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The ternary hybrid nanofluids have potential in different technological arenas such as biomedical engineering, solar energy, atomic reactors, the automotive industry, and heat pipes. Given these facts, along with the recent advancements in nanotechnology and their extensive applications, this research focuses on the MoS₂-Fe₃O₄-ZrO₂/CH₃OH ternary nanofluid flow through bidirectional stretching sheets. We have transformed the coupled nonlinear partial differential equations for the advanced model into nondimensional ordinary differential equations using similarity transformations, and then semi-analytically apply the homotopy analysis methodology (HAM). We have displayed the physical features of potential factors graphically alongside the flowing factors based on velocity and temperature. We presented a physical evaluation in tabular format for the rate of heat transmission and compared the results with existing work to ensure their validity. These meaningful outcomes indicate that the axial fluid velocity is compressed by the magnetic interaction, inertial drag, porosity and stretchable ratio, while it is augmented by the Powell-Eyring factor and the changed Hartmann value. The effect of increasing transverse speed boosts inertial drag.

Entropy optimization or entropy plays vital roles in our understanding of numerous various diverse phenomena running from cosmology to science. Their significance is shown in regions of immediate practical interest like provision of global energy as well as in others of a progressively essential flavor, such as the source of order and unpredictability in nature. The purpose of this communication is to investigate some of ongoing and significant outcomes in a way that not only appeals to the entropy expert but also makes them available to the nonexpert looking for an outline of the field. This communication addresses the entropy optimized flow of hybrid nanofluid between two plates accounting Darcy–Forchheimer porous medium. Energy equation is developed through implementation of first law of thermodynamics subject to radiative flux, dissipation and Joule heating. MHD fluid is rotating with angular frequency $\mathrm{\Omega }$. Total entropy rate obtained is subject to thermal irreversibility, friction or dissipation irreversibility, magnetic or Joule heating irreversibility and Darcy–Forchheimer irreversibility via second law of thermodynamics. The nonlinear ordinary system (differential equations) is tackled via homotopy method for series solutions. Behaviors of sundry variables on the velocity, skin friction, temperature, Nusselt number and entropy generation rate are discussed and presented through various plots. Schematic flow diagram is presented. Furthermore, skin friction (drag force) and Nusselt number are discussed numerically. Obtained results analyzed that the entropy rate increases subject to higher radiation parameter and Hartmann and Brinkman numbers.

The prime objective of binary chemical reaction (BCR) is concentrated on the study and optimization of chemical reaction to accomplish finest reactor design and performance, which elaborated the interfaces of flow phenomena, reaction kinetics and heat and mass transport. The reactor performance is likely to be linked to the reaction operating constraints and feed composition through the aforementioned factors. The applications of BCR are generally in the petroleum and petrochemical regions, but with the help of chemical engineering and reaction chemistry concepts, it could be used in different areas, like waste treatment, chemical pharmaceuticals, nanoparticles in advanced materials, microelectronics, enzyme technology, biochemical engineering, living systems, renewable energy systems, sustainable development, environment/pollution prevention, as well as to optimize a different reaction framework via simulation and modeling methodology. Owing such physical applications in mind, this research deals with the binary chemical reactive flow of non-Newtonian fluid (Walter’s B) subject to activation energy. Stagnation point is accounted. Radiative flux and ohmic heating effects are considered in the development of energy expression. Concentration and microorganism equations are considered. The governing system is altered to ordinary one through the important similarity variables. Results are obtained through bvp4c technique. All results are discussed graphically. Furthermore, surface drag force (skin friction) and heat and mass transfer (Nusselt and Sherwood) rates are calculated and displayed graphically. Significant results are listed in conclusion.