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    Comparative analysis of the fractional order Cahn-Allen equation
    (Elsevier B.V., 2023) Khan, Ibrar; Nawaz, Rashid; Ali, Ali Hasan; Akgul, Ali; Lone, Showkat Ahmad
    This current work presents a comparative study of the fractional-order Cahn-Allen (CA) equation, where the non-integer derivative is taken in the Caputo sense.The Cahn-Allen equation is an equation that assists in the comprehension of phase transitions and pattern formation in physical systems. This equation describes how different phases of matter, such as solids and liquids, change and interact throughout time. We employ two analytical methods: the Laplace Residual Power Series Method (LRPSM) and the New Iterative Method (NIM), to solve the proposed model. The LRPSM is a combination of the Laplace Transform and the Residual Power Series Method, while the New Iterative Method is a modified form of the Adomian Decomposition Method that does not require any type of polynomial or digitization. For the purpose of accuracy and reliability, we compare our findings with other methods and the exact solution used in the literature. Additionally, 2D and 3D plots are generated for various fractional order values denoted as p. These plots illustrate that as the fractional order p approaches 1, the graph of the approximate solution gradually coincides with the graph of the exact solution. © 2023 The Author(s)
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    Öğe
    Scrutinization of local thermal non-equilibrium effects on stagnation point flow of hybrid nanofluid containing gyrotactic microorganisms: a bio-fuel cells and bio-microsystem technology application
    (Springer, 2024) Okasha, Mostafa Mohamed; Abbas, Munawar; Formanova, Shoira; Faiz, Zeshan; Ali, Ali Hasan; Akgül, Ali; Galal, Ahmed M.
    The impact of Stefan blowing on the stagnation point flow of HNF (hybrid nanofluid) across a sheet containing gyrotactic microorganisms under local thermal non-equilibrium conditions (LTNECs) is briefly discussed in this paper. The present work uses a simplified mathematical model to inspect the characteristics of heat transfer in the absence of LTNECs (local thermal equilibrium conditions). LTNECs, traditionally provide two distinct fundamental temperature gradients for the liquid and solid phases simultaneously. A hybrid nanofluid is a mixture of water as the base fluid and single-walled carbon nanotubes and multi-walled carbon nanotubes. Gyrotactic microorganisms are included into nanoparticles to increase their thermal efficiency in a variety of systems, including microbial fuel cells, enzyme biosensors, bacteria powered micromixers, chip-shaped microdevices like bio-microsystems, and micro-volumes like microfluidic devices. This model can also help environmental engineering by enhancing wastewater treatment procedures by allowing microorganisms to break down pollutants more effectively. It advances the development of more productive photo bioreactors, increasing the output of biofuels in the field of renewable energy. Material scientists can utilize this concept to develop controlled nanostructured materials with consistent composition and thermal properties. The considerable similarity transformation is used to build ordinary differential equations for the nonlinear dimensionless system. This problem is solved numerically by using the Bvp4c method. The results determine that when the Stefan blowing parameter increases, fluid flow increases but temperature, mass transfer rate, and heat transfer are decreased.