Khaled Elagamy

The work investigates the effect of varying viscosity on non-Newtonian Eyring–Powell nanoliquid across thin-needle geometry. The work aims to boost transport efficiency and thermal regulation in microbial fuel cells by integrating rheological complexity with nanoparticle-augmented heat and mass transfer. It emphasizes the importance of adjusting fluid properties to achieve enhanced electrochemical performance and greater energy output. The investigation analyses the continuous, two-dimensional stream of an Eyring–Powell nanoliquid with varying viscosity over a moving slender needle, particularly emphasizing its relevance to microbial fuel cells. The flow is analyzed in a permeable zone influenced by dual heat sources, activation energy, and bioconvection driven by motile microorganisms. The variable viscosity of the fluid reflects changes in temperature, concentration, and microorganisms, which substantially influence momentum, heat, and mass transport. By employing the right similarity alterations, the governing partial differential equations are transformed into ordinary differential equations and analytically resolved via the Homotopy perturbation method. The present study provides a substantially more comprehensive physical description by coupling variable viscosity, magnetohydrodynamics, porous media, nonlinear heat generation, activation energy, chemical reaction, nanoparticle transport, and bioconvection of motile microorganisms within a unified framework. This combination of mechanisms has not previously been investigated using the Homotopy perturbation method. The most important discovery was that the transport behavior is controlled by the strong coupling between temperature-dependent viscosity, nanoparticle migration, microorganism bioconvection, and magnetic damping. This showed that these mechanisms can be used to simultaneously control mass transport, flow, and heat transfer. The findings enable more precise prediction and optimization of non-Newtonian bioconvective nanofluid systems by offering a deeper physical understanding of the controlling transport processes. For the design and optimization of microbial fuel cells, bioelectrochemical reactors, biosensors, microfluidic devices, and advanced thermal management systems, where effective control of heat transfer, nanoparticle dispersion, and microorganism distribution was crucial, the results provided helpful guidelines. The findings provide significant theoretical insights for the design of sophisticated energy systems that integrate non-Newtonian nanofluids with biological transport mechanisms.

This research analyzes the wavy, axisymmetric flow of a Ree–Eyring non-Newtonian nanofluid, infused with motile microorganisms, within a porous, tapered cylindrical channel under a transverse magnetic field. This investigation presents a theoretical framework that may inform the improvement of energy efficiency and thermal management in biomedical engineering applications, such as drug delivery systems and microfluidic biosensors. The work provides an extended insight by a contribution to the evaluation of entropy generation, explicitly considering the influence of motile microorganisms, thereby bridging a gap in the existing literature. The comprehensive physical model further incorporates the combined effects of Joule heating, viscous dissipation, nonlinear thermal radiation, and chemical reactions. Methodologically, the governing nonlinear equations of the system were rendered tractable under long-wavelength and low-Reynolds-number assumptions and subsequently solved using the numerical Runge–Kutta–Fehlberg technique. The key conclusion is that, based on the present numerical model, careful selection of magnetic field strength and microorganism motility parameters may reduce irreversible energy losses, potentially improving the net usable work in advanced nanofluid transport systems for biomedical applications, subject to experimental validation. The most significant finding reveals that the magnetic field serves as a dual-purpose control parameter: increasing its strength boosts total entropy generation by 20–30% while simultaneously raising the Bejan number, confirming heat transfer as the dominant irreversibility mechanism in the system. Additionally, nanoparticle concentration diminishes substantially with elevated chemical reaction rates and Schmidt numbers, while microorganism density is highly sensitive to the Péclet number, which causes flow disruptions.

