The study of inclined magnetohydrodynamics (MHD) mixed convective incompressible flow of a fluid with hybrid nanoparticles containing a colloidal combination of nanofluids and base fluid is presented in the current research. Al₂O₃-Cu/H₂O hybrid nanofluid is utilized in the current analysis to enhance the heat transfer analysis. The impact of radiation is also placed at energy equation. The main research methodology includes that the problem provided equations are first transformed into non-dimensional form, and then they are obtained in ordinary differential equations (ODEs) form. Then using the solutions of momentum and transfers equations to solve the given ODEs to get the root of the equation. The main purpose includes the resulting equations are then analytically resolved with the aid of suitable boundary conditions. The results can be discussed with various physical parameters viz., stretched/shrinked-Rayleigh number, stretching/shrinking parameter, Prandtl number, etc. Besides, skin friction and heat transfer coefficient can be examined with suitable similarity transformations. The main significance of the present work is to explain the mixed convective fluid flow on the basis of analytical method. Main findings at the end we found that the transverse and tangential velocities are more for more values of stretched/shrinked-Rayleigh number and mass transpiration for both suction and injection cases. This is the special method it includes stretched/shrinked-Rayleigh number, it contributes major role in this analysis. The purpose of finding the present work is to understand the analytical solution on the basis of mixed convective method.

In this work, we study numerically the periodicity of regular regions embedded in chaotic states for the case of an anisotropic magnetic particle. The particle is in the monodomain regime and subject to an applied magnetic field that depends on time. The dissipative Landau–Lifshitz–Gilbert equation models the particle. To perform the characterization, we compute several two-dimensional phase diagrams in the parameter space for the Lyapunov exponents and the isospikes. We observe multiple transitions among periodic states, revealing complex topological structures in the parameter space typical of dynamic systems. To show the finer details of the regular structures, iterative zooms are performed. In particular, we find islands of synchronization for the magnetization and the driven field and several shrimp structures with different periods.

The main objective of this study is to explore the inventive conception of the magnetohydrodynamic flow of a hybrid nanofluid over-porous stretching/shrinking sheet with the effect of radiation and mass suction/injection. The hybrid nanofluid advances both the manufactured nanofluid of the current region and the base fluid. For the current investigation, hybrid nanofluids comprising two different kinds of nanoparticles, aluminium oxide and ferrofluid, contained in water as a base fluid, are considered. A collection of highly nonlinear partial differential equations is used to model the whole physical problem. These equations are then transformed into highly nonlinear ordinary differential equations using an appropriate similarity technique. The transformed differential equations are nonlinear, and thus it is difficult to analytically solve considering temperature increases. Then, the outcome is described in incomplete gamma function form. The considered physical parameters namely, magnetic field, Inverse Darcy number, velocity slip, suction/injection, temperature jump effects on velocity, temperature, skin friction and Nusselt number profiles are reviewed using plots. The results reveal that magnetic field, and Inverse Darcy number values increase as the momentum boundary layer decreases. Moreover, higher values of heat sources and thermal radiation enhance the thermal boundary layer. The present problem has various applications in manufacturing and technological devices such as cooling systems, condensers, microelectronics, digital cooling, car radiators, nuclear power stations, nano-drag shipments, automobile production, and tumour treatments.

The control effects on the convection dynamics in a viscoelastic fluid-saturated porous medium heated from below and cooled from above are studied. A truncated Galerkin expansion was applied to balance equations to obtain a four-dimensional generalized Lorenz system. The dynamical behavior is mainly characterized by the Lyapunov exponents, bifurcation, and isospike diagrams. The results show that within a range of moderate and high Rayleigh numbers, proportional controller gain is found to enhance the stabilization and destabilization effects on the thermal convection. Furthermore, due to the effect of viscoelasticity, the system exhibits remarkable topological structures of regular regions embedded in chaotic domains.

This study investigates the effect of quantum size and an external magnetic field on the optoelectronic properties of a cylindrical Al${}_x$Ga${}_{1-x}$As/GaAs-based core/shell nanowire. We used the one-band effective mass model to describe the Hamiltonian of an interacting electron-donor impurity system and employed two numerical methods to calculate the ground state energies: the variational and finite element methods. With the finite confinement barrier at the interface between the core and the shell, the cylindrical symmetry of the system revealed proper transcendental equations, leading to the concept of the threshold core radius. Our results show that the optoelectronic properties of the structure strongly depend on core/shell sizes and the strength of the external magnetic field. We found that the maximum probability of finding the electron occurs in either the core or the shell region, depending on the value of the threshold core radius. This threshold radius separates two regions where physical behaviors undergo changes and the applied magnetic field acts as an additional confinement.