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All previously published data on the dynamics of ethylene glycol conveying copper and gold nanoparticles over a convective surface, nothing is known about the importance of dual branch solutions. Hybrid nanofluids improve the thermal conductivity of the fluid. The nanoparticles copper and gold having ethylene glycol as a base fluid are used here. The flow problem is described over a stretching/shrinking surface with the influence of Ohmic heating, non-linear radiation, and a convectively heated surface. Furthermore, the magnetic field strength is applied perpendicular to the direction of the flow. To control the fluid, flow-governing equations are numerically solved by using bvp4c, a built-in approach in MATLAB. For hybrid nanomaterials, the consequence of different physical parameters is discussed graphically and with tabular data. A comparison with previous findings reveals that the present findings are in good agreement. The results revealed that the coefficient of skin friction for the physically stable branch declines over a certain range of shrinking parameters; nonetheless, for the unstable branch, the reverse pattern is discovered. The magnetic force diminishes the flow field and energy dispersion in the upper branch but improves it in the lower branch.

An investigation of an axisymmetric mixed convective boundary layer flow of silver-titanium dioxide/water (Ag−TiO2/H2O) hybrid nanofluid towards vertically and rotating stretching cylinder with entropy generation is conducted. The Cattaneo-Christov theory and joule heating effect are used to analyze the features of thermal energy. Moreover, the magnetic impact and convective boundary conditions on the vertical surface also considered in the current investigation. The developing equations for momentum, energy and entropy generation are modelled and by the usage of similarity variables to transform into the system of nonlinear ordinary differential equations (ODEs). The solutions of nonlinear ODEs are obtained numerically with the assistance of BVP4C MATLAB built-in scheme. The graphical consequences and relevant physical reasoning regarding the velocity, temperature, and concentration profiles are discussed. It is noteworthy that strong estimation of buoyancy ratio and mixed convection parameter enhances axial velocity, but the swirl velocity is diminished. The fluid temperature and concentration both are diminished due to thermal and solutal stratification effects. It is also seen that thermal Biot and Eckert numbers enhance the temperature distribution. Further, the Reynold number improves entropy generation.

This study explores the flow irreversibility of the Ellis hybrid nanofluid (containing CoFe2O4−TiO2 nanoparticles) with homogeneous and heterogeneous reactions to a horizontal porous stretching cylinder. The energy transportation aspects are investigated in terms of the influence of joule heating and viscous dissipation. The slip and convective boundary conditions are levied on the cylindrical surface, and the mathematical flow model is transferred to a system of nonlinear ordinary differential equations using suitable transformations. The highly nonlinear systems of equations are numerically solved using the bvp4c approach in MATLAB. The graphical outcomes are obtained and discussed; it is worth noting that incremental estimations of the curvature parameter show opposite behaviors on the Ellis fluid velocity and entropy generation, i.e., the entropy generation profile increases while fluid velocity decreases. The boundary layer thinning shows resistance to impact by elasticity and magnetic field. Further, as the porosity of the liquid phase increases, the momentum of the boundary layer decreases.