https://jcamech.ut.ac.ir/ Journal of Computational Applied Mechanics en daily 1 Wed, 01 Apr 2026 00:00:00 +0330 Wed, 01 Apr 2026 00:00:00 +0330 https://jcamech.ut.ac.ir/article_104817.html Radiation and chemical reaction effects on the steady magnetohydrodynamic (MHD) boundary layer flow of Williamson nanofluid through a porous medium over a horizontally linearly stretching sheet are numerically investigated, incorporating coupled influences of melting heat transfer and nanoparticle dispersion. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using similarity transformations and solved via the fourth-order Runge-Kutta (RK-4) method to generate reference datasets. A novel supervised machine learning framework, Feed-Forward Neural Network optimized with the Backpropagated Levenberg-Marquardt Algorithm (FFNN-BLMA), is proposed, trained on 1001 data points with 70% training, 15% validation, and 15% testing splits. The FFNN-BLMA yields exceptional predictive accuracy with absolute errors ranging from 10⁻⁸ to 10⁻¹⁰ across velocity temperature  and concentration  profiles, validated through 10-fold cross-validation, error histograms, regression analysis, and curve superposition. Parametric studies reveal that increasing the melting parameter  enhances velocity and reduces temperature, while the chemical reaction parameter  diminishes concentration trends consistent with prior literature. Skin friction, Nusselt, and Sherwood numbers are computed to quantify engineering performance. The FFNN-BLMA outperforms traditional RK-4 and analytical methods in accuracy, convergence, and computational efficiency, establishing a robust, discretization-free paradigm for solving complex non-Newtonian multi-physics flow problems with potential extension to fractional-order systems. https://jcamech.ut.ac.ir/article_104821.html This study investigates the unsteady magnetohydrodynamic (MHD) flow of blood-based Au-Cu hybrid nanofluids in cylindrical arteries, integrating thermal radiation, Joule heating, chemical reactions, and Dufour-Soret cross-diffusion effects. These effects are critical for biomedical applications like hyperthermia and targeted drug delivery. A Caputo time-fractional derivative is adopted to capture memory-dependent behaviors of biological fluids, which are typically overlooked by classical models. The governing equations for velocity, temperature, and nanoparticle concentration are transformed via Laplace transforms and solved semi-analytically using the Concentrated Matrix Exponential method. This ensures accuracy and computational efficiency. The results indicate that increasing the fractional-order parameter delays momentum, thermal, and concentration diffusion, thereby reflecting stronger memory effects. Magnetic fields have been shown to reduce velocity but enhance temperature via Joule heating. Furthermore, higher Dufour numbers have been demonstrated to strengthen temperature gradients, while elevated Soret numbers have been shown to intensify concentration gradients. This article’s novelty lies in its integration of fractional calculus with hybrid nanofluid MHD modeling, accounting for complex coupled effects. The proposed model provides more realistic predictions of unsteady biological flows, offering valuable insights for optimizing biomedical therapies and cardiovascular device design. https://jcamech.ut.ac.ir/article_104916.html Understanding how unsteady flow structures control transport and mixing in cylinder wakes is essential for predicting dispersion, heat transfer, and fluctuating forces in many engineering and environmental systems. In this study, we examine the two-dimensional wake of a circular cylinder at a moderate Reynolds number of 500 to determine how coherent flow structures shape entrainment, vortex formation, and downstream mixing. The unsteady flow is computed using a high-resolution finite-element solver, and material transport is analyzed through the extraction of time-dependent stretching patterns that identify repelling and attracting surfaces in the flow. These surfaces provide a direct picture of how fluid parcels are directed, trapped, or released as the wake evolves.The results show that the interaction of repelling and attracting material surfaces governs the timing and geometry of vortex roll-up, the formation of distinct vortical packets, and the onset of chaotic advection farther downstream. Localized mixing hot spots emerge as narrow regions of intense stretching between alternating vortices—features that are not visible from instantaneous flow fields alone. Quantitatively, the computed vortex-shedding frequency corresponds to a Strouhal number of approximately 0.21, consistent with established values for cylinder wakes at this flow regime and confirming the accuracy of the simulation.The study demonstrates that examining the wake through its underlying material structures provides a clearer and more physically transparent interpretation of transport and mixing than traditional