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The purpose of the study is to explore the three-dimensional heat and mass transport dynamics of the magneto-hydrodynamic non-Newtonian (Casson fluid) hybrid nanofluid flow comprised of − as nanoparticles suspended in base liquid water as it passes through a flexible spinning disc. The influence of a magnetic field, rotation parameter, porosity, Darcy−Forchheimer, Arrhenius’s activation energy, chemical reaction, Schmidt number and nanoparticle shape effects are substantial physical features of the investigation. Furthermore, the influence of hybrid nanofluid on Brownian motion and thermophoresis features has been represented using the Buongiorno model. The novelty of the work is intended to contribute to a better understanding of Casson non-Newtonian fluid boundary layer flow.

The governing mathematical equations that explain the flow and heat and mass transport phenomena for fluid domains include the Navier−Stokes equation, the thermal energy equation and the solutal concentration equations. The governing equations are expressed as partial differential equations, which are then converted into a suitable set of non-linear ordinary differential equations by using the necessary similarity variables. The ordinary differential equations are computed by combining the shooting operation with the three-stage Lobatto BVP4c technique.

Graphs and tables are used in the process of analysing the characteristics of velocity distributions, temperature profiles and solutal curves at varying values of the parameters, along with friction drag, heat transfer rate and Sherwood number. It has been revealed that the radial and axial velocities decrease when the Casson parameter value increases and that the rate of heat transmission is higher in hybrid nanofluids with nanoparticles in the shape of a blade. The increase in Brownian motion and thermophoresis parameters causes a rise in the temperature profile. Also, an increase in the activation energy parameter improves the solutal curve. The use of nanoparticles was shown to improve extrusion properties, the rotary heat process and biofuel generation.

All results are presented graphically and all physical quantities are computed and tabulated. The current results are compared to previous investigations and found to agree significantly with them.

The purpose of this study is to investigate the simultaneous effects of normal wall transpiration, stretching strength parameter, velocity slip and nanoparticles on the flow of a ternary hybrid nanofluid through an elastic surface. The goal is to understand the behavior of the flow field, temperature distribution, skin friction and temperature gradient under these conditions, and to explore the existence and nature of solutions under varying parameter values.

The analysis involves expressing the flow field, power-law temperature field, skin friction and temperature gradient in closed-form formulas. The study examines both stretching and shrinking surfaces, distinguishing between unique and dual solutions. The methodology includes deriving exact solutions for exponential and algebraic temperature and temperature rate formulas analytically by deriving the system of governing equations into ordinary differential equations.

The study reveals that for a stretching sheet, the solution is unique, whereas dual solutions are observed for a shrinking surface. Special solutions are provided for various parametric values, showing the behavior of the exponential and algebraic temperature and temperature rate, with a focus on identifying turning points that demarcate the existence and non-existence of single or multiple solutions. The solutions are represented through graphs and tables to facilitate a comprehensive qualitative analysis. The research identifies turning points that determine the presence or absence of single or multiple solutions, uncovering multiple solutions for different parameter sets. These findings are displayed graphically and in tabular form, highlighting the complex interplay between the parameters and the resulting flow behavior.

This analysis contributes to the field by providing new insights into the multiple solution phenomena in ternary hybrid nanofluid flows, particularly under the combined effects of normal wall transpiration, stretching strength, velocity slip and nanoparticle presence. The identification of turning points and the exact solutions for various temperature profiles are of significant value, offering a deeper understanding of the factors influencing the flow and thermal characteristics in such systems. The study’s findings have potential applications in optimizing fluid flow in engineering systems where such conditions are prevalent.

The boundary layer flow of immiscible fluids plays a crucial role across various industries, influencing advancements in industrial processes, environmental systems, healthcare and more. This study explores the thermally radiative boundary layer flow of a shear-driven Ree–Eyring fluid over a nanofluid. The investigation offers valuable insights into the intricate dynamics and heat transfer behavior that arise when a nanofluid, affected by thermal radiation, interacts with a non-Newtonian Ree–Eyring fluid. This analysis contributes to a deeper understanding of the complex interactions governing such systems, which is essential for enhancing efficiency and innovation in multiple applications.

The simulation investigates the convergence of boundary layers under varying shear strengths. A comparative analysis is conducted using γAl2O3 and Al₂O₃ nanoparticles, with water as the base fluid. The model’s numerical outcomes are derived using the bvp4c method through the application of appropriate similarity transformations. The resulting numerical data are then used to produce graphical representations, offering valuable insights into the influence of key parameters on flow behavior and patterns.

The temperature of the Al₂O₃ nanoparticles is always higher than the γAl2O3 nanoparticles, and hence, Al₂O₃ nanoparticles become more significant in the cooling process then γAl2O3 nanoparticles. It is also observed that the fluid velocity for both regions is enhanced by increasing values of the Ree–Eyring fluid parameter.

The results stated are original and new with the thermal radiative boundary layer flow of two immiscible Ree–Eyring fluid and Al₂O₃/γAl2O3 nanofluid.

Thermal energy storage systems use thermal energy to elevate the temperature of a storage substance, enabling the release of energy during a discharge cycle. The storage or retrieval of energy occurs through the heating or cooling of either a liquid or a solid, without undergoing a phase change, within a sensible heat storage system. In a sensible packed bed thermal energy storage system, the structure comprises porous media that form the packed solid material, while fluid occupies the voids. Thus, a cavity, partially filled with a fluid layer and partially with a saturated porous layer, has become important in the investigation of natural convection heat transfer, carrying significant relevance within thermal energy storage systems. Motivated by these insights, the current investigation delves into the convection heat transfer driven by buoyancy and entropy generation within a partially porous cavity that is differentially heated, vertically layered and filled with a hybrid nanofluid.

The investigation encompasses two distinct scenarios. In the first instance, the porous layer is positioned next to the heated wall, while the opposite region consists of a fluid layer. In the second case, the layers switch places, with the fluid layer adjacent to the heated wall. The system of equations for fluid and porous media, along with appropriate initial and boundary conditions, is addressed using the finite difference method. The Tiwari–Das model is used in this investigation, and the viscosity and thermal conductivity are determined using correlations specific to spherical nanoparticles.

Comprehensive numerical simulations have been performed, considering controlling factors such as the Darcy number, nanoparticle volume fraction, Rayleigh number, bottom slit position and Hartmann number. The visual representation of the numerical findings includes streamlines, isotherms and entropy lines, as well as plots illustrating average entropy generation and the average Nusselt number. These representations aim to provide insight into the influence of these parameters across a spectrum of scenarios.

The computational outcomes indicate that with an increase in the Darcy number, the addition of 2.5% magnetite nanoparticles to the GO nanofluid results in an enhanced heat transfer rate, showing increases of 0.567% in Case 1 and 3.894% in Case 2. Compared with Case 2, Case 1 exhibits a 59.90% enhancement in heat transfer within the enclosure. Positioning the porous layer next to the partially cooled wall significantly boosts the average total entropy production, showing a substantial increase of 11.36% at an elevated Rayleigh number value. Positioning the hot slit near the bottom wall leads to a reduction in total entropy generation by 33.20% compared to its placement at the center and by 33.32% in comparison to its proximity to the top wall.