DNI Measurements in the South of Portugal: Long Term Results through Direct Comparison with Global and Diffuse Radiation Measurements and Existing Time Series

The present work describes the measurement effort for direct normal irradiance (DNI) evaluation in the sunny south of Portugal, with a network of eight radiation measurement stations in several locations (including Évora) providing a good coverage of the region. This new initiative for DNI measurement will still need many years (typically 10 or more) to produce a time series which can claim having long term statistical value. This problem can, however, be temporarily mitigated by measuring DNI at the same time as GHI and DHI, in a place where long term series dating back, already exist for those two. It so happens that a long term series (20 years) of global and diffuse solar irradiation exists for the location Évora. So the expectation is to establish correlations with the goal of attributing at least some long term statistical significance to the short and recent DNI series. The paper describes the setup of the measuring stations and presents the preliminary measurements obtained. It further presents the first correlations of monthly averages between normal beam (DNI), global and diffuse radiation. It then uses these correlations, admittedly without acceptable statistical significance (short series of less than one year of measured data), to exemplify how to get a prediction of long term DNI for Évora. This preliminary obtained value is compared to that predicted by the commercial data from Meteonorm.

Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.