Sohaib Abdal

Thermal energy management is a central idea in modern engineering systems such as advanced electronics and renewable uses for heat all rely on it. Hybrid nanofluids, which integrate two distinct types of nanoparticles within a base fluid, enhances their thermal properties, even more than for single‐particle types, but there is still much to learn about their action under electromagnetic fields and chemicals. Thus, MHD Casson hybrid nanofluid bio convection plays a crucial role in boosting heat and mass transfer in areas such as energy storage, cryogenics, and disease prevention. The purpose of this study is to mathematically investigate how Casson hybrid nanofluid flows over a stretched surface respond to magnetohydrodynamic, Hall effect, radiation, bioconvection, and chemical effects using activation energy. In particular, this study explores the scattering of and nanoparticle mixtures in a Casson fluid to understand how skin friction, Nusselt number, and Sherwood number improve with different configurations of magnetic and activation parameters. Using similarity variables, the governing equations of the boundary layer are converted into nonlinear ordinary differential equations. Subsequently, the problems are solved using numerical methods that use Runge–Kutta 4th methods along with the shooting technique. The impact of collective parameters including Casson fluid parameter, magnetic, Brownian motion, thermophoresis, and activation energy, is examined in depth by the systematic study of these factors. An increase in the intensity of magnetism and quantity of nanoparticles raises the Nusselt number, improving how heat is transferred, whereas higher activation energy results in a thinner concentration boundary layer. The findings reveal that higher decreases both tangential and transverse motions due to stronger Lorentz forces, whereas bigger m causes the damping force to reduce and lets more tangential flow occur. Meanwhile, when and rise, the temperature effects become stronger. This is because as the Lewis and Peclet numbers grow, fewer motile microorganisms are present, proving their role in setting bio‐convective behavior. Therefore, the Casson hybrid nanofluid model provides a useful structure for boosting thermal efficiency in applications that depend on magnetohydrodynamics.

This paper investigates the dynamics of a fractal-fractional order energy-saving and emission-reduction chaotic system, extending the original integer-order model using the Caputo fractal-fractional derivative. The existence and uniqueness of the solution are proved using the Banach fixed point theorem, while Ulam–Hyers stability is demonstrated both analytically and numerically. A fourth-order Runge–Kutta numerical scheme is developed for fractal-fractional systems to simulate the transformed system for various fractal and fractional order values. The numerical results show that the considered fractional-ordered system also exhibits chaotic properties across parameter variations, with trajectories showing sensitivity to both fractional parameters [ ] and [ ]. Furthermore, a neural network approach validates the numerical solutions, achieving exceptional performance with mean square error analysis of [ ] at epoch [ ]. The close alignment between integer-order and fractal-fractional-order systems confirms the consistency and physical relevance of the proposed scheme.

The theoretical and computational investigation for non‐Newtonian fluid based nanofluid dynamics due to a parallel plate channel is carried out. A comparative analysis for heat and mass transfer of micropolar Casson nanofluid (TC4/kerosene oil) and hybrid nanofluid (TC4 + nichrome/kerosene oil) is made numerically. The additional physical aspects include the presence of nonlinear radiative heat flux, a uniform magnetic field, and a porous medium. The two plates are permeable. The laws of conservation of mass, momentum, angular momentum, energy, and concentration are formulated as a coupled set of partial differential equations. These controlling equations are transformed into corresponding ordinary differential equations. Runge–Kutta (RK) method, along with the shooting technique, is harnessed to evaluate numerical findings of dependent quantities of physical importance. This is observed with a large input of magnetic parameter M, Casson parameter β, and porosity parameter P₀, the linear velocity and spinning velocity are increased near the walls, but it slows down towards the center of channel. The surging values of Rd and enhance fluid temperature while it diminishes for increasing values of Re and Pr. Moreover, with increasing inputs of the temperature ratio parameter the thermal distribution is improved. The thermal distribution is larger for hybrid nanofluids than nanofluids flows. The findings of this study have practical applications in engineering fields, including heat exchangers (HEXs), cooling systems, and renewable energy systems. They can also enhance the efficiency of thermal processes in heavy industries, electronics, and computing devices.

