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Öğe A comparative study of two-phase flow of an infusion of gyrotactic microorganisms and dust particles in trihybrid nanofluid with melting phenomena and Soret–Dufour effects(Springer Science and Business Media LLC, 2024-12-27) Munawar Abbas; Mostafa Mohamed Okasha; Nargiza Kamolova; Ali Hasan Ali; Ibrahim Mahariq; Ali Akgül; Ahmed M. GalalBackground: This investigation's main goal is to examine the impacts of Soret and Dufour on Marangoni convective flow of dusty trihybrid nanofluid over a Plate containing gyrotactic microorganisms, heat generation, and melting processes. A trihybrid nanofluid containing nanoparticles of Magnesium oxide MgO, Titanium dioxide TiO2, and Silver Ag in a water-based fluid. This proposed model is used to contrast the activity of dual well-known trihybrid nanofluid models for thermal conductivity, the Hamilton–Crosser model and the Yamada-Ota model. Methods: An appropriate similarity variable is utilized to reduce governing partial differential equations to couple nonlinear ordinary differential equations. After that the system of equations is numerically solved using the effective Bvp4c Method. Applications: Especially in high-performance cooling applications like electronics and aeronautical engineering, this comprehensive study could be very helpful in enhancing thermal management systems. With regard to the introduction of bio-convection brought about by the presence of gyrotactic bacteria, this model can be applied to advanced bio-engineering applications such as bioreactors and medical equipment. Understanding the behavior of these complex fluids under gradients in concentration and Soret–Dufour effects may also lead to improvements in the production and processing of materials, where precise temperature and concentration controls are critical. Results: The temperature and velocity distributions of the dusty ternary hybrid nanofluid are shown to be predominant with higher melting parameters; while, the concentration and microorganism distributions show the opposite pattern.Öğe A hybrid fractional model for cervical cancer due to human papillomavirus infection(Elsevier BV, 2025-03) Ali Akgül; Nauman Ahmed; Sadiya Ali Rano; Qasem Al-MdallalNumerous scientific and engineering applications exist for thermofluids. The primary cause of cervical cancer is the human papillomavirus (HPV), and thermos-fluid is crucial for identifying, treating, and understanding the cancerous phenomenon. In this work, a hybrid fractional order mathematical model of cervical cancer with modified parameters is studied. The proposed model consists of three fractional order nonlinear differential equations. The Grünwald Letnikov method is used to approximate the hybrid operator. A nonstandard finite difference scheme for the GL approximation is obtained to study the proposed model. Stability analysis of the used method is given, existence and uniqueness of solution to the hybrid model are given. Comparative studies between the two schemes is given. Convergence of the state variables is also shown to converge to true equilibrium points according to the stability conditions of the reproductive number. The effect of the order of fractional derivatives can also be observed in the simulations. In the end, concluding remarks are also given in the conclusion section that reflect the whole current research.Öğe A new plentiful solutions for nanosolitons of ionic (NSIW) waves spread the length of microtubules in (MLC) living cells(Springer Science and Business Media LLC, 2025-02-20) Loubna Ouahid; M. A. Abdou; Jameelah S. Al Shahrani; A. Mohamed Abdel-Baset; Ali Akgül; Murad Khan HassaniThis article describes the developed Paul-Painlike method (PPM) to provide striking ODE of the nanosoliton of the ionic waves (NSIW) that spread the length of microtubules in live cells. Furthermore, Auxiliary Equation Approach (AEA) and Sardar Sub Equation Approach (SSEA) have been utilized similarly and concurrently to determine solutions for this particular model. In providing a physical explanation, various solitary wave structures are visually represented. These solutions include the anti-kink, kink shape, singular kink wave shape, and periodic bright, bright-dark and dark-singular soliton solution. Additionally, graphical illustrations (both 2-D and 3-D) demonstrate how the various parameters utilized affect the validity of analytical results. Furthermore, the uniqueness of the solutions we derived is highlighted by comparing the differences with earlier solutions of the model. The solutions produced may be beneficial in a number of significant investigations in medicine, as well as biology. The results demonstrate the effectiveness of the proposed techniques for determining many optical solitons of nonlinear evolution equations.