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.