The impact of primary parametric excitations on the bifurcation behavior and chaotic oscillations of a cantilever beam construction is examined in the existing study. The results provide valuable insights into dynamic transitions, resonance conditions, and stability thresholds. This innovation is crucial in technical applications, including aerospace and civil engineering, as slight parametric variations to stimulate complex nonlinear behavior endanger structural safety. The fundamental methodology relies on the non-perturbative approach, primarily developed by the confidential He’s frequency formula. This methodology is adopted to convert a weak oscillator of a nonlinear ordinary differential equation into a linear one. An excellent agreement is obtained between the two equations. The current approach is appropriate, based on basic ideas, and produces peculiarly high numerical precision. The stability performance is assessed in various scenarios. The current method reduces assessed complexity, and the explanation is significant in the mathematical execution of nonlinear parametric issues. The dynamics of nonlinear simulation are examined via bifurcation illustrations, analytical essential elements that affect system behavior. The largest Lyapunov exponent elucidates chaotic and periodic oscillations, providing insight into long-term stability and the genesis of chaos.

The flow of Eyring-Powell nanofluids containing motile microorganisms within the conical space between a rotating disc and cone is of significant relevance to bioreactor design, biotechnological processing, targeted microbial transport, and materials engineering. This study focuses on the steady, incompressible, non-Newtonian behavior of such a system, incorporating the effects of a vertically applied magnetic field, Ohmic dissipation, chemical reactions, and heat generation/absorption. The governing partial differential equations for momentum, energy, nanoparticle concentration, and microorganism density are transformed into a system of coupled nonlinear ordinary differential equations via suitable similarity transformations and solved numerically using the shooting method in Mathematica. The results reveal that increasing fluid elasticity (Weissenberg number) drastically suppresses axial pumping velocity, leading to reduced cell densities, slower production rates, and diminished product yield in bioreactor applications. Conversely, swirl velocity and mixing intensity are enhanced. The applied magnetic field increases tangential drag, raising the torque and power required for impeller rotation. For optimal fuel mixing or nutrient distribution, a lower chemical reaction rate is recommended. Furthermore, increases in the Lewis and Péclet numbers indicate a degradation in microbial presence, providing critical insights for the operational tuning of microbial bioreactors. The study underscores the importance of rheological, magnetic, and biochemical parameters in the design and optimization of advanced biofuel production systems and rotating thermal devices.

Purpose: Scrutinizing the nonlinear Mathieu oscillator is significant in realizing intricate behavior in practical systems, offering insights into engineering, physics, and applied mathematics, such as mechanical vibrations and structural stability. The point of this study is to acquire the frequency amplitude of parametric non-linear problems. Methodology: The basic methodology is established on the non-perturbative approach (NPA), which is constructed principally in He’s frequency formulation (HFF). The NPA converts a weakly nonlinear second-order oscillator of ordinary differential equation (ODE) into a linear one. The approach response results freely from the usual perturbation methodologies. Accordingly, the investigation aims to leave all regular perturbation techniques aside and estimate responses of small amplitude parametric elements devoid of constraints. Besides, the procedure is unlimited to establish optimum responses of the nonlinear high-amplitude oscillations. A rapid measure of the oscillation-amplitude connection is needed to derive succeeding estimations of responses to parametric non-linear oscillations. The Mathematica Software program (MS) is working to validate the derived parametric ODE, demonstrating the primary formulation. Results: The stability performance is examined across several situations. The present procedure is based on pure principles, is appropriate, and produces exceptionally high numerical accuracy. The present technique decreases measured complexity; the construction is valuable for the mathematical implementation of nonlinear parametric problems. The nonlinear dynamics of the model are analyzed through bifurcation diagrams, identifying critical parameters that influence system behavior. The Poincaré map further reveals periodic and chaotic oscillations, shedding light on long-term stability and chaos emergence.