The purpose and novelty of our study include the scrutinization of the unsteady flow and heat characteristics of the unsteady Sutterby nano-fluid flow across an elongated cone using slip boundary conditions. The bioconvection of gyrotactic micro-organisms, Cattaneo–Christov, and thermal radiative fluxes with magnetic fields are significant physical aspects of the study. Anisotropic constraints on the cone surface are taken into account. The leading formulation is transmuted into ordinary differential formate via similarity functions. Five coupled equations with nonlinear terms are resolved numerically through the utilization of a MATLAB code for the Runge–Kutta procedure. The parameters of buoyancy ratio, the porosity of medium, and bioconvection Rayleigh number decrease x-direction velocity. The slip parameter retard y-direction velocity. The temperature for Sutterby fluids is at a hotter level, but its velocity is vividly slower compared to those of nanofluids. The temperature profile improves directly with thermophoresis, v-velocity slip, and random motion of nanoentities.

This study addresses thermal transportation associated with dissipated flow of a Maxwell Sutterby nanofluid caused by an elongating surface. The fluid passes across Darcy–Forchheimer sponge medium and it is affected by electromagnetic field applied along the normal surface. Appropriate similarity transforms are employed to convert the controlling partial differential equations into ordinary differential form, which are then resolved numerically with implementation of Runge–Kutta method and shooting approach. The computational analysis for physical insight is attempted for varying inputs of pertinent parameters. The output revealed that the velocity of fluid for shear thickening is slower than that of shear thinning. The fluid temperature increases directly with Eckert number, and parameters of Cattaneo–Christov diffusion, radiation, electric field, magnetic field, Brownian motion and thermophoresis. The Nusselt number explicitly elevated as the values of radiation and Hartmann number, as well as Brownian motion, improved. The nanoparticle volume fraction diminishes against Prandtl number and Lewis number.

Rotating flow for hybrid nanofluid over a stretching surface in the presence of magnetic effect is examined numerically. Hybrid nanofluid consists of graphene oxide and molybdenum disulfide in water base fluid. The inclusion of more than one nanoparticle is carried out due to some outstanding features such as astonishing thermal conduction, which are substantial in heat exchangers, nanotechnology, electronics, and material sciences. In order to attain numerical resolution, the partial differential formulation has been transformed into the corresponding ordinary differential equations. By implementation of apposite similarity variables, the classical Runge–Kutta method and shooting argument have been held to yield finding for the dependent quantities. Thermal transportation enhancement is the need of the day, so this study is made to meet the necessity of industries. A velocity component shows an upsurge with raise in the magnetic field parameter. The magnitude of the velocity component for hybrid nanofluid has a lower boundary as compared to single nanofluid. The temperature profile expressed that hybrid nanofluid is more effective than single nanofluid. These investigations are applicable to the field of the biomedical, automotive industry, nuclear cooling systems, and heat exchangers.

In this article, we explore how activation energy and varied transit parameters influence the two-dimensional stagnation point motion of nano-biofilm of Sutterby fluids incorporating gyrotactic microbes across a porous straining/shrinking sheet. Prior investigations implied that fluid viscosity as well as thermal conductance are temperature based. This research proposes that fluid viscosity, heat capacity and nanofluid attributes are all modified by solute concentration. According to some empirical research, the viscosity as well as heat conductivity of nanoparticles are highly based on the concentration of nanoparticles instead of only the temperature. The shooting approach with the RK-4 technique is applied to acquire analytical results. We contrast our outcomes with those in the existing research and examine their consistency and reliability. The graphic performance of relevant factors on heat, velocity, density and motile concentration domains are depicted and discussed. The skin friction factor, Nusselt number, Sherwood number and the motile density are determined. As the concentration-dependent properties are updated, the speed, temperature, concentration and motile density profiles are enhanced, but for all concentration-varying factors, other physical quantities deteriorate.