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The purpose of this paper is to develop robust metamodels, which allow propagating parametric uncertainties, in the presence of localized nonlinearities, with reduced cost and without significant loss of accuracy.

The proposed metamodels combine the generalized polynomial chaos expansion (gPCE) for the uncertainty propagation and reduced order models (ROMs). Based on the computation of deterministic responses, the gPCE requires prohibitive computational time for large-size finite element models, large number of uncertain parameters and presence of nonlinearities. To overcome this issue, a first metamodel is created by combining the gPCE and a ROM based on the enrichment of the truncated Ritz basis using static residuals taking into account the stochastic and nonlinear effects. The extension to the Craig–Bampton approach leads to a second metamodel.

Implementing the metamodels to approximate the time responses of a frame and a coupled micro-beams structure containing localized nonlinearities and stochastic parameters permits to significantly reduce computation cost with acceptable loss of accuracy, with respect to the reference Latin Hypercube Sampling method.

The proposed combination of the gPCE and the ROMs leads to a computationally efficient and accurate tool for robust design in the presence of parametric uncertainties and localized nonlinearities.

To provide a finite volume code, based on Cartesian coordinates, for studying combined conductive and radiative heat transfer in three‐dimensional irregular geometries.

In the present study, a three‐dimensional blocked‐off‐region procedure was presented and implemented in a numerical code based on the finite volume method to model combined conductive and radiative heat transfer in complex geometries. This formulation was developed and tested in three‐dimensional complex enclosures with diffuse reflective surfaces and containing gray absorbing‐emitting and isotropically scattering medium. This approach was applied to analyze the effect of the main of thermoradiative parameters on the temperature and flux values for three‐dimensional L‐shaped enclosure.

The proposed isotropic model leads to satisfactory solutions with comparison to reference data, which entitles us to extend it to anisotropic diffusion cases or to non‐gray media. The blocked‐off‐region procedure traits both straight and curvilinear boundaries. For curved or inclined boundaries, a fine or a non‐uniform grid is needed.

This paper offers a simple Cartesian practical technique to study the combined conductive and radiative heat transfer in three‐dimensional complex enclosures with both straight and curvilinear boundaries.

This study aims to develop a decision support tool to improve planning for the rehabilitation of water distribution networks (WDN) using the analytical hierarchy process (AHP) method and the urgency level score.

In this paper the AHP method was used to outclass the indicators having a strong influence on the deterioration of the pipes and the score of the level of urgency is calculated to establish the rehabilitation program (short, medium and long term). The proposed model was tested for the case of the city of Souk-Ahras in Algeria.

Based on the judgments of twenty-four experts, the relative weights of the three physical, operational and environmental criteria of the pipeline were calculated and found to be equal to 35.40%, 55.60% and 9.00%, respectively. The two indicators, number of failures and pressure, were found to have the highest overall weights. The results of this article can be used to improve decision-making in WDN rehabilitation planning in Algeria.

The main objective of water companies is to provide citizens with good quality drinking water in sufficient quantity. However, over time, WDN age, degrade and deteriorate. This degradation leads to a drop in the performance through the degradation of water quality and an increase in loss rates. WDN rehabilitation is one of the most widely adopted solutions to address these drawbacks.

Application of a hybrid method (AHP- Level of Emergency) for the planning of the rehabilitation of WDN in Algeria.

The modern day has seen an increase in the prevalence of the improvement of high-performance thermal systems for the enhancement of heat transmission. Numerous studies and research projects have been carried out to acquire an understanding of heat transport performance for their functional application to heat conveyance augmentation. The idea of this study is to inspect the entropy production in Darcy-Forchheimer Ree-Eyring nanofluid containing bioconvection flow toward a stretching surface is the topic of discussion in this paper. It is also important to take into account the influence of gravitational forces, double stratification, heat source–sink and thermal radiation. In light of the second rule of thermodynamics, a model of the generation of total entropy is presented.

Incorporating boundary layer assumptions allows one to derive the governing system of partial differential equations. The dimensional flow model is transformed into a non-dimensional representation by applying the appropriate transformations. To deal with dimensionless flow expressions, the built-in shooting method and the BVP4c code in the Matlab software are used. Graphical analysis is performed on the data to investigate the variation in velocity, temperature, concentration, motile microorganisms, Bejan number and entropy production concerning the involved parameters.