Öğe A numerical study of the fractional SIR epidemic model of an infectious disease via the reproducing kernel Hilbert space method(Elsevier, 2025) Nourhane Attia; Ali AkgülIn this chapter, we explore the application of the reproducing kernel Hilbert-space (RK-HS) method to solve a fractional SIR epidemic model that is non-linear with unidentified parameters. This model is of significant importance in epidemiology and medical science for understanding the dynamics of disease spread and control. Our contribution lies in the application of the RK-HS method to this particular fractional SIR model, which, to the best of our knowledge, has not been previously explored. The RK-HS method demonstrates consistent convergence between exact and numerical solutions, making it a valuable tool for solving fractional differential equations. Its mesh-free nature adds to its simplicity and effectiveness. The numerical results are discussed, demonstrating the method's efficiency and accuracy through a comparison with the Adomian decomposition method. Our study concludes that the RK-HS method is a powerful and effective tool for solving non-linear fractional SIR models and offers valuable insights into the dynamics of infectious-disease propagation. The method's versatility in handling complex mathematical models paves the way for further research and applications in a variety of scientific fields.Öğe A Study of Indium phosphide and line graph of subdivision graph of H-naphtalenic nano-sheet via irregularity indices(Mongolian Journals Online, 2025-05-06) Iftikhar Ali; Muhammad Haroon Aftab; Ali AkgülIn this article, we have taken the molecular graph of indium phosphide InP[m, n] and line graph of subdivision graph of H-naphtalenicnano-sheet L(S(H(r, s))). Irregularity indices play an important role to describe the quantitative characterization of the non-regular graphs. In various problems and applications, particularly in subject of chemistry and material engineering irregular indices have so many uses, thus it is very important to know about the irregularity of a molecular structure. Moreover, the evaluation of the irregularity of graphs is an important not only for QSPR and QSAR but also very effective for the measuring the entropy, melting and boiling points, enthalpy of vaporization and toxicity. We have also discussed the graphical behaviors of the above indicated structures.Öğe Abundant soliton solutions in saturated ferromagnetic materials modeled via the fractional Kraenkel–Manna–Merle system(Springer Science and Business Media LLC, 2025-02-25) Loubna Ouahid; Maryam Alshahrani; A. Mohamed Abdel-Baset; M. A. Abdou; Ali Akgül; Murad Khan HassaniThe Modified Generalized Riccati Equation Mapping Technique is employed to discover novel solutions for the Fractional Kraenkel-Manna-Merle system. In this system, a nonlinear of ultra_short wave pulse propagates across saturated ferromagnetic-materials by very low conductance. The beta-derivative is used to analyze the fractional performance of the proposed system. Combo-multi soliton shape, anti-bell-shaped solitons, kink bright-dark shape are the results of the applications. The results obtained are original and unfamiliar to the reader, as they had not been published previously. For a few chosen solutions, two dimensional, and three dimensional are shown to offer important insights into the behavior and properties of the solutions. These detailed exact solutions and wave phenomena contribute to a deeper understanding of this equation. This work opens up new possibilities for exploring wave phenomena in more complexly structured nonlinear.Öğe Analytic solutions of the time-fractional Boiti-Leon-Manna-Pempinelli equation via novel transformation technique(Springer Science and Business Media LLC, 2025-05-20) Bushra Yasmeen; Khalil Ahmad; Ali Akgül; Qasem Al-MdallalThis paper presents new analytical solutions for the time-fractional Boiti-Leon-Manna-Pempinelli (BLMP) equation, a crucial model for physical phenomena. Our approach yields novel wave solutions, whose propagation and dynamics are examined for diverse parameter values. The obtained solutions contain rational and natural logarithm functions. The graphical representations of the attained solutions are represented by plotted graphs with suitable parameters. The plotted graphs show different solitons and nonlinear wave solutions. The examination of these solutions involves a comprehensive analysis of their propagation and dynamics through analytic techniques. Our results with existing literature and found that our approach yields more accurate and efficient solutions. The novelty of these solutions is essential for understanding nonlinear behavior and natural phenomena. By developing analytical methods for nonlinear equations, this work advances our knowledge of complex systems. The results provide valuable insights into the equation’s behavior, shedding light on the underlying physical mechanisms. This research contributes to the development of analytical methods for nonlinear equations, fostering future research in the field. The findings are relevant to various areas of physics, including wave dynamics and nonlinear systems.