A fundamental problem in heat transfer is the convective cooling of the heated walls of a channel. We find steady two-dimensional (2D) flows that maximize the heat removed from fixed-temperature walls for a given rate of energy used to drive the flow, Pe (Pe is the Peclet number, a dimensionless flow speed). For parabolic (Poiseuille) flow, the heat transfer scales as Pe. Starting from Poiseuil...

A comparison is made between the Hagen-Poiseuille flow in rigid tubes and networks on one side and the time-independent one-dimensional Navier-Stokes flow in elastic tubes and networks on the other. Analytical relations, a Poiseuille network flow model and two finite element Navier-Stokes one-dimensional flow models have been developed and used in this investigation. The comparison highlights t...

In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein  polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution o...

The statistical properties of fully developed planar turbulent Couette–Poiseuille flow result from the simultaneous imposition of a mean wall shear force together with a mean pressure force. Despite the fact that pure Poiseuille flow and pure Couette flow are the two extremes of Couette–Poiseuille flow, the statistical properties of the latter have proved resistant to scaling approaches that co...

A new universal theory for flow instability and turbulent transition is proposed in this study. Flow instability and turbulence transition have been challenging subjects for fluid dynamics for a century. The critical condition of turbulent transition from theory and experiments differs largely from each other for Poiseuille flows. This enigma has not been clarified so far owing to the difficult...

This paper introduces a new approach for active fluid flows control: the vision-based approach. By using vision, dense flow velocity maps can be estimated and used in an observer-free closed-loop scheme to control a flow. This new approach is validated on a 2D plane Poiseuille flow and is proven to outperform the existing Poiseuille flow control appraches which use a limited number of available...

The linear stability of plane Poiseuille flow at low Reynolds number of a conducting Oldroyd fluid in the presence of a transverse magnetic field has been investigated numerically. Spectral tau method with expansions in Chebyshev polynomials is used to solve the Orr-Sommerfeld equation. It is found that viscoelastic parameters have destabilizing effect and magnetic field has a stabilizing effec...