/pdf/the-navier-stokes-alpha-model-of-fluid-turbulence-4iwnn4rhnh.pdf

The Navier–Stokes-alpha model of fluid turbulence

Based on a modified Darcy's law, Stokes’ first problem was investigated for a second grade fluid in a porous half-space with a heated flat plate. Exact solutions of the velocity and temperature fields were obtained using Fourier sine transforms. In contrast to the classical Stokes’ first problem, there is a steady-state solution for the second grade fluid in the porous half-space, which is a damping exponential function with respect to the distance from the flat plate. The well-known solutions for Newtonian fluids in non-porous or porous half-space appear in limiting cases of our solutions.

Stokes’ first problem for a second grade fluid in a porous half-space with heated boundary

https://www.tpbin.com/Uploads/Subjects/05202608-1a60-4d58-a298-db324372cb37.pdf

Viscosity and thermal conductivity of nanofluids containing multi-walled carbon nanotubes stabilized by chitosan

In this paper we discuss recent progress in using the Camassa–Holm equations to model turbulent flows. The Camassa–Holm equations, given their special geometric and physical properties, appear particularly well suited for studying turbulent flows. We identify the steady solution of the Camassa–Holm equation with the mean flow of the Reynolds equation and compare the results with empirical data for turbulent flows in channels and pipes. The data suggest that the constant α version of the Camassa–Holm equations, derived under the assumptions that the fluctuation statistics are isotropic and homogeneous, holds to order α distance from the boundaries. Near a boundary, these assumptions are no longer valid and the length scale α is seen to depend on the distance to the nearest wall. Thus, a turbulent flow is divided into two regions: the constant α region away from boundaries, and the near wall region. In the near wall region, Reynolds number scaling conditions imply that α decreases as Reynolds number increas...

A connection between the Camassa–Holm equations and turbulent flows in channels and pipes

/pdf/the-camassa-holm-equations-and-turbulence-57jir5u6ys.pdf

J.E. Dunn

Papers

Fluids of differential type: Critical review and thermodynamic analysis