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Thermophoresis deposition of particles is a crucial stage in the spread of microparticles over temperature gradients and is significant for aerosol and electrical technologies. To track changes in mass deposition, the effect of particle thermophoresis is therefore seen in a mixed convective flow of Williamson hybrid nanofluids upon a stretching/shrinking sheet.

The PDEs are transformed into ordinary differential equations (ODEs) using the similarity technique and then the bvp4c solver is employed for the altered transformed equations. The main factors influencing the heat, mass and flow profiles are displayed graphically.

The findings imply that the larger effects of the thermophoretic parameter cause the mass transfer rate to drop for both solutions. In addition, the suggested hybrid nanoparticles significantly increase the heat transfer rate in both outcomes. Hybrid nanoparticles work well for producing the most energy possible. They are essential in causing the flow to accelerate at a high pace.

The consistent results of this analysis have the potential to boost the competence of thermal energy systems.

It has not yet been attempted to incorporate hybrid nanofluids and thermophoretic particle deposition impact across a vertical stretching/shrinking sheet subject to double-diffusive mixed convection flow in a Williamson model. The numerical method has been validated by comparing the generated numerical results with the published work.

Nanosized honeycomb-configured materials are used in modern technology, thermal science and chemical engineering due to their high ultra thermic relevance. This study aims to scrutinize the heat transmission features of magnetohydrodynamic (MHD) honeycomb-structured graphene nanofluid flow within two squeezed parallel plates under Joule dissipation and solar thermal radiation impacts.

Mass, energy and momentum preservation laws are assumed to find the mathematical model. A set of unified ordinary differential equations with nonlinear behavior is used to express the correlated partial differential equations of the established models, adopting a reasonable similarity adjustment. An approximate convergent numerical solution to these equations is evaluated by the shooting scheme with the Runge–Kutta–Fehlberg (RKF45) technique.

The impression of pertinent evolving parameters on the temperature, fluid velocity, entropy generation, skin friction coefficients and the heat transference rate is explored. Further, the significance of the irreversibility nature of heat transfer due to evolving flow parameters are evaluated. It is noted that the heat transference rate performance is improved due to the imposition of the allied magnetic field, Joule dissipation, heat absorption, squeezing and thermal buoyancy parameters. The entropy generation upsurges due to rising magnetic field strength while its intensification is declined by enhancing the porosity parameter.

The uniqueness of this research work is the numerical evaluation of MHD honeycomb-structured graphene nanofluid flow within two squeezed parallel plates under Joule dissipation and solar thermal radiation impacts. Furthermore, regression models are devised to forecast the correlation between the rate of thermal heat transmission and persistent flow parameters.

The purpose of the study is to analytically as well as numerically investigate the weight of throughflow on the onset of Casson nanofluid layer in a permeable matrix. This study examines both the marginal and over stable kind of convective movement in the system.

A double-phase model is used for Casson nanofluid, which integrates the impacts of thermophoresis and Brownian wave, whereas for flow in the porous matrix the altered Darcy model is occupied under the statement that nanoparticle flux is disappear on the boundaries. The resultant eigenvalue problem is resolved analytically as well as numerically with the help of Galerkin process with the Casson nanofluid Rayleigh–Darcy number as the eigenvalue.

The findings revealed that the throughflow factor postpones the arrival of convective flow and reduces the extent of convective cells, whereas the Casson factor, the Casson nanoparticle Rayleigh–Darcy number and the reformed diffusivity ratio promote convective motion and also decrease the extent of convective cells.

Controlling the convective movement in heat transfer systems that generate high heat flux is a real mechanical challenge. The proposed framework proved that the use of throughflow is one of the most important ways to control the convective movement in Casson nanofluid. To the best of the authors’ knowledge, no inspection has been established in the literature that studies the outcome of throughflow on the Casson nanofluid convective flow in a porous medium layer. However, the convective flow of Casson nanofluid finds many applications in improving heat transmission and energy efficiency in a range of thermal systems, such as the cooling of heat-generating elements in electronic devices, heat exchangers, pharmaceutical practices and hybrid-powered engines, where throughflow can play a significant role in controlling the convective motion.

This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect.

