Entropy generation analysis of eccentric cylinders pair sources on nanofluid natural convection with non-Boussinesq state

In this study, the natural convection heat transfer and entropy generation in horizontal eccentric cylinders with different arrangements of two constant temperature sources are investigated numerically. The distance between eccentric cylinders was filled with pure fluid and Cu_ water nanofluid. The sources with constant temperature T_h and T_c were located on the inner and outer cylinders and the other walls were assumed to be insulated. Governing equations were formulated by using Boussinesq approximation and non-Boussinesq state (density inversion) and were solved on a non-uniform mesh in eccentric cylinders by using the finite volume method. The numerical calculation was carried out for Rayleigh number (${10}^4?\text{Ra}?5\times {10}^5$), volume fraction of nanoparticles ($0?\mathrm{\Phi }?0.08$) and different arrangements of heat sources with different angles in Pr = 13.31 and constant eccentricity (e_v = 0.7). The results were compared with concentric cylinders and presented from streamlines and isotherms flow field, local and average Nusselt number, local and total entropy generation. The results showed that eccentricity, different arrangements, discrete constant temperature sources and non-Boussinesq state affected the best state of heat transfer. In addition, increasing Rayleigh number and volume fractions of nanoparticles caused an increase in the rate of heat transfer and total entropy generation. It was concluded that Boussinesq approximation and eccentric cylinders had higher rate of heat transfer and entropy generation than non-Boussinesq state and concentric cylinders, respectively. The results indicated which arrangements and kinds of cylinders were optimum and applicable to use in industry and heat exchanger.     

Nanofluid and porous fins effect on natural convection and entropy generation of flow inside a cavity

In the present study, natural convection of Cu-water nanofluid in a cavity with an array of porous fins on its hot wall has been numerically analyzed using two-phase approach. Use of porous fins, instead of solid ones, improves conduction while could have negligible effect on convection as flow can pass through them. Therefore, the effects of the number of fins and their length on heat transfer enhancement and entropy generation are scrutinized. The study has been conducted for the certain pertinent parameters of Rayleigh number (Ra = ${10}^4$ to ${10}^6$), Darcy number (Da = ${10}^{-1}$ to ${10}^{-4}$), and the nanoparticle volume fraction ($\phi$ = $0$ to $0.04$) and results are investigated in terms of heat transfer, entropy generation and performance coefficient (PEC). Numerical results indicate that adding porous fins with a high Darcy number improves heat transfer while fins with a low Darcy number can weaken the convection and decline Nusselt number. In strong flow fields an increase in either the length or the number of fins has insignificant effect on Nu. Also, low concentration of nanoparticles enhances the heat transfer more than high values of nanoparticles. On the other hand, entropy generation decreases by increasing the number of fins and PEC enhances by using porous fins in most of the studied cases. PEC of pure fluid is higher than the nanofluid at low Ra numbers, while opposite fact is observed for high Ra values.     

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.     

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.     

Numerical investigation of natural convection of Al2O3-water nanofluid in a wavy cavity with conductive inner block using Buongiorno’s two-phase model

By employing the finite element method, thermophoresis and Brownian diffusion are studied numerically relating to the natural convection in a wavy cavity that is filled with an ${\text{Al}}_2{\text{O}}_3$-water nanofluid possessing a central heat-conducting solid block that is influenced by the local heater located on the bottom wall. An isothermal condition is established in the two wavy vertical walls, while adiabatic condition is for the top horizontal wall. Partial heating is applied to the bottom of the horizontal wall, while the remaining part remains in the adiabatic condition. Empirical correlations are employed for the thermal conductivity and dynamic viscosity of the nanofluid. The number of oscillations ($1?N\le 4$), Rayleigh number (${10}^3?\mathit{Ra}\le {10}^6$), nanoparticles volume fraction ($0??\le 0.04$) and dimensionless length of the bottom heater ($0.2?H?0.8$) govern the parameters in this study. The grid independency test, as well as experimental and numerical data from other published works, was employed to validate the developed computational code comprehensively. Based on the obtained results, it was found that the heat transfer inside the cavity is enhanced by introducing nanoparticles as well as a selection of optimal number of oscillations.     

A modified θ projection model for constant load creep curves-II. Application of creep life prediction

To minimize the deviation of the predicted creep curves obtained under constant load conditions by the original θ projection model, a new modified version that can be expressed by $\epsilon ={\theta }_1\left(1-e^{-{\theta }_{2}t}\right)+{\theta }_3\left(e^{{\theta }_4{e}^{{\theta }_5\epsilon }t}-1\right)$, was derived and experimentally validated in our last study. In the present study, the predictive capability of the modified θ projection model was investigated by comparing the simulated and experimentally determined creep curves of K465 and DZ125 superalloys over a range of temperatures and stresses. Furthermore, the linear relationship between creep temperature and initial stress was extended to the 5-parameter model. The results indicated that the modified model could be used as a creep life prediction method, as it described the creep curve shape and resulted in predictions that fall within a specified error interval. Meanwhile, this modified model provides a more accurate way of describing creep curves under constant load conditions. The limitations and future direction of the modified model were also discussed. In addition, this modified θ projection model shows great potential for the evaluation and assessment of the service safety of structural materials used in components governed by creep deformation.     

New bounds on local strain fields inside random heterogeneous materials

A methodology is presented for bounding the higher $L^p$ norms, $2⩽p⩽\infty$, of the local strain inside random media. We present optimal lower bounds that are given in terms of the applied loading and volume fractions for random two phase composites. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to applied loads. These results deliver tight upper bounds on the macroscopic strength domains for statistically defined heterogeneous media.     

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 ($\dot{\epsilon }⩾5{\text{s}}^{-1}$).