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The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.

The trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.

The profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.

Moreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.

Nonlinear mixed-convective entropy optimized the flow of hyperbolic-tangent nanofluid (HTN) with magnetohydrodynamics (MHD) process is considered over a vertical slendering surface. The impression of activation energy is incorporated in the modeling with the significance of nonlinear radiation, dissipative-function, heat generation/consumption connection and Joule heating. Research in this area has practical applications in the design of efficient heat exchangers, thermal management systems or nanomaterial-based devices.

Suitable set of variables is introduced to transform the PDEs (Partial differential equations) system into required ODEs (Ordinary differential equations) system. The transformed ODEs system is then solved numerically via finite difference method. Graphical artworks are made to predict the control of applicable transport parameters on surface entropy, Bejan number, Sherwood number, skin-friction, Nusselt number, temperature, velocity and concentration fields.

It is noticed from present numerical examination that Bejan number aggravates for improved estimations of concentration-difference parameter a_2, Eckert number E_c, thermal ratio parameter ?_w and radiation parameter R_d, whereas surface entropy condenses for flow performance index n, temperature-difference parameter a_1, thermodiffusion parameter N_t and mixed convection parameter ?. Sherwood number is enriched with the amplification of pedesis-motion parameter N_b, while opposite development is perceived for thermodiffusion parameter. Lastly, outcomes are matched with formerly published data to authenticate the present numerical investigation.

To the best of the authors' knowledge, no investigation has been reported yet that explains the entropic behavior with activation energy in the flowing of hyperbolic-tangent mixed-convective nanomaterial due to a vertical slendering surface.

This study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.

The governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.

Graphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.

The reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.

Adhesively bonded joints are used in many fields, especially in the automotive, marine, aviation, defense and outdoor industries. Adhesive bonding offers advantages over traditional mechanical methods, including the ability to join diverse materials, even load distribution and efficient thermal-electrical insulation. This study aims to investigate the mechanical properties of adhesively bonded joints, focusing on adherends produced with auxetic and flat surfaces adhered with varying adhesive thicknesses.

The research uses three-dimensional (3D)-printed materials, polyethylene terephthalate glycol and polylactic acid, and two adhesive types with ductile and brittle properties for single lap joints, analyzing their mechanical performance through tensile testing. The adhesion region of one of these adherends was formed with a flat surface and the other with an auxetic surface. Adhesively bonded joints were produced with 0.2, 0.3 and 0.4 mm bonding thickness.

Results reveal that auxetic adherends exhibit higher strength compared to flat surfaces. Interestingly, the strength of ductile adhesives in auxetic bonded joints increases with adhesive thickness, while brittle adhesive strength decreases with thicker auxetic bonds. Moreover, the auxetic structure displays reduced elongation under comparable force.

The findings emphasize the intricate interplay between adhesive type, bonded surface configuration of adherend and bonding thickness, crucial for understanding the mechanical behavior of adhesively bonded joints in the context of 3D-printed materials.

The purpose of this study is to explore numerical scrutinization of micropolar and Walters-B non-Newtonian fluids motion under the influence of thermal radiation and chemical reaction.

The two fluids micropolar and Walters-B liquid are considered to start flowing from the slot to the stretching sheet. A magnetic field of constant strength is imposed on their flow transversely. The problems on heat and mass transport are set up with thermal, chemical reaction, heat generation, etc. to form partial differential equations. These equations were simplified into a dimensionless form and solved using spectral homotopy analysis method (SHAM). SHAM uses the basic concept of both Chebyshev pseudospectral method and homotopy analysis method to obtain numerical computations of the problem.

The outcomes for encountered flow parameters for temperature, velocity and concentration are presented with the aid of figures. It is observed that both the velocity and angular velocity of micropolar and Walters-B and thermal boundary layers increase with increase in the thermal radiation parameter. The decrease in velocity and decrease in angular velocity occurred are a result of increase in chemical reaction. It is hoped that the present study will enhance the understanding of boundary layer flow of micropolar and Walters-B non-Newtonian fluid under the influences of thermal radiation, thermal conductivity and chemical reaction as applied in various engineering processes.

All results are presented graphically and all physical quantities are computed and tabulated.

This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions.

The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions.

The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases.

The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.

The purpose of this paper is to present an applied method to design the low-speed contact between a mass and surface of a beam using an analytical solution based on the first-order shear deformation beam theory. Also, a simulation of impact process is carried out by ABAQUS finite element (FE) code.

In theoretical formulation, first strains and stresses are obtained, then kinetic and potential energies are written, and using a combination of Ritz and Lagrange methods, a set of system of motion equations in the form of mass, stiffness and force matrices is obtained. Finally, the motion equations are solved using Runge–Kutta fourth order method.

The von Mises stress contours at the impact point and contact force from the ABAQUS simulation are illustrated and it is revealed that the theoretical solution is in good agreement with the FE code. The effect of changes in projectile speed, projectile diameter and projectile mass on the results is carefully examined with particular attention to evaluate histories of the impact force and beam recess. One of the important results is that changes in projectile speed have a greater effect on the results than changes in projectile diameter, and also changes in projectile mass have the least effect.

This paper presents a combination of methods of energy, Ritz and Lagrange and also FE code to simulate the problem of sandwich beams under low velocity impact.

A parabolic trough solar collector is an advanced concentrated solar power technology that significantly captures radiant energy. Solar power will help different sectors reach their energy needs in areas where traditional fuels are in use. This study aims to examine the sensitivity analysis for optimizing the heat transfer and entropy generation in the Jeffrey magnetohydrodynamic hybrid nanofluid flow under the influence of motile gyrotactic microorganisms with solar radiation in the parabolic trough solar collectors. The influences of viscous dissipation and Ohmic heating are also considered in this investigation.

Governing partial differential equations are derived via boundary layer assumptions and nondimensionalized with the help of suitable similarity transformations. The resulting higher-order coupled ordinary differential equations are numerically investigated using the Runga-Kutta fourth-order numerical approach with the shooting technique in the computational MATLAB tool.

The numerical outcomes of influential parameters are presented graphically for velocity, temperature, entropy generation, Bejan number, drag coefficient and Nusselt number. It is observed that escalating the values of melting heat parameter and the Prandl number enhances the Nusselt number, while reverse effect is observed with an enhancement in the magnetic field parameter and bioconvection Lewis number. Increasing the magnetic field and bioconvection diffusion parameter improves the entropy and Bejan number.

Nanotechnology has captured the interest of researchers due to its engrossing performance and wide range of applications in heat transfer and solar energy storage. There are numerous advantages of hybrid nanofluids over traditional heat transfer fluids. In addition, the upswing suspension of the motile gyrotactic microorganisms improves the hybrid nanofluid stability, enhancing the performance of the solar collector. The use of solar energy reduces the industry’s dependency on fossil fuels.

This study aims to analyze the two-dimensional ferrofluid flow in porous media. The effects of changes in parameters such as permeability parameter, buoyancy parameter, Reynolds and Prandtl numbers, radiation parameter, velocity slip parameter, energy dissipation parameter and viscosity parameter on the velocity and temperature profile are displayed numerically and graphically.

By using simplification, nonlinear differential equations are converted into ordinary nonlinear equations. Modeling is done in the Cartesian coordinate system. The finite element method (FEM) and the Akbari-Ganji method (AGM) are used to solve the present problem. The finite element model determines each parameter’s effect on the fluid’s velocity and temperature.

The results show that if the viscosity parameter increases, the temperature of the fluid increases, but the velocity of the fluid decreases. As can be seen in the figures, by increasing the permeability parameter, a reduction in velocity and an enhancement in fluid temperature are observed. When the Reynolds number increases, an increase in fluid velocity and temperature is observed. If the speed slip parameter increases, the speed decreases, and as the energy dissipation parameter increases, the temperature also increases.

When considering factors like thermal conductivity and variable viscosity in this context, they can significantly impact velocity slippage conditions. The primary objective of the present study is to assess the influence of thermal conductivity parameters and variable viscosity within a porous medium on ferrofluid behavior. This particular flow configuration is chosen due to the essential role of ferrofluids and their extensive use in engineering, industry and medicine.

This study investigates the flow and heat transfer in a magnetohydrodynamic (MHD) ternary hybrid nanofluid (HNF), considering the effects of viscous dissipation and radiation.

The transport equations are transformed into nondimensional partial differential equations. The local nonsimilarity (LNS) technique is implemented to truncate nonsimilar dimensionless system. The LNS truncated equation can be treated as ordinary differential equations. The numerical results of the equation are accomplished through the implementation of the bvp4c solver, which leverages the fourth-order three-stage Lobatto IIIa formula as a finite difference scheme.

The findings of a comparative investigation carried out under diverse physical limitations demonstrate that ternary HNFs exhibit remarkably elevated thermal efficiency in contrast to conventional nanofluids.

The LNS approach (Mahesh et al., 2023; Khan et al., 20223; Farooq et al., 2023) that we have proposed is not currently being used to clarify the dynamical issue of HNF via porous media. The LNS method, in conjunction with the bvp4c up to its second truncation level, yields numerical solutions to nonlinear-coupled PDEs. Relevant results of the topic at hand, obtained by adjusting the appropriate parameters, are explained and shown visually via tables and diagrams.