Abstract We analyze the asymptotic behavior of a class of extensible beam models governed by a nonlocal structural damping mechanism of the form , where . The coefficient is a degenerate ‐function depending on the linear energy of the system and determines the intensity of the damping. Our main result establishes that, for each , the ‐semigroup generated by the weak solutions of the problem admits a compact global attractor , where denotes the unstable manifold emanating from the set of stationary points. Moreover, we show the upper semicontinuity of the family of global attractors with respect to the fractional exponent .

Abstract The combined effects of heat radiation and magnetohydrodynamics (MHD)s on flow across a stretched sheet with viscous dissipation are the main focus of the computational study. A hybrid nanofluid made up of silver and MgO nanoparticles floating in water is used in the investigation. Fluid dynamics are impacted by the presence of a magnetic field, even though hybrid nanoparticles increase thermal conductivity, and heat transfer efficiency. The controlling partial differential equations are transformed into ordinary differential equations using the proper similarity transformations. The MAPLE software and an estimated spectral Chebyshev collocation are then used to solve these equations. A systematic analysis and graphical presentation of the effects of different factors on velocity, temperature, and concentration profiles are provided. The results reveal that the application of a magnetic field suppresses the fluid velocity by approximately 25%–30% while increasing the temperature by nearly 15%–18%, due to resistive heating induced by Lorentz forces. An increase in the Prandtl number from 1.0 to 7.0 reduces the thermal boundary‐layer thickness by nearly 35%, indicating improved thermal control. A higher Eckert number enhances viscous dissipation, leading to a 10%–12% rise in wall temperature. Similarly, increasing the Schmidt number decreases solute concentration by about 20%–25%, reflecting reduced mass diffusivity. Porosity enhances momentum transport, while heat absorption diminishes concentration distribution. These findings provide light on the solutal and thermal behavior of hybrid nanofluids under electromagnetic influences, which may find use in cooling and thermal energy systems where efficient heat control is critical.

Abstract This study examines the magnetohydrodynamic (MHD) flow of Casson fluid over a vertical plate, accounting for the combined effects of Newtonian heating, internal heat generation, thermal radiation, and chemical reactions. The physical model is formulated through three key components: the momentum, energy, and concentration equations, incorporating Newtonian heating at the boundary. These equations are transformed into a dimensionless form using appropriate nondimensional parameters. The analysis employs the generalized Fourier's law and the Caputo–Fabrizio fractional derivative with a non‐singular kernel to capture memory effects in the system. Exact analytical solutions for velocity, temperature, and concentration are derived using the Laplace transform technique. The effects of various physical parameters on the fluid dynamics are visualized and analyzed through graphical results generated using MATLAB. The results indicate that temperature decreases with an increasing Prandtl number, while velocity enhances with larger thermal and solutal Grashof numbers. Moreover, higher values of the fractional parameter lead to increased temperatures, whereas concentration decreases with an increasing Schmidt number. The novelty of this work lies in its unified treatment of multiple interacting physical mechanisms using a non‐singular fractional calculus framework, which provides a more realistic and general description of practical MHD flows. This approach offers direct relevance to engineering applications such as polymer processing, biomedical fluid modeling, chemical reactor design, metallurgical operations, and MHD‐based energy systems, where precise control of heat and mass transfer in non‐Newtonian fluids is essential. This study has practical relevance to a range of engineering and industrial applications, such as thermal management in cooling systems, optimization of heat exchangers, chemical reactor control, and processes involving non‐Newtonian fluids. The combined influence of heat generation, radiation, and chemical reactions is especially relevant to polymer processing, biomedical flows (e.g., blood analogues), and metallurgical operations that require precise control over thermal and concentration fields, particularly in the context of the Caputo–Fabrizio derivative.

Abstract A coupled problem of chemo‐mechanics for the case of viscoelastic reaction product is considered within the framework based on the chemical affinity tensor. A chemical reaction localized at the transformation front is studied. Two modes of the reaction front propagation called kinetic and quasi‐equilibrium modes are distinguished. In the kinetic mode, the propagation of the front is driven by the normal component of the chemical affinity tensor defining corresponding configurational force. Quasi‐equilibrium mode corresponds to the propagation of the front at which a chemical equilibrium is maintained. 1D problem statement is considered in detail. Kinetic equations determining the front velocity are derived analytically for both modes. It is shown that the choice of the mode is dictated by the parameter defined by characteristic times of diffusion, chemical reaction, and mass supply through the outer boundary. This dimensionless parameter plays the role of the Damköhler number used in chemical engineering. Special attention is paid to considering nonstationary diffusion and motivation of using stationary diffusion approximation.

Abstract This study presents a nonlinear thermo‐mechanical framework for analyzing stress and deformation in shaft‐mounted rotating disks made of transversely isotropic materials with radially graded density. The model incorporates the combined effects of centrifugal forces, external radial traction, axial constraint, and a steady‐state thermal gradient. Utilizing Seth's transition theory, closed‐form analytical solutions are derived for radial displacement, radial stress, and hoop stress under axisymmetric conditions. The formulation is validated against classical isotropic solutions and finite element simulations, showing excellent agreement with deviations below 2%. Parametric studies reveal that positive density gradation (e.g., m = 2) reduces peak hoop stress by ∼14% and radial displacement by ∼12%, while negative gradation (e.g., m = −0.5) increases them by ∼9% and ∼8%, respectively. Axial loading significantly amplifies stress concentrations, particularly at the bore, and thermal gradients further elevate stress levels and advance the onset of yielding. It is conclusively shown that yielding initiates at the inner bore, with the critical angular velocity reduced by ∼15% under combined thermo‐mechanical loading. The proposed analytical model provides a robust tool for the design and optimization of advanced rotating components in aerospace, energy storage, and hydromechatronic systems.