Öğe Analytical dynamics to the interactions of a diffusive mussel–algae model(Elsevier BV, 2025-06) Muhammad Jawaz; Muhammad Shahzad; Nauman Ahmed; Muhammad Zafarullah Baber; Muhammad Iqbal; Ali AkgülThis paper examines the diffusive mussel–algae model and explores soliton solutions and wave structures using advanced analytical techniques, particularly the new auxiliary equation method. The proposed method reveals a variety of solution types, including hyperbolic, parabolic, and mixed forms. These closed-form results provide the nature of the current problem. These solutions are validated against known results and numerical simulations. Additionally, we describe two-dimensional and three-dimensional graphical representations of the solutions, illustrating their spatial and temporal dynamics. This study enhances the theoretical understanding of mussel algae interactions and offers practical insights for eco-logical management, showcasing the contributions of the approach to resolving complex ecological dynamicsÖğe Chaos and proportional integral derivative (PID) control on cancer dynamics with fractal fractional operator(Elsevier BV, 2025-06) Muhammad Farman; Kottakkaran Sooppy Nisar; Khadija Jamil; Ali Akgül; Aceng Sambas; Mustafa Bayram; Mustafa Habib; Murad Khan HassaniThis study presents a cancer dynamics model incorporating a fractal-fractional operator with a Mittag-Leffler kernel to capture complex interactions among cancer cells, tumor suppressor cells, immune cells, and oncolytic viruses. The model aims to enhance understanding of tumor-immune dynamics and improve treatment strategies. The existence and uniqueness of the solution are established using fixed point theory under the Lipschitz condition. Lyapunov stability of the system is also analyzed in the context of the fractal-fractional operator. To address chaotic behavior in cancer progression, chaos and Proportional-Integral-Derivative (PID) control techniques are implemented. These control methods effectively stabilize the system and regulate treatment administration. Numerical simulations illustrate the influence of fractional-order derivatives on tumor suppression and immune response, confirming the model's effectiveness in reflecting real-world cancer dynamics.Öğe Characteristics of elastic deformation on Boger hybrid nanofluid using modified Hamilton–Crosser model: a local thermal nonequilibrium model(Springer Science and Business Media LLC, 2025-01-15) Mostafa Mohamed Okasha; Munawar Abbas; Muyassar Norberdiyeva; Dyana Aziz Bayz; Ibrahim Mahariq; Ansar Abbas; Ali Akgül; Ahmed M. GalalIn this investigation, elastic deformation characteristics on surface tension gradient flow of Boger hybrid fluid over a plate using modified Hamilton-Crosser Model are examined. The modeling takes into account the influence of local thermal nonequilibrium (LTNE). The expanded Cattaneo-Christov theory, which takes relaxation times into account, is the current theory for mass and heat transmission. Excellent heat transmission is offered by the energy equation-based LTNE model for both the liquid and solid phases. Therefore, in this work, two thermal distributions are used for both the liquid and solid phases. It can be applied to materials science to improve heat transmission procedures and nanotechnology, where accurate temperature control is essential for applications like electronic device cooling systems, microfluidic devices, and biomedical applications. Better modeling of complicated fluids in these systems is made possible by the addition of elastic deformation and LTNE, which enhances the systems' stability and efficiency, particularly under nonequilibrium heat conditions. The Bvp4c method is used to solve the model equation system numerically once the relevant similarity variables have condensed. To illustrate how different physical conditions affect the involved distributions, the findings are graphed. Results show that Boger fluid exhibits enhanced velocity at increasing solvent percent parameter values.Öğe Coherent manipulation of Goos–Hänchen shifts by forward and backward currents of complex conductivity in chiral medium(Springer Science and Business Media LLC, 2025-04-17) Zia Ul Haq; Iftikhar Ahmad; Bakht Amin Bacha; Ali Akgül; Murad Khan HassaniThe birefringence of reflection and transmission as well as their corresponding Goos-Hänchen shifts are investigated with complex conductivity in a four level chiral atomic medium. The left circularly polarized (LCP) beam and right circularly polarized (RCP) beam obey the normalization condition with forward and backward currents as well as coupled driving fields parameters at the interface of a lossy chiral medium of and polystyrene. For the birefringent transmission, the positive GH-shifts are reported while for the birefringent reflection, the negative GH-shifts are measured. The maximum GH-shift in reflections of RCP and LCP beams is measured to and that in the transmission is measured to with forward and backward currents of complex conductivity. Furthermore, maximum values of GH-shifts in reflection and transmission of LCP beams are calculated to and RCP beams are calculated to with control field Rabi frequency and backward current variation. The results indicate possible uses in the designing of optical and conductive sensors.