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This research utilizes the bvp4c method to conduct a detailed numerical analysis of the hydrothermal behavior of magnetized hybrid nanofluids flowing across a permeable curved surface. The study explores the impact of crucial parameters such as curvature, magnetic field strength, viscosity and suction/injection, alongside the heat absorption coefficient, on the transport properties of copper (Cu) and ferric oxide (Fe₃O₄) nanomaterial’s suspended in water. Results reveal that as the curvature parameter increases, velocity profiles exhibit a decrease under suction conditions and an increase under injection conditions for both conventional and hybrid nanofluids. Furthermore, higher magnetic parameters are found to decrease velocities in general. Hybrid nanofluids display enhanced velocity and thermal performance compared to conventional nanofluids, manifesting higher skin friction and heat transfer rates. Temperature profiles exhibit a complex interplay with curvature, magnetic parameters and the injection/suction scenario, where injection conditions intensify thermal effects. The incorporation of the heat absorption coefficient further amplifies the thermal efficiency of hybrid nanofluids. These findings, supported by previous research, offer valuable insights for optimizing industrial processes, especially in sectors like ceramics, plastics and polymers, where efficient heat management is paramount.

This paper investigates the influence of magneto-tangent hyperbolic nanofluid on the flow of a tri-hybrid nanoliquid consisting of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}$ particles suspended in $\mathrm{\text{EG}}$. The entropy production is encountered in this analysis. The fluid flows over a stretch sheet is considered. In addition, the energy equation also assumes the existence of a uniform heat source or sink and thermal radiation. Furthermore, the concentration equation emphasizes the chemical reaction. The current proposed model yields a set of nonlinear governing equations. The modeled formulation is transformed into a dimensionless system through the application of a suitable alteration. The complex nonlinear equation system was solved using the bvp4c through numerical methods. The main motive of this exploration is to emphasize the rate of heat and mass transfer in a flow of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}/\mathrm{\text{EG}}$-based hybrid nanofluid across a stretch sheet. The graphical study illustrates that Weissenberg number and magnetic field enhancement result in decreasing the velocity. But thermal layer, entropy production, and Bejan number are enhanced with larger values of Weissenberg number and magnetic field. This study focuses on different profiles with various flow parameters. Furthermore, we have compared the tri-hybrid nanofluid with the hybrid and mono nanofluid in all the figures and tabular format. Additionally, we have compared tri-hybrid, hybrid, and mono nanofluid using graphs for velocity, temperature, concentration, entropy production, and Bejan number.

The aim of this study is to analyze heat transfer over two horizontal concentric cylinders in the influence of MHD, internal heat source containing porous nanofluids and thermal radiation are considered. The novelty of this work is internal heat source and porous media of H₂O–Cu nanofluids with the Lorentz effect are investigated and its applications are cooling systems, and heat exchangers. In addition, transformation for the momentum and energy equation is applied to obtain a set of ODEs for governing equations in the heat transfer flows. Further, the numerical technique BVP4C is used to solve the resulting system of nonlinear, coupled equations with boundary conditions. The influence of Hartmann number, volume fraction, radiation parameter, internal heat source parameter, Darcy number and different nanoparticles are examined in velocity and temperature profiles. The results show good agreement with the existing work of velocity and temperature graphs. Moreover, they reveal that thermal radiation significantly influences temperature distribution within the annulus, leading to a higher heat transfer rate. Furthermore, the presence of a porous medium and internal heat source modulates the flow patterns. This study provides optimizing MHD nanofluid systems for engineering applications such as thermal management systems, hyperthermia treatment in cancer therapy, food processing, rotating machinery and cooling systems.

This study highlights the combined effect of heat and mass transfer on MHD Maxwell fluid under time-dependent generalized boundary conditions for velocity, temperature, and concentration. The classical calculus due to the fact that it is assumed as the instant rate of change of the output when the input level changes. Therefore, it is not able to include the previous state of the system called the memory effect. But in the fractional calculus (FC), the rate of change is affected by all points of the considered interval, so it can incorporate the previous history/memory effects of any system. Due to this reason, we applied the modern definition of fractional derivatives (local and nonlocals kernels). Here, the order of fractional derivative will be treated as an index of memory. The exact and semi-analytical solutions are obtained using the integral transform and inversion algorithm. Several important properties of different parameters are analyzed by graphs. Interesting results are revealed by this investigation due to their vast applications in engineering and applied sciences.

The theoretical study focuses on the examination of the convective flow of Oldroyd-B fluid with ramped wall velocity and temperature. The fluid is confined on an extended, unbounded vertical plate saturated within the permeable medium. To depict the fluid flow, the coupled partial differential equations are settled by using the Caputo (C) and Caputo Fabrizio (CF) differential time derivatives. The mathematical analysis of the fractionalized models of fluid flow is performed by Laplace transform (LT). The complexity of temperature and velocity profile is explored by numerical inversion algorithms of Stehfest and Tzou. The fractionalized solutions of the temperature and velocity profile have been traced out under fractional and other different parameters considered. The physical impacts of associated parameters are elucidated with the assistance of the graph using the software MATHCAD 15. We noticed the significant influence of the fractional parameter (memory effects) and other parameters on the dynamics of the fluid flow. Shear stress at the wall and Nusselt number also are considered. It’s brought into notice the fractional-order model (CF) is the best fit in describing the memory effects in comparison to the C model. An analysis of the comparison between the solution of velocity and temperature profile for ramped wall temperature and velocity and constant wall temperature and velocity is also performed.

The objective of this study is to conduct a numerical examination of the influence of nonlinear chemical reaction and heat source or sink on magnetohydrodynamic (MHD) heat and mass transmission nanofluid flow through a shrinking permeable surface. In addition, the investigation considers thermal radiation and the occurrence of viscous dissipation. Ethylene glycol (EG) is used as the primary fluid medium, whilst the nanoparticles consist of nickel–zinc ferrite. The use of nanofluid flow has garnered significant interest as a result of its potential applications across several sectors. Nanofluids possess a notable benefit in comparison to traditional fluids as a consequence of their enhanced heat transfer capabilities. This advantage may be ascribed to the inclusion of nanoparticles, which augment thermal conductivity and therefore lead to enhanced heat dissipation and efficiency. The mathematical flow model, which is formulated using nonlinear partial differential equations (PDEs), may be transformed into a set of ordinary differential equations (ODEs) by the application of suitable similarity conversions. In order to address the complexities of the nonlinear system, the bvp4c and shooting techniques are used inside the MATLAB program, a widely utilized commercial platform, to effectively solve the associated ODEs by numerical means. This study presents a graphical analysis of the effects of flow parameters on several variables of interest.