Inverted solar stills: A comprehensive review of designs, mathematical models, performance, and modern combinations

AK Hussein, FL Rashid, AM Abed, M Al-Khaleel… - Sustainability, 2022 - mdpi.com
Fresh water is scarce, making it a worldwide issue. In order to address global freshwater
demand, a filtration technique is needed. Solar distillation (SD) that purifies brackish and …

Natural convection within inversed T-shaped enclosure filled by nano-enhanced phase change material: Numerical investigation

A Abderrahmane, M Al-Khaleel, A Mourad, H Laidoudi… - Nanomaterials, 2022 - mdpi.com
Energy saving has always been a topic of great interest. The usage of nano-enhanced
phase change material NePCM is one of the energy-saving methods that has gained …

2D MHD mixed convection in a zigzag trapezoidal thermal energy storage system using NEPCM

A Abderrahmane, O Younis, M Al-Khaleel, H Laidoudi… - Nanomaterials, 2022 - mdpi.com
In a magnetic field, two-dimensional (2D) mixed convection is investigated within a
zigzagged trapezoidal chamber. The lower side of the trapezoidal chamber is irregular, in …

Enhancing the melting process of shell-and-tube PCM thermal energy storage unit using modified tube design

A Abderrahmane, NAA Qasem, A Mourad… - Nanomaterials, 2022 - mdpi.com
Recently, phase change materials (PCMs) have gained great attention from engineers and
researchers due to their exceptional properties for thermal energy storing, which would …

Atomic solution for certain Gardner equation

M Al-Khaleel, S Al-Sharif, A AlJarrah - Symmetry, 2023 - mdpi.com
In this paper, a new technique using a tensor product is presented in order to provide exact
solutions to some certain fractional differential equations. Particularly, the well-known third …

[HTML][HTML] Analytical solutions for autonomous differential equations with weighted derivatives

R AlAhmad, M Al-Khaleel - Partial Differential Equations in Applied …, 2024 - Elsevier
In this work, we introduce a new definition of weighted derivatives along with corresponding
integral operators, which aim to facilitate the solution of both linear and non-linear …

Fully discrete Schwarz waveform relaxation analysis for the heat equation on a finite spatial domain

RD Haynes, K Mohammad - ESAIM: Mathematical Modelling and …, 2023 - esaim-m2an.org
Schwarz waveform relaxation methods provide space-time parallelism for the solution of
time dependent partial differential equations. The algorithms are differentiated by the choice …

Parameter Optimization in Waveform Relaxation for Fractional-Order Circuits

SL Wu, M Al-Khaleel - … Transactions on Circuits and Systems I …, 2017 - ieeexplore.ieee.org
The longitudinal waveform relaxation (WR) proposed by Gander and Ruehli converges
faster than the classical WR method. For the former, a free parameter α is contained, which …

A mathematical analysis of discrete waveform relaxation algorithms for transmission line type circuits

M Al-Khaleel, SL Wu - 2021 IEEE Asia-Pacific Conference on …, 2021 - ieeexplore.ieee.org
Convergence rate is greatly improved by using the new waveform relaxation (WR) methods,
known as optimized waveform relaxation (OWR) algorithms, over the classical ones due to …

On solutions of linear and nonlinear fractional differential equations with application to fractional order RC type circuits

R AlAhmad, M Al-Khaleel, H Almefleh - Journal of Computational and …, 2024 - Elsevier
In this paper, we solve a class of fractional differential equations of order α∈(0, 1) in Caputo–
Fabrizio sense. Importantly, we highlight relations between the Caputo–Fabrizio and …