Abstract In the current study, the flow characteristics of a mononano‐fluid () and a hybrid nanofluid () driven by a rotating disk revolving at a constant angular velocity are analyzed. The distribution of flow consists of nonlinear thermal radiation, heat absorption or generation, binary chemical reactions, and thermal stratification. The leading structure of governing PDEs of flow is changed into ordinary boundary value problem (BVP) by applying suitable similarity transformations. The fifth‐order Runge–Kutta–Felberg (RKF) method with shooting methodology is then employed to solve numerically the subsequent structure of equations. The charts and graphs are employed to show the comprehensive analysis of findings. One of the intriguing findings shows that as variable porosity and variable permeability parameters increase, the slope of the fluid's velocity along with the radial axis, as well as the rotational velocity for both liquids are simultaneously decreasing and increasing, respectively. However, for temperature profiles, opposite effects are viewed. Based on the statistical analysis presented in this article, we can infer that the correlation coefficients for four major physical quantities, , , , and , are quite significant. Consequently, there is a strong correlation between the parameters and the physical characteristics. Our current study is significant as it applies the classical rotating disk flow to contemporary hybrid nanofluids that have a variety of chemical and thermal impacts.

Abstract In this paper, we consider a system of coupled wave equations of Kirchhoff‐type with logarithmic source terms. The system is dissipated using two nonlinear frictional‐type damping terms, which act within the domain and are modulated by a time‐dependent coefficient. We examine the interaction between the damping mechanisms and the logarithmic source terms under specific conditions. Using the standard Faedo–Galerkin method and the potential well approach, we prove the global existence of solutions to the system. The stability of the system is proved using the multiplier method and some properties of convex functions and logarithmic inequalities. We establish general decay results in which exponential and polynomial decay are special cases. Our results are derived without imposing any restrictive growth assumptions on the nonlinear frictional damping terms. Furthermore, our decay rates depend on the nonlinear frictional damping terms, the logarithmic source terms, and the time‐dependent coefficient. The findings in this paper significantly improve and generalize earlier results in the literature.

Abstract This computational study investigates the 3D flow, heat transfer, and mass transport properties of nanofluids, micropolar nanofluids, and Maxwell nanofluids over a stretching sheet in a rotating frame. This analysis employs the Buongiorno model, which incorporates binary chemical processes and Arrhenius activation energy. The governing equations are transformed via similarity variables and solved numerically with MATLAB's bvp4c solver. Validation against published data reveals outstanding consistency in velocity gradients and skin friction coefficients, with relative errors less than 1%. Results indicate that increasing the magnetic field and rotation reduces velocities but increases temperature and nanoparticle concentration. The rmophoresis and Brownian motion elevate temperature while lowering the Nusselt number. The Maxwell nanofluid exhibits the slowest flow, the highest temperature, and concentration profiles, and lower Sherwood and Nusselt numbers compared to the other fluids under study. These results provide light on the unique thermal and hydrodynamic characteristics of complex nanofluids and have been confirmed against previous research. Optimizing nanofluid‐based thermal systems with rotation, magnetic fields, and non‐Newtonian effects—such as those used in rotating heat exchangers and microelectronic cooling—requires this knowledge.

Abstract Two‐dimensional, laminar, steady‐state MHD (magnetohydrodynamic) Darcy‐Forchheimer MWCNT‐MoS 2 /micropolar water‐base hybridized nanofluid flowing over shrinking/stretching sheet is considered. The thermal radiation, heat sink/source influences have also been taken into account. Ordinary differential equations (ODEs) system is achieved by the implication of similarity transformations on PDEs (partial differential equations). The resulting equations are numerically solved by the implication of shooting scheme through Maple software. The double solutions are generated at multiple ranges of applied parameters. Therefore, stability analysis of the outcomes has been made and first‐branch solution is stable, while second‐branch is unstable. The influence of volume fractions of nanoparticles and specified flow parameters are determined on the couple stress, skin friction, Sherwood and Nusselt numbers. An increment in volume‐fraction of nanoparticle increases the Sherwood number and decreases Nusselt number. The increase in nanoparticle's volume fractions increases velocity profile. The velocity reduces due to an augmentation in micro‐material, Darcy‐Forchheimer and suction parameters. The increasing Biot number, nanoparticle's volume‐fractions and radiation increase the temperature profiles. An increment in chemical reaction, suction and Schmidt number cause to a decrement in concentration profiles.

Abstract The concept of dissipativity plays a crucial role in the analysis of control systems. Dissipative energy functionals, also known as Hamiltonians, storage functions, or Lyapunov functions, depending on the setting, are extremely valuable to analyze and control the behavior of dynamical systems, but in general circumstances they are very difficult to compute, and not fully understood. In this paper, we consider passive linear time‐varying (LTV) systems, under mild regularity assumptions, and their associated storage functions, as a necessary step to analyze general nonlinear systems. We demonstrate that every passive LTV system must have at least one time‐varying positive semidefinite quadratic storage function, greatly reducing our search scope. Now, focusing on quadratic storage functions, we analyze in detail their necessary regularity, which is lesser than continuous. Moreover, we prove that the rank of quadratic storage functions is non‐increasing in time, allowing us to introduce a novel null space decomposition, under much weaker assumptions than the one needed for general matrix functions. Additionally, we show a necessary kernel condition for the quadratic storage function, allowing us to reduce our search scope even further.