Öğe Comparative analysis of hall current impact on MHD laminar surface tension gradient 3D flow of propylene glycol based tetra hybrid nanofluid with generalized fick's and fourier's perspective(Elsevier BV, 2025-03) Munawar Abbas; Shirin Shomurotova; Qasem Al-Mdallal; Ali Akgül; Zuhair Jastaneyah; Hakim AL GarallehExamine the significance of the Cattaneo-Christov flux model on the Marangoni convection 3D flow of tetra hybrid nanofluid combined with Hall current in the present study. When exposed to a fluctuating magnetic flux, it demonstrates electrical conductivity over a stretchy sheet. Using the Cattaneo-Christov double diffusion (CCDD) model, the problem is simulated. In this work, the CCDD model is used to analyze the mass and heat transmission tetra hybrid nanofluid. Basic Fourier's and Fick's laws are generalized by their application. A tetra hybrid nanofluid consisting of Molybdenum disulfide (Mos2), copper (Cu), Silicon dioxide (SiO2) and cobalt ferrite (CoFe2o4), propylene glycol (C3H8O2) as the base fluid is used. This model is essential for precisely predicting the behaviors of heat transfer in nanofluid flows since it takes thermal relaxation time into consideration. Its uses include optimizing heat exchanger performance, enhancing cooling systems in electronics, and better thermal management in microfluidic devices. The basic set of equations is resolved employing the numerical technique (bvp4c). The nanofluid, hybrid, trihybrid, and tetra hybrid nanofluid graphs are all compared. The stretching ratio parameter indicates rising trends in the flow distributions, although the opposite performance is observed for thermal and concentration distributions. Rate of heat and mass transmission improve of tetra hybrid, trihybrid, hybrid nanofluids as increase the values of Marangoni convection.Öğe Comparison study of modified and classical Hamilton-Crosser models for electrophoretic and thermophoretic particle deposition in stagnation point flow of diamond -SiC-Co3O4/diathermic oil-based trihybrid nanofluid(Springer, 2024) Ahmed M. Galal; Sahar Ahmed Idris; Munawar Abbas; Shaxnoza Saydaxmetova; Ali Hasan Ali; Humaira Kanwal; Ali AkgülThe current work examines the impact of heat generation on the stagnation point flow of a magnetized trihybrid nanofluid around a rotating sphere with electrophoretic and thermophoretic particle deposition. The trihybrid (Diamond –SiC–Co3O4/Do) nanofluid flow model consists of nanoparticles of Cobalt oxide (Co3O4), diamond (ND), and silicon carbide (SiC) dissolved in diathermic oil (DO). By comparing the modified model with the classical Hamilton–Crosser model, this study aims to investigate the heat transfer rate of a trihybrid nanofluid based on diamond –SiC–Co3O4/ diathermic oil. Through the analysis of trihybrid nanofluids based on diamond –SiC–Co3O4/Do diathermic oil, this model can optimize heat transmission in systems that need effective thermal management, like chemical reactors, electronics cooling, and energy storage. Trihybrid nanofluids' special qualities improve thermal conductivity, stability, and deposition control, which raises operational efficiency and dependability. It also helps with the design of sophisticated cooling systems for automotive and aerospace applications. These governing equations were solved with MATLAB's bvp4c tool after being transformed into ordinary differential equations via similarity variables. Results imply that, when compared to the classical model, the modified model accurately predicts higher heat transfer rates. As a consequence, trihybrid nanofluid heat transfer properties are better understood and thermal conductivity models are more accurate. The study shows that the concentration profile improved for both classical and modified Hamilton–Crosser models to enhance the values of electrophoretic particle deposition; while, inverse behavior is observed for thermophoretic particle deposition.