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The purpose of this study is to consider the effects that buoyancy arising from the combination of both thermal and concentration gradients can have on the mixed convection boundary-layer flow near a forward stagnation point with the effect of Stefan blowing being included. Ad suitable choice for the functional forms of the outer flow and the wall temperature and concentration enables the problem to be reduced to a similarity form involving the dimensionless parameters, λ (mixed convection), κ (Stefan blowing) and N (relative strength of concentration driven buoyancy to that of thermal driven), as well as the Prandtl and Schmidt numbers. Numerical solutions to this similarity system for a range of representative parameter values indicate a finite, non-zero range of κ where there can be four solutions in opposing flow with only one solution in aiding flow. Asymptotic solutions for large values of N and κ are derived, the latter having two different structures in the opposing flow.

This paper sets up a similarity problem to examine the effects of Stefan blowing on a mixed convection flow with the aims of solving the equations numerically and complementing the results with appropriate asymptotic analysis.

The findings of the study include multiple solution branches, saddle-node bifurcations and singularities appearing in the solution.

The authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere.

This study aims to investigate the flow behavior of aluminum oxide–water nanofluid with variable viscosity flowing through the microchannel parallel with the ground, with low aspect ratio. The study focuses on the first and second law analyses of Poiseuille flow using water as the base fluid with alumina nanoparticles suspended in it. Combined effects of thermal radiation, viscous dissipation, variable viscosity, nanoparticle shape factor and volume fraction on the thermal performance are studied and the in-built irreversibility in the process is examined.

The governing equations with dimensions are reduced to non-dimensional equations by using dimensionless quantities. Then, the Runge–Kutta–Fehlberg shooting scheme tackles the present non-linear equations.

The outcomes of the present analysis reveal that the activation energy parameter with its increase, depletes the exergetic effectiveness of the system, thus defending the fact to keep the activation energy parameter the lowest as possible for the system efficiency. In addition, thermal radiation and Biot number enhance the release of heat energy, thereby cooling the system. Bejan number graph exhibits the decreasing behavior for the increased nanoparticle shape factor, whereas the temperature enhances with the rise in nanoparticle shape factor.

The effects of nanoparticle shape factor in Poiseuille flow for alumina–water nanoliquid in low aspect ratio microchannel is inspected at the earliest. Exergetic effectiveness of the system is studied and heat transfer characteristics are explored for thermal radiation effect and activation energy parameter. Besides, BeηSphere>BeηBlades.

This paper aims to address the magnetohydrodynamic boundary layer flow of hybrid mixture across a stretching surface under the influence of electric field.

The local similarity transformations are implemented to reformulate the governing partial differential equations into coupled non-linear ordinary differential equations of higher order. The numerical solutions are obtained for the simplified governing equations with the aid of finite difference technique.

The velocity, temperature and entropy generation are examined thoroughly for the effects of different budding parameters related to present analysis by means of graphs. It is obtained that owing to the effect of magnetic field along with slip factor, the fluid motion slowdown. However, the flow velocity enhances for the rising estimations of an electric field which tends to resolve sticky effects.

The three-dimensional plots are drawn to understand the nature of physical quantities. To ensure the precision, the obtained solutions are compared with the existing one for certain specific conditions. A good concurrence is observed between the proposed results and previously recorded outcomes.

The purpose of this study is to provide that porous media and viscous dissipation are crucial considerations when working with hybrid nanofluids in various applications.Recent years have witnessed significant progress in optimizing these fluids for enhanced heat transfer within porous (Darcy–Forchheimer) structures, offering promising solutions for various industries seeking improved thermalmanagement and energy efficiency.

The first step is to transform the original partial differential equations into a system of first-order ordinary differential equations (ODEs). The fourth-order Runge–Kutta method is chosen for its accuracy in solving ODEs. The present study investigates the free convective boundary layer flow of hybrid nanofluids over a moving thin inclined needle with the slip flow brought about by inclined Lorentz force and Darcy–Forchheimer porous matrix, viscous dissipation.

It is found that slip conditions (velocity and Thermal) exist for a range of the natural convection boundary layer flow. In the hybrid nanofluid flow, which consists of Al₂O₃ and Fe₃O₄ are nanoparticles, H₂O − C₂H₆O₂ (50:50) are considered as the base fluid. The consequence of the governing parameter on the momentum and temperature profile distribution is graphically depicted. The range of the variables is 1 ≤ M ≤ 4, 1 ≤ d ≤ 2.5, 1 ≤ δ ≤ 4, 1 ≤ Fr ≤ 7, 1 ≤ Kr ≤ 7 and 0.5≤λ ≤ 3.5. The Nusselt number and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in Table 4. These analyses elucidate that upsurges in the value of the Fr noticeably diminish the momentum and temperature. It is investigated to see if the contemporary results are in outstanding promise with the outcomes reported in earlier works.

The results can be very helpful to improve the energy efficiency of thermal systems.

The hybrid nanofluids in heat transfer have the potential to improve the energy efficiency and performance of a wide range of systems.

