Statistical Analysis of the Effect of Nanoparticles Volume Fraction on Turbulent Forced Convective Heat Transfer Coefficient of Nanofluid in a Circular Tube

In this paper, the statistical analysis of the effect of nanoparticles volume fraction on one of the most important thermal characteristics turbulent flow of nanofluid i.e. convection heat transfer coefficient, inside a circular tube with uniform wall heat flux is investigated numerically. Also, water as a base fluid and Al2O3 as suspended particles with a diameter of 36 nm are considered. Heat transfer characteristics are computed using the solution of elliptic equations based on discrete the finite volume method and the second order upwind. The relationship between pressure and velocity using SIMPLEC algorithm is established. In this study, the variation of volume fraction of nanoparticles is assumed in the range of 0 to 6%. The best probability distribution function of the heat transfer parameters are selected using chi square test that various probability distribution such as: Gamma, Normal, Lognormal, Gumbel, and Frechet are evaluated based on numerical analysis of tube flow. After reviewing the results, it was found that with increasing volume fraction of nanoparticles, the convective heat transfer coefficient increases. On the other hand, the convective heat transfer coefficients with regard to variation of volume fraction of nanoparticles follow Gumbel Max probability distribution function

FIRST OREDR RELIABILITY METHOD OF STRACTURS USINGA IMPRVED HARMONY SEARCH OPTIMIZATION

The first order reliability method (FORM) is widely used to estimate the failure probability of structures. Appropriate evaluation of the reliability index is more important to estimate the failure probability in FORM. Generally, the iterative mathematical formula of FORM (i.e. Hasofer and Lind- Rackwitz and Fiessler (HL-RF)) was shown the instable solution of reliability index in highly nonlinear problems. The harmony search algorithm can be estimated the reliability index for concave and convex reliability problems due to capability and not need the gradient vector of random variables. In this paper, a global-best harmony search (GHS) algorithm with small harmony memory was proposed. In proposed GHS, a dynamical bandwidth, which is computed based on number of random variables, is proposed to adjust the harmony memory by a random generation with Normal distribution function. Accuracy and robustness of the proposed GHS have been compared with the HL-RF and stability transformation method (STM) through several limit state functions to that have been taken from. The results indicate that the HL-RF formula of FORM was not converged in several nonlinear examples. The proposed GHS was converged as similar as the STM results but it is more efficient )there is required less iterations to converge than STM). The GHS algorithm has top performance both of accuracy fast convergence rate

Conjugate and Directional Chaos Control Methods for Reliability Analysis of CNT–Reinforced Nanocomposite Beams under Buckling Forces; A Comparative Study

The efficiency and robustness of reliability methods are two important factors in the first-order reliability method (FORM). The conjugate choice control (CCC) and directional chaos control method (DCC) are developed to improve the robustness and efficiency of the FORM formula using the stability transformation method. In this paper, the CCC and DCC methods are applied for the reliability analysis of a nanocomposite beam as a complex engineering problem, which is reinforced by carbon nanotubes (CNTs) under buckling force. The probabilistic model for nanocomposite beam is developed through the buckling failure mode which is computed by using the Euler-Bernoulli beam model. The robustness and efficiency CCC and DCC are compared using the stable solution and a number of call limit state functions. The results demonstrate that the CCC method is more robust than the DCC in this case, while the DCC method is simpler than the CCC

An Enhanced HL-RF Method for the Computation of Structural Failure Probability Based On Relaxed Approach

The computation of structural failure probability is vital importance in the reliability analysis and may be carried out on the basis of the first-order reliability method using various mathematical iterative approaches such as Hasofer-Lind and Rackwitz-Fiessler (HL-RF). This method may not converge in complicated problems and nonlinear limit state functions, which usually shows itself in the form of periodic, bifurcation and chaos solution. In this paper, the HL-RF method has been improved based on the relaxed method to overcome these numerical instabilities. An appropriate relaxed coefficient has been defined, ranging between 0 and 1, to enhance the HL-RF method. This coefficient can be computed using the information from the new and previous iterations of the HL-RF algorithm based on second-order fitting. Capability, robustness and efficiency of the proposed algorithm have been studied by results of several examples compared to the HL-RF. Results illustrated that the proposed method is more efficient and robust in the computation of the failure probability compared to the HL-RF method

Reliability Analysis of Corroded Reinforced Concrete Beams Using Enhanced HL-RF Method

Steel corrosion of bars in concrete structures is a complex process which leads to the reduction of the cross-section bars and decreasing the resistance of the concrete and steel materials. In this study, reliability analysis of a reinforced concrete beam with corrosion defects under the distributed load was investigated using the enhanced Hasofer-Lind and Rackwitz-Fiessler (EHL-RF) method based on relaxed approach. Robustness of the EHL-RF algorithm was compared with the HL-RF using a complicated example. It was seen that the EHL-RF algorithm is more robust than the HL-RF method. Finally, the effects of corrosion time were investigated using the EHL-RF algorithm for a reinforced concrete beam based on flexural strength in the pitting and general corrosion. The model uncertainties were considered in the resistance and load terms of flexural strength limit state function. The results illustrated that increasing the corrosion time-period leads to increase in the failure probability of the corroded concrete beam

Self-adaptive conjugate method for a robust and efficient performance measure approach for reliability-based design optimization

The advanced mean value and hybrid mean value methods are commonly used to evaluate the probabilistic constraint of reliability-based design optimization (RBDO) problems. These iterative methods can yield unstable solutions to highly nonlinear performance functions. The conjugate gradient analysis (CGA) and modified chaos control (MCC) algorithms have recently been employed to achieve the stabilization of reliability analysis in RBDO problems. However, the CGA and the MCC methods can be inefficient for convex performance functions. In this paper, a self-adaptive conjugate gradient (SCG) method is proposed to improve the efficiency of the minimum performance target point (MPTP) search based on an adaptive conjugate scalar factor for highly nonlinear concave and convex problems. With this aim, the conjugate search direction is adaptively computed using the mean value of the previous performance function with a limited conjugate scalar factor. The efficiency and robustness of the proposed SCG algorithm are compared with those of different reliability methods using five nonlinear concave/convex reliability problems and two mathematical/structural RBDO examples. The results indicate that the SCG method accurately converges after less iterations compared to other existing reliability methods. The SCG method is a robust iterative formula for inverse reliability analysis and RBDO