Study of MHD mixed convection stagnation point flow of carreau fluid with gyrotactic micro-motile organisms

Hydrothermal transport of a chemically reactive bioconvective hybrid nanofluid with activation energy in MHD stagnation-point flow over a stretching surface

MHD Front and rear stagnation-point flow of a moving permeable flat surface

This work examines the influence of activation energy, magnetic field (MF), and quadratic thermal radiation (Q-TR) on the stagnation-point flow generated by an off-centered rotating disk (O-CRD) subjected to Soret and Dufour effects (S-DE). Furthermore, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using suitable similarity variables. Additionally, the numerical solutions are obtained for reduced ODEs using the Runge–Kutta–Fehlberg fourth-fifth order (RKF-45) technique. Furthermore, the response surface methodology (RSM) is utilized to assess the heat transportation rate of the fluid flow. The impact of non-dimensional parameters on the liquid profiles is shown graphically. The results indicate that the MF parameter decreases fluid velocity, whereas an increase in the rotational parameter increases the flow near the disk. An increase in the Soret number enhances the concentration profile. The temperature profile enhances as the radiation parameter intensifies. These results provide a better understanding of complicated transport processes, which help to develop and improve engineering systems that utilize high-temperature rotating machinery, chemical processing, and sophisticated thermal management.

Enhancing engine efficiency, augmenting energy production in solar thermal systems, and reducing friction and wear in tribological contexts are key applications of ternary hybrid nanofluids comprising aluminium oxide, copper, and molybdenum disulfide nanoparticles dispersed in engine oil. This study presents a comparative analysis of the induced magnetic field and heat transfer characteristics of Carreau nanofluid flow over a vertical and an inclined stretching cylinder, highlighting the effects of thermal radiation, viscous dissipation, and stagnation point flow. The research formulates governing equations based on momentum, magnetic induction, and energy principles, converting them into nonlinear ordinary differential equations using appropriate transformations. The bvp4c solver in MATLAB is used to solve the linearised ordinary differential equations. The results indicate that the heat source/sink, magnetic field, thermal radiation parameter, and Eckert and Biot numbers contribute to enhancing the heat transfer. Ternary hybrid nanofluids excel in heat transfer and fluid motion compared to conventional nanofluids. Skin friction and local Nusselt number are computed and graphically represented for a vertical cylinder in comparison to an inclined cylinder.

ABSTRACT The off‐centered stagnation point flow (S‐PF) phenomenon is important in many technical domains where flow patterns affect efficiency and performance. In these systems, the interplay between asymmetric flow and disk rotation influences the temperature boundary layer and concentration gradients, either augmenting or impeding heat and mass transfer rates. Earliest studies focused on stagnation flows or considered only a few thermal or chemical effects, leaving the combined influence of off‐centered asymmetry. Hence, this work fills that gap by examining the significance of thermophoretic particle deposition on the off‐centered S‐PF of fluid via a rotating disk subjected to activation energy. Moreover, the artificial neural network is used to estimate the heat transmission rate as a function of various factors. Increased magnetic field and permeability parameters decrease the momentum field. The concentration profile decreases as the thermophoretic coefficient increases.

Growing expectations for superior engine performance, fuel efficiency, and durability are fueling innovation in advanced heat transfer fluids and tribological technologies, aimed at reducing friction and wear, and enhancing overall efficiency in automotive and lubrication engineering. This study examines stagnation-point flow of ternary hybrid nanofluids around a horizontal stretching cylinder, accounting for the effects of a porous medium, Joule heating, a heat source/sink, thermal diffusion, and molecular motion on fluid velocity, heat transfer, and mass transfer. Similarity transformations are used to convert a system of partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs), which are then reduced to first-order ODEs. The MATLAB bvp4c solver is utilized to numerically resolve the converted ODEs, yielding graphical representations of velocity, temperature, and concentration profiles. The findings reveal that the Eckert and Biot numbers, magnetic field strength, heat source/sink, thermal diffusion, and molecular motion parameters collectively enhance thermal efficiency in ternary hybrid nanofluids by 26.62% over the nanofluid. Conversely, porosity and curvature parameters are found to deteriorate thermal efficiency. Furthermore, the magnetic field, porosity, and curvature parameters are observed to augment the velocity of the ternary hybrid nanofluid.

