Convergence analysis of the Neumann–Neumann waveform relaxation method for time-fractional RC circuits

Wu, Shu‐Lin; Al-Khaleel, Mohammad

doi:10.1016/j.simpat.2016.01.002

Cited by 20 publications

(11 citation statements)

References 20 publications

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“…Various numerical methods can be exploited in order to find solutions of the differential equations whether in parallel or in sequential (see, e.g., [ 45 , 46 , 47 , 48 ]). Here, the main equations and accompanying initial boundary conditions are addressed using the Galerkin finite element method.…”

Section: Numerical Methodologymentioning

confidence: 99%

Natural Convection within Inversed T-Shaped Enclosure Filled by Nano-Enhanced Phase Change Material: Numerical Investigation

et al. 2022

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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 increasing interest. In the current report, we intend to simulate the natural convection flow of NePCM inside an inverse T-shaped enclosure. The complex nature of the flow results from the following factors: the enclosure contains a hot trapezoidal fin on the bottom wall, the enclosure is saturated with pours media, and it is exposed to a magnetic field. The governing equations of the studied system are numerically addressed by the higher order Galerkin finite element method (GFEM). The impacts of the Darcy number (Da = 10−2–10−5), Rayleigh number (Ra = 103–106), nanoparticle volume fraction (φ = 0–0.08), and Hartmann number (Ha = 0–100) are analyzed. The results indicate that both local and average Nusselt numbers were considerably affected by Ra and Da values, while the influence of other parameters was negligible. Increasing Ra (increasing buoyancy force) from 103 to 106 enhanced the maximum average Nusselt number by 740%, while increasing Da (increasing the permeability) from 10−5 to 10−2 enhanced both the maximum average Nusselt number and the maximum local Nusselt number by the same rate (360%).

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Section: Numerical Methodologymentioning

confidence: 99%

Natural Convection within Inversed T-Shaped Enclosure Filled by Nano-Enhanced Phase Change Material: Numerical Investigation

et al. 2022

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“…Roughly speaking, in engineering and applied sciences, mathematical modeling, analysis, and techniques are widely used (see for instance [ 47 , 48 , 49 , 50 , 51 ]). With that has been said, an enthalpy–porosity analysis is a well-used approach for assessing unstable heat transfer situations, such as PCM phase transitions.…”

Section: Mathematical Modelmentioning

confidence: 99%

Enhancing the Melting Process of Shell-and-Tube PCM Thermal Energy Storage Unit Using Modified Tube Design

et al. 2022

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Recently, phase change materials (PCMs) have gained great attention from engineers and researchers due to their exceptional properties for thermal energy storing, which would effectively aid in reducing carbon footprint and support the global transition of using renewable energy. The current research attempts to enhance the thermal performance of a shell-and-tube heat exchanger by means of using PCM and a modified tube design. The enthalpy–porosity method is employed for modelling the phase change. Paraffin wax is treated as PCM and poured within the annulus; the annulus comprises a circular shell and a fined wavy (trefoil-shaped) tube. In addition, copper nanoparticles are incorporated with the base PCM to enhance the thermal conductivity and melting rate. Effects of many factors, including nanoparticle concentration, the orientation of the interior wavy tube, and the fin length, were examined. Results obtained from the current model imply that Cu nanoparticles added to PCM materials improve thermal and melting properties while reducing entropy formation. The highest results (27% decrease in melting time) are obtained when a concentration of nanoparticles of 8% is used. Additionally, the fins’ location is critical because fins with 45° inclination could achieve a 50% expedition in the melting process.

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“…Water Mass (m 1 ): h such numerical techniques and mathematical tools play a substantial role in solving the various problems that appear in different applications in applied sciences and engineering (see, e.g., [26][27][28][29][30][31][32]).…”

Section: Mathematical Modeling and Equationsmentioning

confidence: 99%

Inverted Solar Stills: A Comprehensive Review of Designs, Mathematical Models, Performance, and Modern Combinations

et al. 2022

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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 subterranean water has been proven to be a promising green technology. It produces distilled water which can be used as potable water for drinking and other purposes. The designs, operations, and configurations of several inverted solar stills are thoroughly examined in this article. All techniques for solar water distillation to separate saltwater from freshwater have the same fundamental idea. It has been demonstrated that for a specified mass of water in the top basin, the daily output of an inverted absorber double-basin solar still (IASS) grows with increasing water depth in the bottom basin. Nevertheless, as the water depth in the bottom basin rises from 1 cm to 5 cm, the output of an inverted absorber double-basin solar system falls by about 27%. At water depths of 4, 6, and 8 cm, the daily yields from inverted absorber solar stills paired with a refrigeration cycle (RIASS) were 6.4, 10.08, and 9.5 L/day, respectively. The results also showed a substantial rise in water temperature in the inverted absorber solar still as a result of lower bottom heat loss and larger absorptivity. In this study, the emphasis on energy, efficiency, and environmental concerns remains with the modified multi-wick basin-type inverted absorber solar panel. The performance of the inverted trickling solar still was assessed with a 60 ppm average salinity under various sun radiation, feed water flow rate, and existence conditions for natural convection. It was found that the still could produce 2.55 L/day m2 of fresh water, a 15% increase. Brackish water with a salinity of 6000 ppm was used to test the still in November at tilt angles of 47° and 32°. Condensate production at the specified angles was 2.8 and 2 L/d, respectively. A total output of 6.907, 5.681, and 4.650 kg/m2/day was also generated using the modified multi-wick basin-type inverted absorber solar still (MMWBIASS) at water depths of 1, 2, and 3 cm, respectively. With black cotton wicks, the MMWBIASS had a total thermal efficiency of 34.04%, 28.17%, and 23.61%.

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Convergence analysis of the Neumann–Neumann waveform relaxation method for time-fractional RC circuits

Cited by 20 publications

References 20 publications

Natural Convection within Inversed T-Shaped Enclosure Filled by Nano-Enhanced Phase Change Material: Numerical Investigation

Natural Convection within Inversed T-Shaped Enclosure Filled by Nano-Enhanced Phase Change Material: Numerical Investigation

Enhancing the Melting Process of Shell-and-Tube PCM Thermal Energy Storage Unit Using Modified Tube Design

Inverted Solar Stills: A Comprehensive Review of Designs, Mathematical Models, Performance, and Modern Combinations

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