instantaneous diagnostics. The novelty of this work lies in treating these material surfaces as the primary organizational framework of the wake and in showing how they determine preferential entrainment routes and dominant mixing pathways. This perspective offers a foundation for developing future strategies aimed at enhancing scalar transport or reducing unsteady loading in flows around bluff bodies. https://jcamech.ut.ac.ir/article_104934.html Bio-inspired wing geometries provide a promising pathway for enhancing the aerodynamic efficiency of micro–air vehicles (MAVs), particularly in low-Reynolds-number flight regimes. This study presents a detailed computational analysis of turbulent airflow over a hummingbird-inspired wing operating in gliding conditions, focusing on the aerodynamic mechanisms essential for micro-UAV design. A simplified, biologically motivated wing planform—preserving the characteristic aspect ratio and chord distribution while omitting feather-level complexity—is modelled to isolate the dominant flow physics. Numerical simulations are performed using ANSYS FLUENT with the k–ε turbulence model to evaluate lift, drag, pressure distribution, and flow topology across inlet velocities of 5, 10, and 15 m/s. The results show that the hummingbird-based wing maintains stable aerodynamic performance under all flow conditions, with lift increasing steadily with velocity and peaking at 15 m/s, accompanied by the expected drag augmentation. Pressure and velocity fields confirm the formation of biologically consistent high-pressure regions beneath the wing and low-pressure zones above it, intensifying with increasing speed. A comparative assessment of full-wing and symmetry-based half-wing simulations demonstrates that the latter accurately reproduces aerodynamic trends while substantially reducing computational cost. The findings offer actionable insights into the development of efficient gliding micro-UAVs inspired by natural flyers and establish a foundation for future research in flapping-wing aerodynamics and aeroelastic fluid–structure interaction (FSI). https://jcamech.ut.ac.ir/article_105241.html In this work, rectangular plate samples are designed and fabricated using four arrangements: pure epoxy with a stiffener, pure epoxy plate without a stiffener, homogeneous composite plate with 0.5% Vf and a stiffener, and homogeneous composite plate with a FGM stiffener. The mathematical model is formulated based on the first-order shear deformation theory (FSDT). The free vibration test is conducted, and the signal is analyzed to obtain the free vibration characteristics. The results show that the homogeneous composite plate with 2% Vf and FGM stiffener exhibited a significant improvement in the natural frequency. However, using a Functionally Graded Material (FGM) stiffener and increasing the nano-volume fraction increases the natural frequency. Also, the plate without any filler (pure epoxy) and without a stiffener has the lowest frequencies among the composite plates employed. The discrepancy between the analytical and experimental techniques was no more than 10%. https://jcamech.ut.ac.ir/article_105340.html This examination numerically inspects the influences of key factors on the flow and heat transmission of a Casson fluid over a nonlinearly stretching sheet in a permeable medium, considering inconstant viscosity and a magnetic field. The boundary-layer equations were cracked applying the Runge–Kutta technique, with results confirmed by MATLAB’s bvp5c solver and validated against published data. Results show that velocity rises with higher Prandtl number and the nonlinear factor of the stretching sheet but drops with higher porosity factor, Forchheimer number, Casson factor, magnetic field factor, and viscosity variation factor. Temperature declines with Prandtl number and the nonlinear factor of the stretching sheet but enlargements with other parameters. The nonlinear factor of the stretching sheet boosts skin friction and heat transmission, whereas higher porosity factor, Forchheimer number, viscosity variation factor, magnetic field factor, and Casson factor lessen them. The findings offer insight into the mutual effects of non-Newtonian performance, magnetic field, and permeable media on boundary layer flow and thermal transportation. https://jcamech.ut.ac.ir/article_105750.html The Mars Ingenuity helicopter, a coaxial rotor aerial vehicle, is a pioneering venture into extraterrestrial flight. Rotorcraft technology plays a significant role in future mission development, as it offers advantages for specific applications, particularly in rugged terrain or confined spaces. Mars' landscape presents challenges, including unpredictable wind patterns and dust particles. To fly in the thin, predominantly carbon-dioxide-based atmosphere, rotor blades are designed for efficiency in low density environments with a large blade diameter. This work examines the aerodynamic performance of the blade