An analysis was performed to determine the error that results from the estimation of the wall shear rates based on linear and quadratic curve-fittings of the measured velocity profiles. For steady, fully developed flow in a straight vessel, the error for the linear method is linearly related to the distance between the probe and the wall, dr1, and the error for the quadratic method is zero. With pulsatile flow, especially a physiological pulsatile flow in a large artery, the thickness of the velocity boundary layer, delta is small, and the error in the estimation of wall shear based on curve fitting is much higher than that with steady flow. In addition, there is a phase lag between the actual shear rate and the measured one. In oscillatory flow, the error increases with the distance ratio dr1/delta and, for a quadratic method, also with the distance ratio dr2/dr1, where dr2 is the distance of the second probe from the wall. The quadratic method has a distinct advantage in accuracy over the linear method when dr1/delta << 1, i.e. when the first velocity point is well within the boundary layer. The use of this analysis in arterial flow involves many simplifications, including Newtonian fluid, rigid walls, and the linear summation of the harmonic components, and can provide more qualitative than quantitative guidance.

A two-dimensional numerical model was developed to determine the effect of the non-Newtonian behavior of blood on a pulsatile flow at the aortic bifurcation. The blood rheology was described by a weak-form Casson equation. The successive-over-relaxation (SOR) method was used to solve both the vorticity and Poisson equations numerically. It was disclosed that the non-Newtonian property of blood did not drastically change the flow patterns, but caused an appreciable increase in the shear stresses and a slightly higher resistance to both flow separations and the phase shifts between flow layers.

The flow induced by a disk rotating at the bottom of a cylindrical tank is characterised using numerical techniques – computation of steady solutions or time-averaged two-dimensional and three-dimensional direct simulations – as well as laser-Doppler velocimetry measurements. Axisymmetric steady solutions reveal the structure of the toroidal flow located at the periphery of the central solid body rotation region. When viewed in a meridional plane, this flow cell is found to be bordered by four layers, two at the solid boundaries, one at the free surface and one located at the edge of the central region, which possesses a sinuous shape. The cell intensity and geometry are determined for several fluid-layer aspect ratios; the flow is shown to depend very weakly on Froude number (associated with surface deformation) or on Reynolds number if sufficiently large. The paper then focuses on the high Reynolds number regime for which the flow has become unsteady and three-dimensional while the surface is still almost flat. Direct numerical simulations show that the averaged flow shares many similarities with the above steady axisymmetric solutions. Experimental measurements corroborate most of the numerical results and also allow for the spatio-temporal characterisation of the fluctuations, in particular the azimuthal structure and frequency spectrum. Mean azimuthal velocity profiles obtained in this transitional regime are eventually compared to existing theoretical models.

This paper aims to study the convective heat transfer behavior of aqueous suspensions of nanodiamond particles flowing through a horizontal tube heated under a constant heat flux condition. Consideration is given to the effects of particle concentration and Reynolds number on heat transfer enhancement. It is found that (i) significant enhancement of heat transfer performance due to suspension of nanodiamond particles in the circular tube flow is observed in comparison with pure water as the working fluid, (ii) the enhancement is intensified with an increase in the Reynolds number and the nanodiamond concentration, and (iii) substantial amplification of heat transfer performance is not attributed purely to the enhancement of thermal conductivity due to suspension of nanodiamond particles.

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