Öğe Computational analysis of Yamada–Ota and Xue models for surface tension gradient impact on radiative 3D flow of trihybrid nanofluid with Soret–Dufour effects(Springer Science and Business Media LLC, 2024-12-23) Sayer Obaid Alharbi; Munawar Abbas; Ahmed Babeker Elhag; Abdullah A. Faqihi; Ali AkgülThis article discusses the significance of Soret and Dufour, non-uniform heat generation, activation energy on radiative 3D flow of trihybrid nanofluid over a sheet with Marangoni convection. The energy equation takes into consideration the impacts of the heat generation, while the concentration equation takes activation energy into account. This trihybrid nanofluid is based on ethylene glycol and contains nanoparticles of titanium dioxide (TiO2), cobalt ferrite (CoFe2O), and aluminum oxide (Al2O3). For the case of trihybrid nanoparticles, the Yamada–Ota and Xue nanofluid models have been modified. This model is helpful for optimizing heating and cooling systems in fields like energy systems, microelectronics, and aerospace engineering where exact control of thermal properties is essential. By adjusting the characteristics of nanofluids, it also enhances heat transfer rates, which is a critical component in the development of solar collectors and high-efficiency heat exchangers. By using the necessary similarity transformations, non-linear ODEs are obtained from the controlling PDEs. The shooting method (BVP4c) can be utilized to solve this system of highly nonlinear equations numerically. As the surface tension gradient parameter is increased, the velocity distribution, mass transfer, and heat transfer rates all increase but the performance of the thermal and solutal profiles is opposite.Öğe Corrigendum to “Second Order Slip Micropolar MHD Hybrid Nanofluid Flow over a Stretching Surface with Uniform Heat Source and Activation Energy: Numerical Computational Approach” [Results in Engineering 25 (2025) 104060](Elsevier BV, 2025-03) Syed Arshad Abas; Hakeem Ullah; Mehreen Fiza; Ali Akgül; Aasim Ullah Jan; Magda Abd El-Rahman; Seham M. Al-MekhlafiThe authors regrets that the last name of fourth author and the grant number in the acknowledgement section has been corrected as shown below: 1. Correct last name of Ali Akgul as Akgül2. Corrected Acknowledgment: Magda Abd El-Rahman extends their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/39/46>.The authors would like to apologise for any inconvenience caused.Öğe Dynamical analysis of fractional hepatitis B model with Gaussian uncertainties using extended residual power series algorithm(Springer Science and Business Media LLC, 2025-03-07) Qursam Fatima; Mubashir Qayyum; Murad Khan Hassani; Ali AkgülHepatitis B virus (HBV) is a significant global health concern, causing acute and chronic liver diseases, including cirrhosis and hepatocellular carcinoma. This manuscript extends existing mathematical models for HBV by introducing a treatment compartment to improve understanding, diagnosis, and treatment strategies. A stability analysis is conducted for disease-free equilibrium and to address the inherent uncertainties in parameter values, Gaussian fuzzy numbers are incorporated, resulting in a more realistic predictive framework. For solution purposes, the extended residual power series algorithm, which combines the Taylor series with a residual function and an integral transform, is applied. The accuracy of the obtained solutions is assessed by calculating the associated errors. The robustness of the model is further evaluated using r-cut values for lower and upper bounds.A graphical analysis is also performed to examine the influence of different parameters on the solution profiles, enhancing the understanding of disease dynamics. The analysis reveals that the proposed methodology effectively explains the dynamics of epidemic systems and provides new perspectives with potential applications in biology, engineering, and medicine.Öğe Expanding the frontiers of additive manufacturing: Higher microstructure identification through probability modeling(Elsevier BV, 2025-06) Muhammad Shoaib; Muhammad Idrees; Hakeem Ullah; Aasim Ullah Jan; Touqeer Ahmad; Ali Akgül; Magda Abd El-Rahman; Seham M. Al-MekhlafiProbabilistic models and machine learning methods create a step forward in making predictions for additive manufacturing (AM) microstructure. In this probabilistic framework, it became possible to express modifications in the properties of metal, polymer, ceramic, and composite microstructures. Process parameters and material consistency reached maximum levels through the use of statistical modeling along with finite element analysis (FEA) and Gaussian process regression (GPR). Experimental validation through AM process parameters, microstructural values, and material characteristics led to 40 % fewer metal and polymer microstructure variations with simultaneous strength increases. The computational system demonstrated its resistance to process modifications through a validated sensitivity analysis. Additionally covered were scalability issues, computing needs, and possible real-time adaption. These results help AM approaches in aerospace and biomedical engineering to be scalable and performable.