The partial differential equations that governed the problem will undergo a transformation into a set of similarity equations. Following this transformation, a numerical solution will be obtained using the boundary value problem solver, bvp4c, built in the MATLAB software. Later, analysis and discussion are conducted to specifically examine how various physical parameters affect both the flow characteristics and the thermal properties of the hybrid nanofluid.

Dual solutions are discovered to occur for the case of shrinking disk (λ < 0). Stronger suction triggers the critical values’ expansion and delays the boundary layer separation. Through stability analysis, it is determined that one of the solutions is stable, whereas the other solution exhibits instability, over time. Moreover, volume fraction upsurge enhances skin friction and heat transfer in hybrid nanofluid. The hybrid nanofluid’s heat transfer also heightened with the influence of radiation.

Flow over a shrinking disk has received limited research focus, in contrast to the extensively studied axisymmetric flow problem over a diverse set of geometries such as flat surfaces, curved surfaces and cylinder. Hence, this study highlights the axisymmetric flow due to a shrinking disk under radiation influence, using hybrid nanofluids containing CuO and Ag. Upon additional analysis, it is evidently shows that only one of the solutions exhibits stability, making it a physically dependable choice in practical applications. The authors are very confident that the findings of this study are novel, with several practical uses of hybrid nanofluids in modern industry.

The purpose of this study is to investigate the Dynamics of micropolar – water B Fluids flow simultaneously under the influence of thermal radiation and Soret–Dufour Mechanisms.

The thermal radiation contribution, the chemical change and heat generation take fluidity into account. The flow equations are used to produce a series of dimensionless equations with appropriate nondimensional quantities. By using the spectral homotopy analysis method (SHAM), simplified dimensionless equations have been quantitatively solved. With Chebyshev pseudospectral technique, SHAM integrates the approach of the well-known method of homotopical analysis to the set of altered equations. In terms of velocity, concentration and temperature profiles, the impacts of Prandtl number, chemical reaction and thermal radiation are studied. All findings are visually shown and all physical values are calculated and tabulated.

The results indicate that an increase in the variable viscosity leads to speed and temperature increases. Based on the transport nature of micropolar Walters B fluids, the thermal conductivity has great impact on the Prandtl number and decrease the velocity and temperature. The current research was very well supported by prior literature works. The results in this paper are anticipated to be helpful for biotechnology, food processing and boiling. It is used primarily in refrigerating systems, tensile heating to large-scale heating and oil pipeline reduction.

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

The purpose of this study is to examine the melting heat transfer of magnetohydrodynamics Casson nanofluid flow with viscous dissipation, radiation, and complete slip effects on a porous stretching sheet. Since, the study of melting heat transfer has mesmerized the attention of scientists and engineers in the sense of its enormous uses in industrial processes, solidification, casting, and technology.

Bejan number and entropy are analyzed. Exploration of irreversibility is modeled using the thermodynamics second law. There is a discussion on thermophoresis and Brownian diffusion along with first-order chemical reactions. Adequate transformations are introduced to convert the controlling partial differential equations to ordinary differential equations. The three-phase Lobatto solvers (bvp5c) are used to obtain numerical solutions of the transmitted equations.

The effects of various factors on temperature, velocity, concentration, Bejan number and entropy rate are shown graphically. The velocity field is enhanced by increasing the melting heat parameter, and it declines for growing magnetic parameters. Temperature is decreased for increasing parametric values of melting heat, porous and Casson parameters. A 7% decrease in the Sherwood distribution is seen when we increase the Brownian motion parameter from 0.1 to 0.2. Similarly, an 11% decrement is found in the Nusselt distribution for increasing the Brinkman number from 0.5 to 1.

Entropy and Bejan number experience dual tendencies whenever the melting heat parameter increases. Nusselt number and skin friction experience the opposite behavior for the increasing values of melting parameter. Sherwood number decreases for the increasing values of melting parameter. The velocity profile is directly related to the melting parameter and inversely related to porous and magnetic parameters. Thermophoresis and Brinkman parameters boost the temperature profile and it is controlled by melting and porous parameters. Some notable fields where the present study is used inevitably are silicon wafering, geothermal energy recovery and semiconductor manufacturing.

