Nanotechnology plays a vital role in heat transport due to its wide range of applications, significantly contributing to fields such as bioengineering, space exploration, biosensor research, semiconductor technology, and advanced electronics. The primary objective of this analysis is to examine the Casson fluid model for heat and mass transport between stretchy rotating disks, incorporating copper and titanium oxide nanoparticles into a sodium alginate base fluid. This analysis encompasses the effects of mixed convection, chemical reactions, convective conditions, activation energy, and thermal radiation. The bvp4c method is utilized to solve the resultant equations. Tables and Figures offer a clear depiction of the results. Understanding the thermal characteristics of hybrid fluids is crucial to energy systems, biological fluid dynamics, and engineering applications, where fluid flow and heat transfer are critical to system performance. At lower disk, the skin friction improved by 10.24% and 12.36% relative to the higher values of the magnetic and Cason parameters. The Schmidt number reduces mass-transfer gradients by 18.1%, whereas the activation energy decreases by 13.7%. The volume fractions of the selected nanoparticles vary from 0.02 to 0.04, and the heat transfer rates for the hybrid nanofluid increases 12% for the hybrid nanofluid as compared to the nanofluid. The hybrid nanofluid significantly affects flow distributions.

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 study investigates the steady two-dimensional natural-convection flow and heat and mass transfer of a Cu–Al2O3/water thixotropic hybrid nanofluid over a vertically stretching sheet. The boundary-layer model incorporates magnetic effects, thermal radiation, heat generation, viscous dissipation, Joule heating, melting, chemical reaction, species diffusion, and motile microorganisms. By applying suitable similarity transformations, the governing partial differential equations are reduced to a system of nonlinear ordinary differential equations and solved numerically using MATLAB bvp4c. The results show that the magnetic field suppresses the velocity profile, whereas melting enhances it. Temperature increases with the heat source parameter but decreases with radiation and melting, while nanoparticle concentration declines with higher Schmidt number and chemical reaction. In addition, microorganism concentration decreases with the bioconvection Lewis number and increases with the Peclet number and microorganism concentration difference parameter.

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.