Öğe Exploring the fixed point theory and numerical modeling of fish harvesting system with Allee effect(Springer Science and Business Media LLC, 2025-04-24) Muhammad Waqas Yasin; Mobeen Akhtar; Nauman Ahmed; Ali Akgül; Qasem Al-MdallalFish harvesting has a major role in nutritive food that is easily accessible for human nourishment. In this article, a reaction-diffusion fish harvesting model with the Allee effect is analyzed. The study of population models is a need of this hour because by using precautionary measures, mankind can handle the issue of food better. The basic mathematical properties are studied such as equilibrium analysis, stability, and consistency of this model. The Implicit finite difference and backward Euler methods are used for the computational results of the underlying model. The linear analysis of both schemes is derived and schemes are unconditionally stable. By using the Taylor series consistency of both schemes is proved. The positivity of the Implicit finite difference scheme is proved by using the induction technique. A test problem has been used for the numerical results. For the various values of the parameters, the simulations are drawn. The dynamical properties of continuous models, like positivity, are absent from the simulations produced by the backward Euler scheme. Implicit finite difference scheme preserves the dynamical properties of the model such as positivity, consistency, and stability. Simulations of the test problem prove the effectiveness of the Implicit finite difference scheme.Öğe Investigating slip velocity effects on thermal and mass transport in magnetized nanoparticle squeeze flow via numerical scheme(SAGE Publications, 2025-04-24) Danish Ali; Hakeem Ullah; Mehreen Fiza; Aasim Ullah Jan; Ali Akgül; AS Hendy; Saeed IslamEfficient control over heat and mass transport in confined fluid systems is essential for applications in biomedical devices, lubrication systems, and industrial cooling technologies. However, conventional studies often overlook the combined impact of velocity slip, magnetic effects, and nanoparticle concentration on squeeze flow, leading to gaps in understanding heat and mass transport mechanisms under dynamic compression. This research addresses this gap by investigating the influence of nanoparticle volume fraction, magnetic field intensity, velocity slip, Schmidt number, and squeeze number on the Cu-water based Magnetohydrodynamic (MHD) unsteady squeezing flow using a numerical approach. The governing nonlinear differential equations are solved using the bvp4c solver in MATLAB. Results indicate that the skin friction coefficient decreases with the increasing squeeze number, with values reaching -3.3907 for S = 1.0, aligning closely with already published results. Similarly, the Nusselt number decreases as S increases, with a computed value of 1.1195 at S = 1.0. The application of a stronger magnetic field reduces the velocity profile, while higher Schmidt numbers suppresses diffusion. The slip parameter has negligible impact on the concentration profile, while an increase in the squeeze number slightly elevates the concentration. This study provides quantitative insights into the combined effects of slip velocity, MHD, and nanoparticle concentration on squeeze flow, offering valuable implications for microfluidic cooling systems, biomedical transport, and high-performance lubrication technologies.Öğe Local thermal non-equilibrium effects on Marangoni convective flow of Casson fluid with elastic deformation: Perspective of Cattaneo-Christov flux model(Elsevier BV, 2025-05) Munawar Abbas; Ali Akgül; Talib K. Ibrahim; Qasem Al-Mdallal; Umid Turdialiyev; Hafiz Muhammad Ghazi; Zuhair Jastaneyah; Hakim AL GarallehThis work investigates the effects of local thermal non-equilibrium impacts on the chemical reactive flow of Casson fluid under elastic deformation over a sheet. The modified theory for mass and heat transport is the generalized CattaneoChristov theory, which takes into consideration the importance of relaxation times. Chemical reactors, heat exchangers, and geothermal systems are examples of engineering applications where precise temperature control between various materials or phases is required to maximize performance and efficiency. These applications depend on local thermal non-equilibrium conditions. In systems that use non-Newtonian fluids, as those found in polymer manufacturing, petroleum drilling, and food industry applications, this model can be applied to maximize heat and mass transmission. The CattaneoChristov heat flow theory provides a more accurate depiction of thermal behaviour in such fluids by accounting for thermal relaxation effects. In chemically reactive situations, these effects are crucial for increasing energy conversion, speeding up reaction rates, and creating efficient heat management systems. The relevant similarity variables are condensed, and then the model equation system is numerically resolved using the bvp4c method. The higher the interphase heat transfer value, the lower the thermal profile of the Casson fluid's solid and fluid phases.