In the current study, we investigate the stagnation-point flow of a MHD nanofluid toward stretching sheet in porous media with suction or injection. Whereas, the contribution of the velocity, temperature, and nanoparticle distributions to identify the advantages or disadvantages that nanoparticles like bacteria, microbes and viruses, cause in the flow stretching sheet is what makes this work significan. A new procedure is suggested for the analytical treatment of the governing system of partial differential equations, where the boundary condition at infinity is converted from the unbounded domain to the bounded domain by using some transformations and then modified adomian decomposition method is utilized. The effects of parameters (porous medium, magnetic number, surface heat flux, suction or injection and Prandtl number) on velocity, temperature and concentration profiles are shown graphically and analyzed. Finally, we compared our obtained results with the other techniques used before in literature.

Combined influence of surface permeability and reactive diffusion on magneto-radiative stagnation-point nanofluid flow over a stretching surface

This paper examines the influence of the unsteadiness parameter on the maximum wall shear stress in an unsteady stagnation-point boundary layer over a vertical flat plate with oscillatory wall blowing or suction. The analysis considers a two-dimensional, incompressible, viscous flow impinging on the plate, with time-periodic variations in both the free-stream velocity and the wall blowing/suction rate. The formulation follows the approach of Blyth and Hall. Using similarity transformations, the time-dependent Navier–Stokes equations are reduced to a single nonlinear ordinary differential equation governing the boundary layer. This equation is solved numerically using a fully implicit finite-difference scheme. Wall shear stress is obtained from the second derivative of the similarity function, and its maximum value is tracked over time to characterize the flow dynamics. Results show that increasing the blowing parameter raises the peak shear stress, whereas larger unsteadiness reduces it. For each set of flow conditions, the shear stress reaches a maximum at a specific oscillation frequency before asymptotically approaching a steady-state trend. Higher unsteadiness delays the occurrence of this peak and diminishes its magnitude. In certain parameter ranges, the shear stress exhibits erratic behavior, indicating incipient divergence. Keywords: similarity solution, stagnation-point flow, unsteadiness, oscillation, blowing.

Stagnation point flow analysis in an inductively coupled plasma reactor for advanced deposition techniques

Oblique stagnation point flow of hybrid nanofluid on a stretching sheet with modified thermal conductivity models and Darcy's law

Scrutinizing stagnation-point flow close to a deforming cylinder in Reiner-Rivlin fluid due to homogeneous-heterogeneous chemical reactions

This study investigates boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet embedded in a porous medium, with emphasis on the effects of suction, blowing, thermal radiation, and heat generation. The governing nonlinear boundary layer equations are numerically solved using the Taylor wavelet method. The results show that suction enhances flow stability by reducing the boundary layer thickness and promoting heat transfer, whereas blowing destabilizes the flow, leading to an increase in boundary layer thickness and a reduction in heat transfer. Thermal radiation raises the temperature within the boundary layer, and heat generation further amplifies this effect, causing additional thickening of the thermal boundary layer. The porous medium introduces resistance, which reduces fluid velocity and intensifies the temperature gradient near the surface. The effectiveness of the Taylor wavelet method in solving nonlinear boundary layer problems is demonstrated. The findings provide valuable insights for optimizing heat and mass transfer in engineering applications such as cooling technologies, material processing, and energy systems.

ABSTRACT This study explores the mass and heat transfer in a radiative second-grade liquid consisting of a tetra-hybrid nanofluid on a shrinking/stretching cylinder, including diffusion-thermo and thermal diffusion. The correlations of the Yamada–Ota and Hamilton–Crosser models are utilized to determine the thermal conductivity of a tetra-hybrid nanofluid. Furthermore, stagnation point flow and activation energy are considered. The set of ordinary differential equations is formulated using similarity transformations and solved numerically by the finite difference method. The radiative second-grade viscoelastic flow over a shrinking cylinder with a tetra-hybrid nanofluid is considered. Darcy’s Forchheimer model in the energy equation is novel and explores new perspectives on thermal management in energy systems and heat exchanger design. A higher Forchheimer number and magnetic parameter slow the flow, while increasing the second-grade viscoelastic parameter lowers the nanofluid velocity by up to 14%. Conversely, the temperature increases as the Forchheimer number, Dufour number, Soret number and heat sink parameter increase. This results in a 9%–12% increase in the Nusselt number. The upper branch solutions are significant rather than the lower branch solutions in the velocity fields. Such improved upper-branch velocity simulations are used in oil recovery and polymer processing.

