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A novel type of heat transfer fluid known as hybrid nanofluids is used to improve the efficiency of heat exchangers. It is observed from literature evidence that hybrid nanofluids outperform single nanofluids in terms of thermal performance. This study aims to address the stagnation point flow induced by Williamson hybrid nanofluids across a vertical plate. This fluid is drenched under the influence of mixed convection in a Darcy–Forchheimer porous medium with heat source/sink and entropy generation.

By applying the proper similarity transformation, the partial differential equations that represent the leading model of the flow problem are reduced to ordinary differential equations. For the boundary value problem of the fourth-order code (bvp4c), a built-in MATLAB finite difference code is used to tackle the flow problem and carry out the dual numerical solutions.

The shear stress decreases, but the rate of heat transfer increases because of their greater influence on the permeability parameter and Weissenberg number for both solutions. The ability of hybrid nanofluids to strengthen heat transfer with the incorporation of a porous medium is demonstrated in this study.

The findings may be highly beneficial in raising the energy efficiency of thermal systems.

The originality of the research lies in the investigation of the Darcy–Forchheimer stagnation point flow of a Williamson hybrid nanofluid across a vertical plate, considering buoyancy forces, which introduces another layer of complexity to the flow problem. This aspect has not been extensively studied before. The results are verified and offer a very favorable balance with the acknowledged papers.

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 work aims to concentrate on the mixed convection of the stagnation point flow of ternary hybrid nanofluids towards vertical Riga plate. Aluminum trioxide (Al₂O₃), silicon dioxide (SiO₂) and titanium dioxide (TiO₂) are regarded as nanoparticles, with water serving as the base fluid. The mathematical model incorporates momentum boundary layer and energy equations. The Grinberg term for the viscous dissipation and the wall parallel Lorentz force coming from the Riga plate are taken into consideration in the context of the energy equation.

Through the use of appropriate nonsimilar transformations, the governing system is transformed into nonlinear nondimensional partial differential equations (PDEs). The numerical method bvp4c (built-in package for MATLAB) is used in this study to simulate governing equations using the local non-similarity (LNS) approach up to the second truncation level.

Numerous graphs and numerical tables expound on the physical properties of the nanofluid temperature and velocity profiles. The local Nusselt correlations and the drag coefficient for pertinent parameters have been computed in tabular form. Additionally, the temperature profile drops while the velocity profile increases when the mixed convection parameter is included to oppose the flow.

The fundamental goal of this work is to comprehend how ternary nanofluids move towards a vertical Riga plate in a mixed convective domain with stagnation point flow.

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.

Several graphs, streamlines, isotherms and 3D plots are illustrated to enlighten the noteworthy fallouts of the investigation. Embedding flow factors for velocity, induced magnetic field and temperature have been determined using parametric analysis.

Ternary hybrid nanofluids has outstanding hydrothermal performance compared to classical mono nanofluids and hybrid nanofluids owing to the presence of triple tiny metallic particles. Ternary hybrid nanofluids are considered as most promising candidates in solar energy, heat exchangers, electronics cooling, automotive cooling, nuclear reactors, automobile, aerospace, biomedical devices, food processing etc. In this work, a ternary hybrid nanofluid flow that contains metallic nanoparticles over a wedge under the prevalence of solar radiating heat, induced magnetic field and the shape factor of nanoparticles is considered. A ternary hybrid nanofluid is synthesized by dispersing iron oxide (Fe3O4), silver (Ag) and magnesium oxide (MgO) nanoparticles in a water (H₂O) base fluid. By employing similarity transformations, we can convert the governing equations into ordinary differential equations and then solve numerically by using the Runge–Kutta–Fehlberg approach.

There is no fund for the research work.

This kind of study may be used to improve the performance of solar collectors, solar energy and solar cells.

This investigation unfolds the hydrothermal changes of radiative water-based Fe₃O₄-Ag-MgO-H₂O ternary hybrid nanofluidic transport past a static and moving wedge in the presence of solar radiating heating and induced magnetic fields. The shape factor of nanoparticles has been considered in this study.

As to different angles of attack and nonlinear problems caused by high temperatures in coexisting hypersonic aircraft, people mainly rely on fluid software for research but lack analysis of flow mechanisms. Owing to computational difficulties, few people use numerical algorithms to combine them for discussion. Hence, this study aims to make a deep inquiry into the laminar flow and heat transfer of compressible Newtonian fluid in hypersonic aircraft with small attack angles.

In this paper, on the basis of mass, momentum and energy conservation laws, the governing equations of the hypersonic boundary layer are established. Viscosity, specific heat capacity and thermal conductivity are considered nonlinear functions concerning temperature. In virtue of the MacCormack finite difference method, the stationary numerical solutions are solved directly, and the validity of the algorithm is verified.

The results demonstrate that at Mach number 5, compared to the 0° attack angle, the maximum temperature near-wall at the 3° attack angle increases by about 25%. An enjoyable phenomenon is discovered, where the position corresponding to the maximum wall shear force shifts back as the attack angle and Mach number increase. The relationship between the near-wall maximum temperature versus attack angle and Mach number is fitted through numerical calculation results.

Empirical formulas can be used to estimate heat transfer characteristics at small attack angles, which will guide the design of aircraft thermal protection systems.

The purpose of this study is to investigate the impact of varying baffle height and spacing distance on heat transfer and cooling performance of electronic components in a baffled horizontal channel, using a Cu-H₂O nanofluid under mixed convection and laminar flow.

The mathematical model is two-dimensional and comprises a system of four governing equations, such as the conservation of continuity, momentum and energy. To obtain numerical solutions for these equations, the finite volume method was used for discretization. A validation process was performed by comparing this study’s results with those of previously published studies. The comparison revealed a close agreement. The numerical study was performed for a wide range of key parameters: The baffle height (0 ≤ h ≤ 0.7), the spacing distance between baffle and blocks (0.25 ≤ w ≤ 3), the Grashof and Reynolds numbers are kept equal to 10⁴ and 75, respectively, the channel aspect ratio is L/H = 10, and the volume fraction of Cu nanoparticles is fixed at φ = 5%.

The results of the study reveal a significant improvement in heat transfer in terms of total Nusselt number of the top and bottom hot components, which exhibited an improvement of 16.89% and 17.23% when the baffle height increases from h = 0 to h = 0.7. Additionally, the study found that reducing the distance between the baffle and the electronic components up to a certain limit can improve the heat transfer rate. Therefore, the optimal height of the baffle was found to be no lower than 0.6, and the recommended distance between the heaters and the baffle was 0.5.

This study provides valuable insights into the optimization of the design of baffled channels for improved heat transfer performance. The findings of study can be used to improve heat exchangers and cooling systems in various applications. The use of Cu-H₂O nanofluid under mixed convection and laminar flow conditions in channel with baffle and electronic components is also unique, making this study an original contribution to the field.

This study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe₃O₄/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.

The dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.

The roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.

The analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

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.