The present study is related to the effects of activation energy and thermophoretic diffusion on steady micropolar fluid along with Brownian motion. The activation energy and thermal conductivity of steady micropolar fluid are also discussed. The equation of motion, angular momentum, temperature, concentration, and their boundary conditions are presented for the micropolar fluid. The detail of geometry reveals the effects of several parameters on the parts of the system. The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. The comparison of the obtained results by the shooting technique and the numerical bvp4c technique is presented. The behavior of local skin friction numbers and couple stress number is tabulated for different parameters, and some figures are plotted to present the different parameters. For uplifting the values of AE for parameter λA, the concentration profile is increased because of the Arrhenius function, and AE increases with the reduction of this function. The increasing values of the parameter of rotation G show the decrement in velocity because of the rotation of the particle of the fluid, so the linear motion decreases. Thermophoresis is responsible for shifting the molecules within the fluid, and due to this, an increment in boundary layer thickness is found, so by a greater value of Nt, the concentration profile decreases and temperature profile goes down.

With respect to bionomical concerns and energy security, the performance of refrigeration systems should be enriched, which can be done by improving the characteristics of working liquids. Nanoliquids have attracted interest in the fields of engineering and industry due to their prominent thermophysical characteristics. Researchers have used nanoliquids as working liquids and noticed significant fluctuations in thermal execution. In this study,  our prime aim was to study the impact of thermal radiation and varying thermal conductivity on a cross‐nanofuid with the addition of a nonuniform heat sink–source, chemical process, and activation energy (AE) together with effects of assisting and opposing buoyancy. Furthermore, the relationship of zero‐mass flux together with the mechanism of thermophoresis and Brownian motion is considered. Traditionalistic transformations gave the ordinary differential equations (ODEs), which are further dealt with the approach of the Shooting Scheme to change the boundary value problem (BVP) into an initial value problem (IVP) and a numerical comparison is made with the Matlab solver package bvp4c. Bvp4c is based upon a collocation scheme, which yields numeric outcomes for nonlinear ODEs with IVP. Impacts of the involved parameters on mass transfer profile, heat, and momentum fields are shown through graphs. Mass transfer of the cross nanofluid increases with increasing values of AE parameter. Values of physical quantities like drag forces, rate of transport of heat and mass in the case of assisting/opposing flow are tabulated. The drag force magnitudes are greater for enhancing values of M, a, and n, while on the other hand, the opposing tendency is seen for We1 and We2. The magnitude of the rate of heat transport (Nusselt number) falls for greater values of m, σ, δ, and Nt, but in contrast, it accelerates for E, Pr, and n.

Heat transport keeps vital impact in field of engineering like heat spacing, air conditioning, refrigeration, and in chemical processing, such as heating of base and final products, heat recovery, tempering of containers, autoclaves, and reactors. This manuscript reveals theoretical and an experimental finding related for heat transport of unsteady cross nanofluid and chemical process with inclined magnetic field over the wedge. Heat transport is scrutinized with the existence of nonuniform heat sink source and radiation. Furthermore, mass transfer is studied with higher order chemical process, thermophoresis, and Brownian motion. Mathematical system produces nonlinear partial differential equations (PDEs) of time‐dependent velocity, energy, and concentration. Moreover, these PDEs changed into the system of nonlinear ordinary differential equations (ODEs). The obtained ODEs are passed out through shooting technique to convert the boundary value problem into initial value problem and further bvp4c took them for numerical solution. Bvp4c is MATLAB procedure, which is most convergent for numerical solution of ODEs based on RK‐45 procedure. Many applicable parameters are inspected graphically and in tabular form. Numerical outcomes related to physical quantities are hashed out in tabular form. Chemical process boosts the heat and mass transport. Higher radiation responses higher temperature and inclined magnetic strength reduces the velocity of cross nanofluid.

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Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick’s second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter α brings about a decrement in fluid velocity and augmentation in thermal conductivity ϵ, thermal radiation Rd, thermophoresis parameter Nt and endothermic/exothermic reaction Ω, and fitted rate constant n accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature.