This study investigates natural convection in rheological granular flow over an inclined heated surface, with applications in heated powder processing, bulk solid drying, food processing, and thermal polymer rheological systems. The rheological effects are modeled through normal stress differences, while buoyancy forces are incorporated using the Boussinesq approximation. Viscous dissipation is also considered to account for internal frictional heating. The governing equations are derived using a continuum framework with conductive heat transfer, and nonlinear thermal conductivity is modeled via Fourier’s law. The resulting coupled nonlinear differential equations are solved numerically using MATLAB’s bvp4c, based on Newton collocation and adaptive discretization. The numerical results are validated against available studies, and the effects of key material parameters on granular volume fraction, velocity, and temperature distributions are examined graphically. The results show that by increasing the pressure-to-gravity force ratio (ξ_1) , thermal buoyancy parameter (ξ_5) , and inclination angle (γ) enhances the granular volume fraction near the inclined heated surface, while reducing it near the free surface. In contrast, higher values of the void distribution force parameter ( ξ _2) reduce the volume fraction near the heated surface but enhance it near the free surface. The heat flux ratio parameter (ξ_6) suppresses temperature throughout the flow domain, whereas viscous dissipation (ξ_4) and inclination angle (γ) enhance the temperature distribution.

A computational study is described of the structural performance of a bumblebee-inspired wing for a Micro Aerial Vehicle (MAV) during the initial downstroke phase of take-off using Finite Element Analysis (FEA). A detailed three-dimensional model of the forewing and hindwing was developed to replicate the morphological and structural features of the insect wing. Static FEA was performed within the ANSYS Workbench to assess stress distribution, strain, and deformation under aerodynamic loading conditions experienced during the first wing stroke, based on a wingspan of 18mm and the species-specific flapping frequency of 130Hz. The results indicate that the natural venation pattern of the wing provides effective load distribution, reducing stress concentrations along the wingspan. Peak Von Mises stresses were localized along the leading edge, following the primary branch of the vein structure, while maximum deformation occurred at the wingtip, consistent with experimentally observed honeybee wing deformation. The static pressure case simulations reveal that maximum deformation (total displacement) is observed to consistently decrease with increasing Young's Modulus. At 2GPa, the wing exhibits the highest displacement of 1189 mu m, and this is strongly reduced to 793 mu m at 3GPa, 595 mu m at 4GPa, and 476 mu m at 5GPa. The Von Mises elastic strain varied significantly with stiffness. The strain decreases when Young's modulus increases for chitin, with values of 3.68 & times;10-3 at 2GPa, 2.45 & times;10-3 at 3GPa, 1.84 & times;10-3 at 4GPa, and 1.47 & times;10-3 at 5GPa. Notably, the Von Mises stress results remained nearly constant across all Young's Modulus values, hovering around 4.93MPa. For the acceleration case, at 2GPa, the maximum total deformation was recorded as 1094 mu m. When the modulus was increased to 3GPa, the displacement reduced to 723 mu m, followed by 547 mu m at 4GPa and 438 mu m at 5GPa. As with the static simulation, in all cases, the displacement was concentrated toward the wing tip, with the largest deformation occurring along the outer regions of the bumblebee wing structure, away from the fixed support. Furthermore, the Von Mises strain recorded when the Young's Modulus was set to 4GPa exceeds that computed in the other three cases (5, 3, and 2GPa). As with the static pressure simulations, the Von Mises stress sustains a consistent value across all the Young's Modulus values, maintaining a peak value of approximately 4.27MPa. Peak Von Mises stress is observed at the leading edge, where the leading vein changes direction to follow the wing contours, which are most susceptible to loading and are subjected to the highest forces resulting from flight. The findings also demonstrate the potential of biomimetic venation layouts to enhance the strength-to-weight ratio in small-scale UAV wings, thereby supporting efficient lift production with minimal weight penalties.

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-epsilon 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).

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.

