Scipedia: RIMNI SPECIAL ISSUE - Numerical Methods and Computational Simulations in Physical Sciences: Advances and Challenges

Coupled Thermal and Solutal Transport in Magnetic Nanofluids with Field-Dependent Viscosity in Porous Media: A Stability Perspective

Scipedia content — Thu, 21 May 2026 10:11:14 +0200

This study investigates the linear stability of double-diffusive convection in magnetic nanofluids (MNFs) within a horizontal porous medium, accounting for field–dependent viscosity (FDV). A modified Buongiorno– type model incorporates Brownian motion, thermophoresis, magnetophoresis, and Darcy resistance. The resulting eigenvalue problem is solved via a Chebyshev pseudospectral–QZ algorithm under rigid–rigid (RR), rigid–free (RF), and free–free (FF) boundary conditions for both water–based (Wb) and ester–based (Eb) MNFs. Results show that magnetic and solutal effects lower the critical Rayleigh number (Rac) from the classical Darcy–Bénard limit of ≈39.48 to as low as ≈23.8, indicating enhanced instability. In contrast, increasing the FDV coefficient (δ), Langevin parameter (αL), and nanoparticle concentration difference (�φ) raises Rac, stabilizing the system. Eb–MNFs exhibit consistently higher Rac values—by 15%–20% compared to Wb–MNFs, due to greater viscosity and lower thermal diffusivity. These findings clarify the interplay of magnetoviscous damping and solutal buoyancy, offering predictive insights for the design of magnetically tunable porous heat exchangers and thermal management systems.

On Nonlinear Monge-Ampère Equations and Their Symmetry Classifications

Scipedia content — Thu, 21 May 2026 10:06:04 +0200

The Monge-Ampère equation (MAE) plays a pivotal role across a broad spectrum of theoretical and applied sciences, with its solutions being essential for advancing various fields. This study explores all forms of the fully nonlinear MAE using Lie group transformations to reduce the equation into solvable forms. Analytical solutions are derived using ansatzbased methods, yielding novel and generalized results that enhance the existing body of knowledge. In particular, solutions for cases with diverse source functions and boundary conditions are obtained, addressing gaps in the literature. Stability of the solutions is studied through both analytical and numerical approaches. Comparisons with existing solutions demonstrate the efficiency and generality of the proposed methods. The results presented in this work are poised to impact numerous applications, providing a robust framework for further research on MAEs.OPEN ACCESS Received: 24/05/2025 Accepted: 07/08/2025 Published: 27/10/2025

Analysis of Burr-XII Lifespan Using Adaptive Progressive Type-II Hybrid Binomial Censoring with Physical Modeling of Polyester and Carbon Fibers

Scipedia content — Thu, 21 May 2026 10:08:04 +0200

This study introduces advanced statistical methods, allowing for more efficient and accurate reliability testing of fibers such as polyester and carbon. Polyester ficbers are suitable for textiles and industrial use due to their wrinkle resistance and affordability, while carbon fibers offer superior strength, thermal stability, and corrosion resistance. To guarantee greater efficiency of inference methodologies and reduce overall testing time, the adaptive Type-II progressive hybrid censoring via binomial removals has gained popularity in reliability analysis and life-testing problems. The proposed scheme allows survival units to be removed at random stages according to a binomial law, thereby reducing experimental time while preserving statistical efficiency. When lifetimes are gathered using the suggested censoring technique, point and interval estimates of the unknown parameters of the Burr-XII model are obtained using both classical and Bayesian approaches. We obtain various Bayesian estimates using the squared loss function. Some numerical methods are employed to obtain the suggested estimators due to their complexity. The various Bayes estimates and related credible intervals are created using Markov chain Monte Carlo techniques. To assess estimator performance, extensive simulation studies are conducted, comparing bias, mean squared error, coverage probabilities, and interval lengths under varying censoring and removal settings. The simulation results confirm that the Bayesian framework, particularly with informative priors, provides more accurate and stable estimates than asymptotic likelihood-based methods. We examine two physics data sets representing polyester and carbon fibers to demonstrate the relevance of the suggested approaches in a real-world setting. These applications highlight the practical value of the proposed approach for material design, maintenance planning, and broader reliability engineering problems.OPEN ACCESS Received: 13/06/2025 Accepted: 12/09/2025 Published: 23/01/2026

Analysis of Airflow Velocity on Microdroplets Using Weibull StressStress Reliability Index under Unified Type-I Progressive Hybrid Data

Scipedia content — Thu, 21 May 2026 10:09:03 +0200

This work presents a novel and comprehensive inferential framework for analyzing the stress-strength reliability parameter,R= P(Y < X), where X and Y denote independent stress and strength variables, respectively, both modeled as Weibull-distributed with a shared shape parameter but distinct scale parameters. A key innovation of this study lies in its integration of the unified Type-I progressively hybrid censoring scheme, which simultaneously accommodates time constraints and partial failure information, conditions often encountered in real-world reliability testing. To estimate R, we propose and evaluate four distinct inferential strategies: two frequentist (maximum likelihood estimation and maximum spacings estimation) and two Bayesian, each tailored to either the likelihood or spacings-based posterior formulation. The Bayesian methods employ Monte Carlo sampling to compute both Bayes point estimates and credible intervals under informative priors, offering robustness in small-sample or heavily censored contexts. An extensive simulation study is conducted to systematically compare the estimators in terms of bias, efficiency, and interval coverage. To validate the practical applicability of our framework, we further analyze two real-world microdroplet datasets, revealing critical insights into stress-tolerance behavior under experimental constraints. This study not only advances methodological tools for reliability inference under hybrid censoring but also establishes a blueprint for combining classical and Bayesian paradigms in stress-strength modeling.OPEN ACCESS Received: 01/07/2025 Accepted: 02/09/2025 Published: 23/01/2026