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.