Nano-powders have revolutionized the beauty and cosmetic industry, introducing groundbreaking innovations in product formulation and skin protection. Cutting-edge cosmetology leverages titania nanopowders to enhance pigmentation and luminosity in various beauty products, including eye shadows, lipsticks, balms, and lotions. These nanoscale particles not only amplify esthetic qualities but also provide advanced functional benefits including improved hydration, durability, facial radiance, and anti-wrinkling characteristics. Furthermore, magnetic nanoparticles have also shown enhanced tunability in emerging cosmetic applications. The intersection of scientific research and cosmetic technology has led to fascinating developments in nanofluid dynamics. Motivated by the manufacturing fluid dynamics of nano-cosmetics, in the present work we investigate the non-Newtonian magnetohydrodynamic (MHD) titania-magnesium oxide/methanol (wood spirit) cosmetic nanoliquid dynamics from a stretching surface with a power-law velocity. The Casson viscoplastic model is deployed for rheological effects. Convective and radiative heat transfer are included in the transport model as are viscous heating, internal heat source and wall transpiration (suction/injection) effects. A Tiwari-Das volume fraction formulation is adopted for nanofluid properties. The primitive conservation equations with associated boundary conditions are transformed into a nonlinear coupled ordinary differential boundary value problem which is solved computationally with the Runge-Kutta Fehlberg technique. Validation with previous studies ignoring nanoparticles is included. The innovative hybrid nanoflow composition, combining MgO and TiO2, demonstrates remarkable potential in both cosmetic and industrial applications. When suspended in non-Newtonian cosmetic creams and exposed to sunlight, the hybrid nanoparticles lead to improved heat transfer properties of hybrid nanofluid suspensions. Notably, they can help mitigate skin tanning during exposure to intense solar radiation, by effectively managing thermal radiation and energy transmission to the skin's surface. Hybrid nanofluids are observed to transfer more energy away from the stretchable surface when internal viscous dissipation and heat generation are present. The optically thin nano-cosmetic fluids simulated using the Rosseland flux model exhibit a decrease in energy transmission rate. Computations also show that as wall suction or injection escalates, skin friction decreases. Overall enhanced thermal management in cosmetic formulations is produced with MgO and TiO2 hybrid nanoparticles relative to only unitary MgO nanoparticles.

In recent years, the Finite Element Method (FEM) has emerged as a cornerstone in the field of seating design, particularly within the aircraft industry. Over the past decade, significant advancements in Finite Element (FE) analysis techniques have revolutionized the seat industry, enabling the creation of safer and more cost-effective seat designs. The accuracy of FE analysis plays a pivotal role in this transformation. In the process of constructing a reliable finite element model, the selection and precise manipulation of key parameters are paramount. These crucial parameters encompass element size, time scale, analysis type, and material model. Properly defining and implementing these parameters ensures that the FE model produces accurate results, closely mirroring real-world performance. Verification of Finite Element Analysis (FEA) results is commonly accomplished through experimental methods. Notably, when the parameters are appropriately integrated into the modelling process, FE analysis outcomes closely align with experimental results. This study aims to leverage the power of FEM in performing static stress analysis and topology optimization of aircraft seats using the SOLIDWORKS commercial finite element platform. By simulating loading conditions, this research calculates static stresses and displacements experienced by the aircraft seat. Through a comprehensive topology optimization study, the weight of the airplane seat is remarkably reduced by up to 30%, while still prioritizing passenger safety. The success of this optimization showcases the potential for substantial weight savings in aircraft seat design without compromising safety standards.

Medical engineering is increasingly deploying nanotechnology and bio-inspired designs in the 21st century. Motivated by studying the spin coating of bio-nanofluid materials, gyrotactic bioconvection nanofluid swirling coating flow from a spinning disk to an isotropic permeable medium is analysed. The balance equations for mass, momentum, thermal, concentration and microorganism species including blowing effects are transformed into ordinary differential equations and then the solutions are obtained numerically through MATLAB bvp4c quadrature. These solutions are further validated with Adomian decomposition method (ADM). Increasing radial momentum slip reduces the radial skin friction and increasing tangential slip suppresses the tangential skin friction. Nusselt number, nanoparticle Sherwood number and micro-organism density number gradient are, respectively, decreased with increment in thermal slip, nanoparticle mass slip and micro-organism slip factors. Combinations of bioconvection and nanofluids provide excellent advantages in designing anti-bacterial and resilient bio-coatings for many devices.

A theoretical study in stagnation point flow is presented where melting heat transfer effects of carbon nanotube (CNT) from a stretching surface is appeared. Both carbon nanotubes like single-wall CNT (SWCNT) and multiwall CNT (MWCNT) are homogeneously dispersed in the base fluid. As the ordinary (or base) fluids, water and kerosene oil are employed. A set of nonlinear ordinary differential equations with appropriate boundary conditions is formed by transforming the governing equations via similarity transformations. The transformed nonlinear ordinary differential equations are then solved numerically using the bvp4c solver in matlab, an efficient numerical finite difference method. The impact of nanoparticle volume fraction, velocity, melting, stretching parameter, and CNT type on transport characteristics are explored and visualized graphically and in tabular forms. Verification of the matlab computations with available data in certain limiting cases is included showing excellent agreement. Existence of dual (upper and lower branch) solution is shown for a certain range of stretching sheet parameter. The obtained dual solutions are examined for velocity and temperature in detail. A stability analysis demonstrates that the first solution is a stable solution, and the second solution is an unstable solution. Local skin friction and local Nusselt number are also computed in order to determine critical values that can permit dual solutions. It is observed that when a dimensionless melting parameter is greater than 1, SWCNT nanofluids attain greater velocities than MWCNT nanofluids for water as well as kerosene oil base fluids. Moreover, the flow is accelerated for SWCNT compared with MWCNT for both water and kerosene oil. With increasing stretching parameter, the heat transfer rate (Nusselt number) increases, whereas skin friction coefficients decrease. Higher skin friction and Nusselt number are obtained for SWCNTs compared to MWCNTs due to their greater density and thermal conductivity. The study is relevant to phase change manufacturing fluid dynamics of nanomaterials.