Fluid flows through rotatory disks are encountered in industrial and practical engineering processes, such as computer storage devices, gas turbine rotators, rotating machinery, air cleaning machines, etc. The primary purpose of this research is to examine the combined aspects of variable electrical conductivity, thermal radiation, Soret and Dufour effects on a magnetohydrodynamic Maxwell single-walled carbon nanotubes–graphene oxide–multi-walled carbon nanotubes–copper (SWCNT–GO–MWCNT–Cu)/sodium alginate tetra-hybrid nanofluid flow through a stretchable rotatory disk.

The modeled administrative equations of the present flow problem are converted to a non-dimensional system of ordinary differential equations by applying suitable similarity conversion and then solved numerically by implementing the bvp4c method. The impressions of noteworthy dimensionless parameters on velocity, temperature, concentration distributions, Nusselt number, skin friction and Sherwood number are reported via graphs and tables.

The authors figured out that the developed values of the rotation parameter diminish the temperature but enhance both the radial and angular velocities. Further, the mass and heat transmission rates are better for tetra-hybrid nanofluids than for ternary and hybrid nanofluids.

The present study emphasizes a special type of fluid called the tetra-hybrid nanofluid. The existing literature has not discussed the Maxwell tetra hybrid nanofluid flow through a stretchable rotatory disk with variable electrical conductivity. Besides, the novel aspects of magnetohydrodynamics, thermal radiation, Soret and Dufour effects are also incorporated into the present flow problem.

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.

The purpose of this study is to analyze the impact of inclined magnetohydrodynamics (MHD) and thermal radiation on the flow of a ternary micropolar nanofluid on a sheet that is expanding and contracting while applying mass transpiration and velocity slip conditions to the flow. The nanofluid, which is composed of Au, Ag and Cu nanoparticles dispersed in water as the base fluid, possesses critical properties for increasing the heat transfer rate and is frequently used in manufacturing and industrial establishments.

The set of governing nonlinear partial differential equations is transformed into a set of nonlinear ordinary differential equations. The outcome of this differential equation is solved and obtained the closed-form solution and energy equation in the form of hypergeometric functions.

The velocity, micro-rotation and temperature field are investigated versus a parametric variation. The physical domains of mass suction or injection and micropolar characteristics play an important role in specifying the presence, singleness and multiplanes of exact solutions. In addition, many nondimensional characteristics of the profiles of temperature, angular velocity and velocity profiles are graphically shown with substantial consequences. Furthermore, adding nanoparticles increases the heat transfer rate of the fluid used in manufacturing and industrial establishments. The current findings may be used for better oil recovery procedures, smart materials such as magnetorheological fluids, targeted medicine administration and increased heat transmission. Concerning environmental cleanup, nanomaterial fabrication and biomedical devices, demonstrate their potential influence in a variety of disciplines.

The originality of this paper is to analyze the impact of inclined MHD at an angle with the ternary nanofluid on a micropolar fluid over an expanding and contracting sheet with thermal radiation effect.

Basically, connections are used to transfer the force supported by structural members to other parts of the structure. The flush end-plate bolted beam to column connection is one type that has been widely used because of its simplicity in fabrication and rapid site erection. The purpose of this study is to determine the moment-rotation curve, moment of resistance (MR) and mode of failure, and the results were compared with existing results for normal flat web connections.

In this study, the connection modeled was the flush end-plate welded with triangular web profile (TriWP) steel beam section and then bolted to a UKC column flange. The bolted flush end-plate semi-rigid beam to column connection was modeled using finite element software. The specimen was modeled using LUSAS 14.3 finite element software, with dimensions and parameters of the finite element model sizes being 200 × 200 × 49.9 UKC, 200 × 100 × 17.8 UKB and 200 × 100 with a thickness of 20 mm for the endplate.

It can be concluded that the MR obtained from the TriWP steel beam section is different from that of the normal flat web steel beam by 28%. The value of MR for the TriWP beam section is lower than that of the normal flat web beam section, but the moment ultimate is higher by 21% than the normal flat web. Therefore, it can be concluded that the TriWP section can resist more acting force than the normal flat web section and is suitable to be used as a new proposed shape to replace the normal flat web section for a certain steel structure based on the end-plate connection behavior.

As a result, the TriWP section has better performance than the flat web section in resisting MR behavior.