this paper. The Prandtl mixing length modelled plane boundary turbulent flow is described by: $frac{du^+}{d{y^+} }+kappa^2{y^+} ^2left( frac{du^+}{d{y^+} }right)^2=1$, together with boundary condition $ {y^+} =0:, u^+=0$. Only an approximate solution to this nonlinear ordinary differential equation (ODE) has been sought so far, however, the exact solution to this ODE has not been obtained. By introducing a transformation, $2kappa y^+=sinh xi$, I successfully find the exact solution of the ODE as follows: $u^+=frac{1}{kappa}ln(2kappa {y^+} +sqrt{1+4kappa^2{y^+} ^2})-frac{2{y^+} }{1+sqrt{1+4kappa^2{y^+} ^2}}$." @default.
- W4282032023 created "2022-06-13" @default.
- W4282032023 creator A5048183710 @default.
- W4282032023 date "2022-06-08" @default.
- W4282032023 modified "2023-09-25" @default.
- W4282032023 title "Closed Form Solution of Plane-Parallel Turbulent Flow Along an Unbounded Plane Surface" @default.
- W4282032023 doi "https://doi.org/10.20944/preprints202111.0008.v4" @default.
- W4282032023 hasPublicationYear "2022" @default.
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