This article examines theoretically and numerically the effect of non-Fourier heat flux on non-Newtonian (Eyring-Powell) Sakiadis convective flow from a moving permeable surface accompanied by a parallel free-stream velocity, as a simulation of polymeric coating processes. The Cattaneo-Christov model is deployed which features thermal relaxation effects as these are important in thermal polymer processing. The physical flow problem is modeled in a Cartesian coordinate system and the governing conservation differential equations and associated boundary conditions are rendered dimensionless by applying suitable transformations. Liquid velocity and thermal distributions are computed considering numerical procedure namely, a shooting method in conjunction with the 5th order Runge-Kutta algorithm (R-K5) executed in a symbolic software. Validation with the three-stage Lobatto IIIA algorithm in MATLAB is included. The impact of key parameters on streamline distributions is also computed. Velocity is increased with increment in Eyring-Powell first parameter for the Sakiadis case whereas it is reduced with Eyring-Powell second parameter for the case where sheet and liquid are inspiring in the similar direction. The special case of Blasius flow is also examined (stationary sheet). For higher injection, there is a solid dampening in the boundary-layer flow for both Sakiadis and Blasius scenarios.

Abstract A theoretical study is presented for the steady magnetohydrodynamic (MHD) boundary layer stagnation point flow of a nano-ferrofluid along a linearly moving stretching sheet, as a simulation of functional magnetic materials processing. Due to having imerging applications in heat transfer, the nano-ferrofluids draw the attention which comprise an aqueous base fluid doped with a variety of magnetic nanoparticles, i.e. magnetite (Fe3O4), cobalt ferrite (CoFe2O4) and Manganese-zinc (Mn-Zn) ferrite. A partial differential equation mathematical model is developed for mass, momentum, magnetic field continuity (induction), and energy with appropriate wall and free stream boundary conditions. Following similarity transformations, the dimensionless resultant nonlinear ordinary differential boundary value problem is solved numerically using the robust bvp4c function in MATLAB which features very efficient 4th order optimized Runge–Kutta quadrature. Dual solutions for the upper branch and lower branch separated by a critical point are identified. Visualization of velocity, temperature, and induced magnetic field function are presented graphically including validation of solutions with previous studies. Furthermore, skin-friction coefficient and the local Nusselt number are also computed. The impact of the controlling parameters, i.e. Prandtl number nanoparticle volume fraction parameter reciprocal of magnetic Prandtl number magnetic parameter and stretching rate ratio parameter have been illustrated through graphs and evaluated when a desire heat transfer can occur. Furthermore, resistance between fluid and the plate can be increased with the growing magnetic Prandtl number values. Increment in magnetic parameter ( ) produces an elevation in the induced magnetic field magnitudes. Skin friction and Nusselt number are found to be greater for cobalt nanoparticles when compared to magnetite and Mn-Zn ferromagnetic nanoparticles when there is an increase in reciprocal magnetic Prandtl number. The simulations provide a deeper insight into the manufacturing flows of functional nano-ferromagnetic materials of relevance to deposition and coating systems.

Prompted by the advancements in hybrid bio‐nano‐swirling magnetic bioreactors, a mathematical model for the swirling flow from a rotating disk bioreactor to a magnetic fluid saturating a porous matrix and containing nanoparticles and gyrotactic micro‐organisms has been developed. An axial magnetic field is administered which is perpendicular to the disk and Hall currents are included. The disk is assumed to be impervious and stretches in the radial direction with a power‐law velocity. The Buongiorno nanoscale, Kuznetsov bioconvection and Darcy porous media models are deployed. Anisotropic momentum, thermal, nanoparticle concentration and motile micro‐organism slip effects are incorporated. Stefan blowing is also simulated. The governing conservation equations are transformed with appropriate variables to ordinary nonlinear differential equations. MATLAB bvp4c shooting quadrature is used to solve the emerging nonlinear, coupled ordinary differential boundary value problem under transformed boundary conditions. Verification with earlier solutions for the non‐magnetic Von Karman bioconvection nanofluid case is conducted. Further validation of the general magnetic model is conducted with the Adomian decomposition method (ADM). Extensive visualization of velocity, temperature, nanoparticle concentration and motile microorganism density number profiles is presented for the impact of various parameters including magnetic interaction parameter, Hall current parameter, Darcy number, momentum slip, thermal slip, nanoparticle slip and microorganism slip. Computations are also performed for skin friction, Nusselt number, Sherwood number and motile micro‐organism density number gradient. The simulations provide a useful benchmark for further studies.