This study proposes that in the combined effects of hybrid nanofluid properties, the inclined Lorentz force, the Darcy–Forchheimer model for porous media and viscous dissipation on the boundary layer flow of a conducting fluid over a moving thin inclined needle. Assessing the potential practical applications of the hybrid nanofluids in inclined needles, this could involve areas such as biomedical engineering, drug delivery systems or microfluidic devices. In future should explore the benefits and limitations of using hybrid nanofluids in these applications.

According to the previous research, bioconvection has been recognized as an important mechanism in current engineering and environmental systems. For example, researchers exploit this mechanism in modern green bioengineering to develop environmentally friendly fuels, fuel cells and photosynthetic microorganisms. This study aims to analyse how this type of convection affects the flow behaviour and heat transfer performance of mixed convection stagnation point flow in alumina-copper/water hybrid nanofluid. Also, the impact of a modified magnetic field on the boundary layer flow is considered.

By applying appropriate transformations, the multivariable differential equations are transformed into a specific sort of ordinary differential equations. Using the bvp4c procedure, the adjusted mathematical model is revealed. Once sufficient assumptions are provided, multiple solutions are able to be produced.

The skin friction coefficient is declined when the nanoparticle concentration is increased in the opposing flow. In contrast, the inclusion of aligned angles displays an upward trend in heat transfer performance. The presence of several solutions is established, which simply leads to a stability analysis, hence verifies the viability of the initial solution.

The current findings are unique and novel for the investigation of mixed bioconvection flow towards a vertical flat plate in a base fluid with the presence of hybrid nanoparticles.

The purpose of this paper is to investigate the bioconvection flow in a porous square cavity saturated with both oxytactic microorganism and nanofluids.

The impacts of the effective parameters such as Rayleigh number, bioconvection number, Peclet number and thermophoretic force, Brownan motion and Lewis number reduces the flow strength in the cavity on the flow strength, oxygen density distribution, motile isoconcentrations and heat transfer performance are investigated using a finite volume approach.

The results obtained showed that the average Nusselt number is increased with Peclet number, Lewis number, Brownian motion and thermophoretic force. Also, the average Sherwood number increased with Brownian motion and Peclet number and decreased with thermophoretic force. It is concluded that the flow strength is pronounced with Rayleigh number, bioconvection number, Peclet number and thermophoretic force. Brownan motion and Lewis number reduce the flow strength in the cavity.

There is no published study in the literature about sensitivity analysis of Brownian motion and thermophoresis force effects on the bioconvection heat transfer in a square cavity filled by both nanofluid and oxytactic microorganisms.

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 study is to investigate the entropy generation in different nanofluids flow over a vertically moving rotating disk. Unlike the classical Karman flow, water-based nanofluids have various suspended nanoparticles, namely, Cu, Ag, Al₂O₃ and TiO₂, and the disk is also moving vertically with time-dependent velocity.

The Keller box technique numerically solves the governing equations after reduction by suitable similarity transformations. The shear stress and heat transport features, along with flow and temperature fields, are numerically computed for different concentrations of the nanoparticles.

This study is done comparatively in between different nanofluids and for the cases of vertical movement of the disk. It is found that heat transfer characteristics rely not only on considered nanofluid but also on disk movement. Moreover, the upward movement of the disk diminishes the heat-transfer characteristics of the fluid for considered nanoparticles. In addition, for the same group of nanoparticles, an entropy generation study is also performed, and an increasing trend is found for all nanoparticles, with alumina nanoparticles dominating the others.

This research is a novel work on a vertically moving rotating surface for the water-conveying nanoparticle fluid flow with entropy generation analysis. The results were found to be in good agreement in the case of pure fluid.

This paper aims to study the fluid flow and heat transfer within the Casson nanofluid confined between disk and cone both rotating with distinct velocities. For a comprehensive investigation, two distinct nano-size particles, namely, silicon dioxide and silicon carbide, are submerged in ethanol taken as the base fluid.

This paper explores the disk and cone contraption mostly encountered for viscosity measurement in various industrial applications such as lubrication industry, hydraulic brakes, pharmaceutical industry, petroleum and gas industry and chemical industry.

It is worth mentioning here that the radially varying temperature profile at the disk surface is taken into the account. The effect of prominent emerging parameters on velocity fields and temperature distribution are studied graphically, while bar graphs are drawn to examine the physical quantities of industrial interest such as surface drag force and heat transfer rate at disk and cone.

To the best of the authors’ knowledge, no study in literature exists that discusses the thermal enhancement of nano-fluidic transport confined between disk and cone both rotating with distinct angular velocities with heat transfer.

This paper aims to elaborate the characteristics of magneto-Maxwell nanoliquid toward moving radiated surface. Flow analysis subject to Darcy–Forchheimer concept is studied. Newtonian heat/mass conditions and heat source aspects are taken into account for modeling. Apposite transformations are introduced for non-dimensionalization process.

Optimal homotopy analysis method is implemented to compute convergent solutions of nonlinear ordinary differential equations.

Temperature field increments when thermophoresis, heat generation and Brownian movement parameters are increased, whereas reverse situation is noticed for larger Prandtl number. The results also witness that concentration distribution has opposite characteristics for larger thermophoresis and Brownian movement parameters. Furthermore, the presented analysis reduces to traditional Darcy relation in the absence of local inertia coefficient.

As per the authors’ knowledge, no such analysis has been yet reported.