The authors have analytically assessed the impact of Darcy Forchheimer's flow of nanofluid due to a spinning disc with slip conditions and microorganisms. The modeled equations are reset into the non-dimensional form of ordinary differential equations. Which are further solved through the BVP4c approach. The results are presented in the form of tables and figures for velocity, mass, energy and motile microbe profiles. The key conclusions are: The rate of skin friction incessantly reduces with the variation of the Weissenberg number, porosity parameter and Forchheimer number. The rising values of the Prandtl number reduce the energy transmission rate while accelerating the mass transfer rate. Similarly, the effect of Nb (Brownian motion) enhances the energy and mass transfer rates. The rate of augments with the flourishing values of bioconvection Lewis and Peclet number. The factor of concentration of microorganisms is reported to have a diminishing effect on the profile. The velocity, energy and entropy generation enhance with the rising values of the Weissenberg number.

According to the findings of the study, a slip flow of Ree-Eyring nanofluid was observed in the presence of entropy production and heat sources/sinks. There are features when the implementations of Darcy–Forchheimer come into play. In addition to that, double stratification with chemical reaction characteristics is presented as a new feature. The flow was caused by the stretching sheet. It has been brought to people's attention that although there are some investigations accessible on the flow of Ree-Eyring nanofluid with double stratification, they are not presented. This research draws attention to a previously unexplored topic and demonstrates a successful attempt to construct a model with distinctive characteristics.

The purpose of this study is to examine the effects of inclination angle on the thermal energy storage capability of a phase change material (PCM) within a disc-shaped container. Different container materials are also tested such as plexiglass and aluminium. This study aims to assess the energy storage capacity, melting behaviour and temperature distributions of PCM with a specific melting range (22°C–26°C) for various governing parameters such as inclination angles, aspect ratios (AR) and temperature differences (ΔT) and compare the melting behaviour and energy storage performance of PCM in aluminium containers to those in plexiglass containers.

A finite volume approach was adopted to evaluate the thermal energy storage capability of PCMs. Five inclination angles ranging from 0° to 180° were considered and the energy storage capacity. Also, the melting behaviour of the PCM and temperature distributions of the container with different materials were tested. Two different AR and ΔT values were chosen as parameters to analyse for their effects on the melting performance of the PCM. Conjugate heat transfer problem is solved to see the effects of conduction mode of heat transfer.

The results of the study indicate that as AR decreases, the effect of the inclination angles on the energy storage capacity of the PCM decreases. For lower ΔT, the difference between the maximum and minimum stored energies was 20.88% for AR = 0.20, whereas it was 6.85% for AR = 0.15. Furthermore, under the same conditions, the PCM stored 8.02% more energy in plexiglass containers than in aluminium containers.

This study contributes to the understanding of the influence of inclination angle, container material, AR and ΔT on the thermal energy storage capabilities of PCM in a novel designed container. The findings highlight the importance of AR in mitigating the effect of the inclination angle on energy storage capacity. Additionally, comparing aluminium and plexiglass containers provides insights into the effect of container material on the melting behaviour and energy storage properties of PCM.

This paper aims to use the Lattice Boltzmann method (LBM) to numerically simulate the natural convection heat transfer of Cu-water nanofluid in an L-shaped enclosure with curved boundaries.

LBM on three different models of curved L-shape cavity using staircase approach is applied to perform a comparative investigation for the effects of curved boundary on fluid flow and heat transfer. The staircase approximation is a straightforward and efficient approach to simulating curved boundaries in LBM.

The effect of curved boundary on natural convection in different parameter ranges of Rayleigh number and nanoparticle volume fraction is investigated. The curved L-shape results are also compared to the rectangular L-shape results that were also achieved in this study. The curved boundary LBM simulation is also validated with existing studies, which shows great accuracy in this study. The results show that the top curved boundary in curved L-shape models causes a notable increase in the Nusselt number values.

Based on existing literature, there is a lack of comparative studies which would specifically examine the effects of curved boundaries on natural convection in closed cavities. Particularly, the application of curved boundaries to an L-shape cavity has not been examined. In this study, curved boundaries are applied to the sharp corners of the bending section in the L-shape and the results of the curved L-shape models are compared to the simple rectangular L-shape model. Hence, a comparative evaluation is performed for the effect of curved boundaries on fluid flow in the L-shape enclosure.