The aim of this study is to investigate the exact solution of the velocity field with the combined effect of heat and mass transfer of incompressible Walter’s-B fluid through porous medium via Atangana–Baleanu–Caputo fractional operator. At time t = 0, Walter’s-B fluid is at rest, after t = 0+, the plate starts to stream with unidirectional velocity. The analytical expressions for the velocity component, microrotational, mass concentration and temperature distribution are obtained by implementing the Laplace transform. The general solution is presented in terms of integral transform. Exact results for concentration, temperature, velocity field, and shear stress are displayed graphically for various parameters such as fractional parameter α, Microrotational parameter β, Prandtl number Pr, Schmidt number Sc, Thermal Grashof number Gr and mass Grashof number Gm.

This research examines the dynamics of heat transfer while highlighting the crucial role of Fourier heat flux concerning the thermodynamic and hydrodynamic characteristics of ternary hybrid nanofluids (HNFs) traversing a disk. The physical model and flow configuration were thoroughly analyzed under the influences of various parameters. The major equations that characterize the flow dynamics are formulated as partial differential equations (PDEs). By utilizing appropriate correspondence variables, the system of PDEs was altered keen on ordinary differential equations (ODEs). The coordination of coupled nonlinear equations is resolved arithmetically utilizing the “bvp4c function in MATLAB.” The influence of the principal appropriate factors on the radial speed, axial speed, and warmth is illustrated realistically. Ultimately, a table is constructed to demonstrate the interrelationships of numerous perilous issues on the Skin friction and Nusselt number. It was observed that an enhancement in the attractive constraint significantly diminishes the speed outline, attributable to the Lorentz influence caused by the applied attractive subject. Additionally, an enhancement in thermal transfer was observed as a consequence of an increase in thermal radiation.

The novel concept of hybrid nanofluids (HNFs) captivated scientists and researchers due to its remarkable thermal conductivities, which led to improved thermal performance. There are several applications for these fluids in the fields of technology and industry. A third-grade Williamson-Casson HNF model for magnetohydrodynamics over an exponentially stretched surface in a DF permeable medium is presented in this work. It covers the impacts of viscous dissipation (VD) as well as the analysis of heat and mass transfer (HMT). The established governing PDEs for momentum, energy, and concentration transfer are transformed into a collection of nonlinear ODEs using similarity transformations (ST). These transformed equations are solved using semi-numerical methods called HAM. It investigates how velocity field (VF), temperature field (TF), and concentration field (CF) are affected by changes in critical parameters such as thermal conductivity, third-grade fluid parameter, DF number, magnetic field (MF) strength, Williamson and Casson fluid parameters, and nanoparticle volume fractions (VLFs). The results show that the presence of an HNF increases thermal conductivity, which improves heat transfer efficiency. Additionally, VD and third-grade fluid characteristics significantly impact fluid flow and energy transfer. The recent research offers important new information for practical applications in thermal engineering systems, biofluid mechanics, and polymer processing.

The integration of nanofluids with porous media has become essential in modern engineering processes because of their ability to meet the ultra-high cooling demands of advanced industrial systems. Their exceptional thermal conductivity also makes nanofluids highly valuable in nanotechnology, electronic device fabrication, and biomedical applications. Motivated by these advantages, the present study investigates the heat and mass transfer behavior of a micropolar nanofluid flowing over a nonlinearly stretching/shrinking slanted surface. Appropriate similarity transformations are employed to reduce the governing system of micropolar nanofluid equations to a set of nonlinear ordinary differential equations, which are solved numerically using the MATLAB bvp4c solver. The analysis reveals a three-solution structure, prompting a stability assessment to determine the physically realizable branch. The results indicate that only the first solution branch is stable and physically meaningful. The findings further show that the microrotation boundary layer thickness increases across all three-solution regimes as the material parameter increases. In addition, an increase in the Grashof number significantly accelerates the fluid velocity. The concentration profile rises with increasing thermophoresis parameter, whereas it diminishes with increasing Brownian motion.

To enhance the productivity of heat exchangers, a new type of heat transfer fluid called hybrid nanofluid was characterized. An abundance of industrial and technological processes depends on heat transfer through these fluid flows, whether in laminar or turbulent conditions. The thermal resistance of the fluid based on a heat transfer system might be increased to improve a significant number of applications. Therefore, the present investigation, establishing a framework for differential equations to examine the influence of thermal radiation and heat source/sink on magnetohydrodynamics (MHD) Marangoni convection flow of hybrid nanofluid (HNF) in a Saturated Porous medium. By introducing new similarity variables, the problem of Marangoni convection is simplified to account for the effects of radiation and porous medium. This study’s originality is the combined impact of the heat source and porous material. The governing nonlinear partial differential equations for momentum and energy are transformed into ordinary differential equations by applying the required similarity adjustment. The shooting strategy is used to achieve numerical solutions for certain modeled ordinary differential equations. Excellent agreement with the shooting technique in the MATLAB (bvp4c) code is demonstrated by a comprehensive numerical comparison conducted for a variety of variables. Investigations are conducted into specific physical characteristics related to temperature and velocity profiles. For several factors, the results are tabulated and graphically analyzed. The velocity plots are increasing with the rise in the Stretching parameter, and volume quantity of copper, while for large values of marangoni parameter, porosity parameter, and Magnetic parameter the opposite trend shows. Larger volume concentrations of copper, larger values of heat source parameter, thermal radiation, and stretching parameter features all increase the temperature pattern, while opposite trends shows for porosity components, magnetic, and marangoni parameter. The graph of streamlines and isotherms are also plotted. The numerical results were compared with previous published work.