A theoretical analysis is made on the unsteady stagnation point flow of a conducting fluid over a flat stretching surface in the presence of magnetic field with chemically reactive species concentration and mass diffusion under Soret and Dufour effects. The governing partial differential equations of continuity, momentum, energy and concentration have been converted to self-similar unsteady equations by using similarity transformations and solved numerically by the Runge-Kutta algorithm with Newton iteration in double precisions along with the shooting method across the boundary layer for the whole transient domain from the initial state to the final steady state flow. The effects of existing flow parameters viz Soret number, Dufour number, chemical reaction parameter, Darcy number and magnetic parameter are shown graphically for the dimensionless velocity, temperature and concentration of the conducting fluid.The velocity of the conducting fluid is seen to decrease across the boundary layer with increasing the magnetic parameter, Prandtl number, Schmidt number and chemical reaction parameter; and the velocity profiles are seen to increase with increasing the thermal Grashof number, mass Grashof number, Soret number, stretching parameter and Dufour number. The temperature is seen to decrease with increasing the Prandtl number, Soret number, stretching parameter, and the same temperature are found to increase with increasing Dufor number and Chemical reaction parameter across the boundary layer.In the same way, the concentration is seen to reduce with increasing Schmidt number, Dufour number, stretching parameter,chemical reaction parameter and but concentration increases with increasing Soret number. Further more, numerical results for the skin friction, Nusselt number and Sherwood number are tabulated for various flow parameters.It is clearly observed from the result that a smooth transition of flow of conducting fluid is seen from unsteady stage to the final steady stage. Skin friction decreases with the increasing magnetic parameter, Schmidt number, Prandtl number and chemical reaction parameter and same skin friction increases with the increasing Soret numbe, Dufour number, thermal and concentration buoyancy parameters, Darcy number, stretching parameter and dimensionless time. Nusselt number is seen to increase with increasing the value of Soret number, Prandtl number, stretching parameter, dimensionless time and the same Nusselt number decreases with increasing the value of Dufour number, chemical reaction parameter and Schmidt number. Sherwood number is seen to decrease with increasing the value of Soret number, Dufour number, Prandtl number and dimensionless time and is seen to increase with increasing Chemical reaction parameter, stretching parameter and Schmidt number. The results obtained in this investigation are seen good agreement with earlier published results in some particular cases.

The present investigation focuses on the transient magnetohydrodynamic (MHD) behaviour of the stagnation-point flow of a Sisko nanofluid past a stretching surface, highlighting the interactive influence of internal heat generation and nano-scale transport mechanisms. The study integrates the rheological complexity of the Sisko model with nanoparticle motion induced by Brownian diffusion and thermophoresis, both of which substantially modify the fluid's momentum, thermal, and solutal layers. Through appropriate similarity transformations, the governing nonlinear partial differential equations are transformed and parameterized into a set of coupled ordinary differential equations, subsequently solved using MATLAB's bvp4c routine. A systematic evaluation of controlling parameters including the Sisko material constant, Brownian diffusion, thermophoretic strength, and heat generation coefficient-has been performed to elucidate their respective impacts on velocity, temperature, and concentration distributions. The findings reveal that nano-scale diffusion processes intensify both thermal and solutal gradients, whereas internal heat generation augments the thermal boundary layer thickness. This study delivers deeper theoretical understanding of non-Newtonian nanofluid dynamics and underscores its significance for enhanced heat transfer applications in polymer extrusion, coating systems, and advanced thermal manufacturing operations.

Shape factor for the cooling of cylindrical battery packs using THNFs through a stagnation point flow

Magnetohydrodynamics stagnation point flow of tangent hyperbolic fluid over a non-flat rotating disk in intuitionistic fuzzy environment

Extension of Homann’s axisymmetric rear stagnation-point flow: Unsteady MHD and heat transfer over a porous surface