Numerical analysis of conjugate natural and mixed convection heat transfer of nanofluids in a square cavity using the two-phase method

In the present study, the problem of conjugate natural and mixed convection of nanofluid in a square cavity containing several pairs of hot and cold cylinders is visualized using non-homogenous two-phase Buongiorno's model. Such configuration is considered as a model of heat exchangers in order to prevent the fluids contained in the pipelines from freezing or condensing. Water-based nanofluids with Cu, Al₂O₃, and TiO₂ nanoparticles at different diameters ($25\text{nm}?d_p?145\text{nm}$) are chosen for investigation. The governing equations together with the specified boundary conditions are solved numerically using the finite volume method based on the SIMPLE algorithm over a wide range of Rayleigh number (${10}^4?\mathit{Ra}?{10}^7$), Richardson number (${10}^{-2}?\mathit{Ri}?{10}^2$) and nanoparticle volume fractions ($0?\phi ?5\%$). Furthermore, the effects of three types of influential factors such as: orientation of conductive wall, thermal conductivity ratio ($0.2?K_r?25$) and conductive obstacles on the fluid flow and heat transfer rate are also investigated. It is found that the heat transfer rate is significantly enhanced by incrementing Rayleigh number and thermal conductivity ratio. It is also observed that at all Rayleigh numbers, the total Nusselt number rises and then reduces with increasing the nanoparticle volume fractions so that there is an optimal volume fraction of the nanoparticles where the heat transfer rate within the enclosure has a maximum value. Finally, the results reveal that by increasing the thermal conductivity of the nanoparticles and Rayleigh number, distribution of solid particles becomes uniform.     

Effect of strain rate on microstructure evolution of a nickel-based superalloy during hot deformation

The hot deformation behavior of a nickel-based superalloy was investigated by means of isothermal compression tests in the strain rate range of 0.001–10 s⁻¹ at 1110 °C. Transmission electron microscope (TEM) and electron backscatter diffraction (EBSD) technique were used to study the effect of strain rate on the microstructure evolution of the alloy during hot deformation. The results revealed that the dynamic recrystallization (DRX) process was stimulated at high strain rates ($\dot{\epsilon }⩾5{\text{s}}^{-1}$) due to the high dislocation density and adiabatic temperature rise. Meanwhile, high nucleation of DRX and low grain growth led to the fine DRX grains. In the strain rate rage of 0.001–1 s⁻¹, the volume fraction of DRX grains increased with the decreasing strain rate, and the grain growth gradually governed the DRX process. Moreover, the strain rate has an important effect on DDRX and CDRX during hot deformation. On the other hand, particular attention was also paid to the evolution of twin boundaries during hot deformation. It was found that there was a lower fraction of Σ3 boundaries at the intermediate strain rate of 1 s⁻¹, while the fractions of Σ3 boundaries were much higher at both the lower strain rates ($\dot{\epsilon }⩽0.1{\text{s}}^{-1}$) and higher strain rates ($\dot{\epsilon }⩾5{\text{s}}^{-1}$).     

Axisymmetric multiquadrics

This paper reviews the previous axisymmetric global interpolation functions used in the context of the dual reciprocity boundary element method and dual reciprocity method of fundamental solutions connected to axisymmetric Laplace operator. It complements our axisymmetric thin plate splines [1] with the axisymmetric form of the Hardy's multiquadrics ${(r^2+r_0^2)}^{m/2}$; m=±1. This new functions can be used in the improved Golberg–Chen–Karur [2] type of approximations. The basic equations are accompanied by a set of related expressions that permit straightforward use of the developed global interpolation functions in a broad spectrum of dual reciprocity boundary element method and method of fundamental solutions, and meshless direct collocation like discrete approximate procedures.     

A modified θ projection model for constant load creep curves-I. Introduction of the model

Estimating long-term creep deformation and life of materials is an effective way to ensure the service safety and to reduce the cost of long-term integrity evaluation of high temperature structural materials. Since the 1980s, the θ projection model has been widely used for predicting creep lives due to its ability to capture the characteristic transitions observed in creep curves obtained under constant true stress conditions. However, the creep rupture behavior under constant load or engineering stress conditions cannot be simulated accurately using this model because of the different stress states. In this paper, creep curves obtained under constant load conditions were analyzed using a modified θ projection model by considering the increase in true stress with creep deformation during the creep tests. This model is expressed as $\epsilon ={\theta }_1\left(1?{\text{e}}^{?{\theta }_{2}t}\right)+{\theta }_3\left(e^{{\theta }_4{e}^{{\theta }_5\epsilon }t}?1\right)$, and was validated using the creep curves of K465 and DZ125 superalloys tested at a range of temperatures and engineering stresses. Moreover, it was shown that the predictive capability of the modified θ projection model was significantly improved over the original one, as it reduces the prediction uncertainty from a range of 10% to 20% to below 5%. Meanwhile, it was shown that the model can be reasonably used for predicting constant stress creep conditions, when appropriate parameters are used. The prediction performance of the modified model will be discussed in another paper. The results of this study show great potential for the evaluation and assessment of the service safety of structural materials used in applications where designs are limited by creep deformation.     

The shape parameter in the Gaussian function II

This is a continuation of our former study, Luh [1], of the shape parameter $\beta$ contained in Gaussian $e^{?\beta |x{|}^2}$, $x\in R^n$. Instead of using the error bound presented by Madych and Nelson [2], here we adopt an improved error bound constructed by Luh to evaluate the influence of $\beta$ on error estimates. This results in a new set of criteria for the optimal choice of $\beta$ and much sharper error estimates for Gaussian interpolation. What is important is that the notorious ill-conditioning of Gaussian interpolation can be greatly relieved because in this approach the fill distance need not be very small.