The investigation of entropy generation in artery stenosis utilizing Sisko nanofluid and motile gyrotactic bacteria is driven by the necessity to enhance biomedical fluid dynamics for superior drug delivery and disease diagnostics. The innovation examines the synergistic impacts of non‐Newtonian fluid behavior, nanoparticle dynamics, and microbe motility on entropy formation, yielding an enhanced understanding of energy dissipation and transport events in biological flows. Therefore, an activated energy chemical reaction is examined in conjunction with the Boussinesq estimation (buoyancy‐driven stream), in which the intensity is introduced as a linear expression of temperature and concentration. Furthermore, the involvement of entropy generation through the current flow may enable one to design more effective systems to control the thermal properties and the flow of nanoliquids. The foremost formulations are mathematically explained and illustrated using a fourth‐order Runge–Kutta procedure. Consequently, a fundamentally meaningful graphical conception of the information is recognized to investigate the influences of the generated nondimensional physical influences. Since viral contagions are known to produce thinner blood infections, it is determined that the presence of microorganisms, which are expressed in buoyant terms, improves flow and increases their velocity. Therefore, by regulating these characteristics, the flow rate may be managed. When diagnosing narrowing channel treatment, most of the heat‐related characteristics discussed here are seen to increase aspects of heat flux.

The study of couple stress in Eyring–Powell nanofluid (EPF) flow over a rough sphere, enriched with motile microorganisms, is crucial for biomedical engineering, environmental sciences, and advanced manufacturing. Therefore, the current work tackles this issue. The flow is exposed to the buoyancy‐driven, with a normal magnetic field (MF), Joule heating, chemical reaction, heat source, and heat radiation influences. Along with slip velocity and appropriate boundary conditions (BCs), the mathematical architecture tests the equations for momentum, energy, nanomaterial volume percentage, and microbe concentration. The importance of this study stems from the application of temperature, speed, and nonmaterial allocations to identify the benefits or drawbacks of nanomaterials and microorganisms such as bacteria, viruses, and germs in the stream close to curved surfaces. It is assumed that this structure has a valuable related parameter in many industrial and engineering manufacturing mechanisms like combustion, conduits, magnified diffusion, sports balls, and flow‐structure interaction between aerodynamics and hydrodynamics. These nonlinear partial differential equations (PDEs) are analyzed via the modified Adomian decomposition method (MADM) to have analytical interpretations of the speed, temperature, nanomaterial volume fraction, and microorganism profiles. Heat dispersion is enhanced with nearly all associated coefficients. Moreover, nanoparticles are significantly concentrated in nearly all parameters, excluding those that already elevate the temperature. This indicates that heat transfer occurs comprehensively, yielding significant advantages in various medical and engineering applications.

Purpose: The aim of the current study is to comparehend an analytical description of different classes of nonlinear Mathieu oscillators. The van der Pol-Duffing-Mathieu oscillator, and the generalized van der Pol-Duffing-Mathieu oscillator are examined. Additionally, the hybrid Rayleigh-van der Pol-Duffing-Mathieu oscillators, as well as the nonlinear Mathieu oscillator, are scrutinized. Method: The non-perturbative approach (NPA) is utilized to convert the nonlinear ordinary differential equations (ODEs), of the illustrated dynamical systems, into linear ones. The approximate solutions are derived independently in the series expansion and without the use of conventional perturbation techniques. Therefore, the goal is to deviate from conventional perturbation techniques and get approximations of small amplitude parametric components without imposing any restrictions. The method is also expanded to determine the best solutions for the nonlinear immense amplitude of fluctuation. Results: The current method offers successive approximations of the solutions of parametric nonlinear fluctuations may be obtained by quickly estimating the frequency-amplitude relationship. The resulting parametric equations are validated, showing high degree of agreement with the original equation. Stability behavior is analyzed under various circumstances. The transition curves, bifurcation diagram, Poincaré map, and phase portrait are also examined using the Floquet theory. Conclusion: The stability regions are found to be diminishing with the rise of the natural frequency, and the excited frequency. Moreover, the achieved regions are found to be growing with the rise of the damping coefficient and the excitation amplitude. The stability settings have been examined by considering the effects of various factors in both the damped and un-damped phases for each situation. In the un-damped state, PolarPlots are examined of the transition curves of the two corresponding solutions, namely Cos- and Sin-oscillations. The conclusions of the acquired results suggested that the approach presented here is highly efficient, robust, founded on solid premises, and remarkably intuitive.