configuration in a quadcopter Mars Ingenuity design using ANSYS FLUENT computational fluid dynamics. A detailed rotor blade model for CFD analysis has been developed for flow behavior around the rotor blades in Mars atmospheric conditions. Data from the Mars 2020 mission and the Mars Ingenuity Helicopter is used as a baseline. Extensive simulations are described for contour plots and flow vectors, focusing on vortex effects and performance in the Mars atmosphere. The study also addresses unsteady airflow around the rotor disk, leading to instabilities such as blade-vortex interactions and retreating blade stall. Future pathways include control aspects of the blade configuration and blade twist. https://jcamech.ut.ac.ir/article_105798.html Dip coating is a key technique in thin film fabrication, widely applied in protective coatings, and material surface engineering. The coating quality depends strongly on the fluid dynamics near substrate edges, where viscoelastic effects and inertial forces can lead to stress concentration and flow instabilities. A viscoelastic fluid model is formulated based on conservation of mass and momentum, with nonlinear governing equations solved using the Langlois recursive approach and the inverse method. Analytical solutions of the stream function provide insight into velocity fields, pressure distribution, and stress behavior near the substrate surface. Results show that stresses and pressure diverge near sharp substrate corners, which can compromise coating durability. Variations in the interface angle significantly alter stress distributions on both the substrate and free surface. Furthermore, inertial forces amplify fluid velocities in the corner region, directly influencing film thickness uniformity and mechanical performance of coated layers. https://jcamech.ut.ac.ir/article_105857.html This study investigates the free vibration behavior of porous functionally graded plates (PFGPs) within the context of nonlocal strain–gradient elasticity theory. Two different porosity distribution types are examined, and the thickness-wise variation of material properties is modeled by means of an enhanced power-law scheme. The kinematic description is formulated based on a refined higher-order shear deformation plate theory that inherently enforces zero transverse shear stresses at the plate surfaces, thus evading the usage of shear correction factors. The governing equations of motion for the nonlocal model are derived via Hamilton’s principle and explained analytically to get the natural frequencies of the PFGPs. A detailed parametric analysis is performed to assess the effects of the nonlocal parameter, internal material length scale, power-law exponent, wave number, and porosity parameters on the vibrational characteristics. The validity and effectiveness of the current preparation are confirmed through comparisons with existing results obtainable in the literature. https://jcamech.ut.ac.ir/article_105859.html The (4+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation is a typical high-order nonlinear integrable partial differential equation (PDE), which plays a crucial role in describing multi-dimensional nonlinear wave phenomena in plasma physics, fluid mechanics, and nonlinear optics. However, its high dimensionality (four spatial variables + one time variable) and strong nonlinear coupling pose significant challenges to constructing a variational formulation and solving soliton solutions. To address this issue, this work focuses on the variational method for the (4+1)-dimensional BLMP equation and proposes a construction strategy for an approximate variational formulation based on the semi-inverse method. Through two-step variable transformations (order-reduction transformation and auxiliary potential function introduction), the high-order and nonlinear terms of the original equation are simplified, and the approximate form of the Lagrangian density F is derived. Consequently, an approximate variational formulation of the (4+1)-dimensional BLMP equation is obtained, and consistency verification confirms that the extremum condition of the functional is exactly equivalent to the solution of the original equation. Notably, the approximate form of F not only balances computational efficiency and physical accuracy but also provides guidance for the improvement of the original equation from an energy perspective. A prominent open problem arising from this work—the exact determination of F from the variational derivative constraint equations—invites mathematical enthusiasts and researchers in nonlinear PDEs to explore innovative solutions, which will advance the general theory of variational principles for high-dimensional nonlinear integrable systems. The research results offer an effective theoretical tool for solving the (4+1)-dimensional BLMP equation and analyzing its dynamic characteristics, with broad application potential in simulating multi-dimensional nonlinear wave phenomena.