The need for efficient nanotechnology has led to unexpected developments. Conserving continuous thermal propagation is essential in many industrial and thermal systems because it improves the efficiency of thermal engineering engines and machinery. Therefore, a promising platform to increase thermal power energy is the hybridization of magnetic nanoparticles in a heat-supporting, non-Newtonian fluid. In light of the above applications, a mathematical model is established to analyze the variable fluid features of the thermally radiative and chemically reactive flow of a micropolar Williamson ternary hybrid nanofluid with electromagnetohydrodynamic and electroosmosis forces on a porous stretching surface. Stratification boundary conditions and variable fluid properties were used to analyze the thermal and solutal behavior of the fluid flow. Furthermore, to measure the disorder of the flow system, entropy generation was considered by the impact of Joule heating and viscous dissipation. To develop the numerical scheme BVP4C in MATLAB, we first converted the mathematical flow model into two ordinary differential equations using a suitable transformation. The graphical and numerical results were determined against several parameters of a ternary hybrid nanofluid ( MWCNT , A l 2 O 3 , SiC ) and unary nanofluid ( A l 2 O 3 ) . The results indicate that the heat transfer rate is more prominent in the ternary hybrid nanofluid than in the unary nanofluid because the addition of nanofluids to the base fluid is used to improve the heat transport rate. It can be seen from the figures that a greater estimation of the magnetic and electric field parameters improves the fluid velocity because, for low values of M ≤ 1 , the aiding force is dominant compared to the retarding force, which results in an improvement in the velocity profile. Furthermore, the entropy generation rate increases for higher values of the Brinkman number and temperature ratio parameter because more heat is produced due to the greater values of Br .

It observers that an object is submerged in a liquid, more pressure is applied to its bottom surface than its top surface, as a result pressure rises within depth of fluids. A buoyancy force is generated due to the pressure difference. In the current investigation, the mathematical formulation of bio-convective stagnation point flow of a radiative Maxwell fluid with multiple slip effect on an exponentially porous stretching surface is analyzed thoroughly. The buoyancy assisting and opposing conditions with magnetic field are discussed in the current investigation. Moreover, the energy and concertation equations are formulated by the utilization of Cattaneo–Christov theory and non-uniform heat source/sink. The flow model is developed in the form of partial derivatives, then use the similarity variables to convert the physical system into nonlinear ordinary derivative. The nonlinear system is tackled numerically with the help of Bvp4c approach on the MATLAB. The graphical upshots for various emerging parameter are observed with two aspects: buoyancy assisting $$\left( {\lambda > 0} \right)$$λ > 0 and buoyancy opposing $$\left( {\lambda < 0} \right)$$λ < 0 . The observation shows that the greater values of mixed convection parameter improves the fluid velocity for assisting flow $$\left( {\lambda > 0} \right)$$λ > 0 , while declining trend is noticing for opposing flow situation $$\left( {\lambda > 0} \right)$$λ > 0 . Further, it is worth noticing that stronger inputs of thermal and concentration relaxation parameter yield lesser thermal and concentration diffusivity, which reduces the temperature and nanoparticles concentration.

With their notable thermal characteristics, fluids incorporating nanoparticles have significant importance in industrial processes. Due to the higher proficiency of hybrid nanofluid, this study is organized to observe the flow phenomenon and thermal characteristics of kerosene-oil-based hybrid ferrofluid in relation to the modified versions of two imperative Yamada–Ota and Xue models. A performance-based comparison is conducted for an incompressible hybrid ferrofluid in relation to the upgraded Yamada–Ota and Xue models. The magnetized flow mechanism in two dimensions is explored over a stretchable, curved sheet. With the ordinary kerosene oil liquid, the ferroparticles, namely cobalt ferrite and magnetite, are merged to form (CoFe₂O₄–Fe₃O₄/kerosene oil) hybrid ferrofluid. Mass and heat transport mechanisms are scrutinized with the execution of activation energy, convective constraints, Joule heating, exponential heat sources, and thermal radiation. Suitable ansatzes are utilized to achieve the dimensionless pattern of the equations that regulate the problem. To numerically explore the dimensionless equations, a powerful bvp4c strategy is implemented. On behalf of both considered models, the characteristics of hybrid ferrofluid relative to pertinent parameters are graphically investigated and comparatively analyzed. This study ensures that the improved Yamada–Ota model yields more proficient outcomes in comparison to the Xue model. Moreover, the concentration field demonstrates an escalating trend with the enhanced activation energy parameter.