The problem of an unsteady 3D boundary layer flow induced by a stretching sheet in a rotating hybrid nanofluid is studied. A dimensionless set of variables is employed to transform the system of partial differential equations (PDEs) to a set of nonlinear ordinary differential equations (ODEs). Then, the system of ODEs is solved numerically using the MATLAB software. The impacts of different parameters, such as copper nanoparticles volume fraction, radiation, rotation, unsteadiness, and stretching parameters are graphically displayed. It is found that two solutions exist for the flow induced by the stretching sheet. Furthermore, the increasing nanoparticle volume fraction enhances the skin friction coefficient. It is noticed that the skin friction coefficient, as well as the heat transfer rate at the surface, decrease as the rotating parameter increases. Additionally, the thermal radiation as well as the unsteadiness parameter stimulate the temperature.

Hybrid nanofluids may exhibit higher thermal conductivity, chemical stability, mechanical resistance and physical strength compared to regular nanofluids. Our aim in this study is to investigate the flow of a water-based alumina-copper hybrid nanofluid in an inclined cylinder with the impact of buoyancy force and a magnetic field. The governing partial differential equations (PDEs) are transformed into a set of similarity ordinary differential equations (ODEs) using a dimensionless set of variables, and then solved numerically using the bvp4c package from MATLAB software. Two solutions exist for both buoyancy opposing (λ < 0) and assisting (λ > 0) flows, whereas a unique solution is found when the buoyancy force is absent (λ = 0). In addition, the impacts of the dimensionless parameters, such as curvature parameter, volume fraction of nanoparticles, inclination angle, mixed convention parameter, and magnetic parameter are analyzed. The results of this study compare well with previously published results. Compared to pure base fluid and regular nanofluid, hybrid nanofluid reduces drag and transfers heat more efficiently.

This study investigates the magnetohydrodynamics of a micropolar fluid consisting of a hybrid nanofluid with mixed convection effects. By using the dimensionless set of variables, the resulting equations of ordinary differential equations are solved numerically using the bvp4c solver in MATLAB. In the present work, the water-based alumina–copper hybrid nanofluid is analytically modeled with modified thermophysical properties. The study reveals that the highest critical value of opposing flow is the hybrid nanofluid (ϕ₁ = ϕ₂ = 2%). By comparing the hybrid nanofluid with Cu–water nanofluid (ϕ₁= 0%, ϕ₂= 1%) as well as water (ϕ₁= 0%, ϕ₂= 0%), hybrid nanoparticle volume fraction enhances the dynamic viscosity performance and surface shear stress. In addition, the augmentation of the nanoparticle volume fraction and magnetic field parameter will increase the physical quantities Re_x^1/2 C_f, Re_x M_x, and Re_x^−1/2 Nu_x. The result from the stability inquiry discloses that the first solution is more physically stable and trustworthy. It is proven that magnetohydrodynamics could contribute to controlling the fluid flow in a system, i.e., engineering operations and the medical field. In addition, this theoretical research can be a benchmark for experimental research.

The study investigates the fluid flow characteristics and heat transfer over an exponentially stretching/shrinking inclined plate immersed in a micropolar fluid. The micropolar fluid model considers the rotational effects of microelements relevant to complex industrial fluid behavior. Using similarity variables, the governing equations for fluid flow and heat transfer are transformed from Partial Differential Equations (PDEs) to Ordinary Differential Equations (ODEs), and appropriate boundary conditions are incorporated to simulate the behavior of the micropolar fluid over the inclined plate. The ODEs are numerically solved using MATLAB software with BVP4c, and the results are compared with previous findings, showing good agreement. The effects of critical parameters such as plate inclination angle, stretching/shrinking rate, and micropolar fluid parameters are examined. Notably, the micropolar parameter significantly influences the skin friction for stretching and shrinking flows. An increase in the micropolar parameter leads to increased skin friction for stretching flows, while for shrinking flows, the skin friction decreases within a specific range of stretching/shrinking values. The behavior of the local couple stress becomes complex as the micropolar parameter increases. Additionally, the local Nusselt number decreases as the micropolar parameter increases for shrinking flows, indicating a reduction in heat transfer from the solid surface during shrinking flow. Moreover, an increase in the Sherwood number suggests a relatively slower mass transfer rate than momentum transfer. These findings offer valuable insights into the behavior of micropolar fluids over exponentially stretching/shrinking inclined plates, guiding optimizing heat transfer and fluid flow in practical engineering systems. ¬

This work presents the steady mixed convection in Al2O3-Cu/water hybrid nanofluids along a vertically stretching/shrinking cylinder with the prescribed surface heat flux and the effects of heat source/sink. The governing hybrid nanofluids model was simplified using a similarity transformation. The bvp4c solver in MATLAB software is used to solve the hybrid nanofluids flow problem numerically. It is observed that two outcomes are feasible for the assisting and opposing flow regions as well as stretching and shrinking cases . Besides that, the effects of the dimensionless parameters are analyzed graphically and tabularly. In particular, the critical point is reduced by 3% when the curvature parameter goes from 0 to 0.1 and from 0.1 to 0.2 when the cylinder is stretched. This means that the higher curvature parameter could delay the process of separating the boundary layer. It is noted that the positive heat source will decrease the fluid motions and reduce the shear stress on the surface. Moreover, Al2O3-Cu/water hybrid nanofluids have better performance in heat transfer and velocity of fluid flow than Al2O3/water nanofluids.