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.

Key developments in the field of nanotechnology have drawn the attention of many scholars toward the interaction of nanoparticles due to their capturing applications in solar energy systems and thermal engineering. Larger consumption of energy posed a challenge for thermal science, so thermal engineering is trying to solve this issue by increasing the thermal conductivity of the fluid. The thermal conductivity of conventional fluid is increased by incorporating the nanoparticles in the base fluid. Keeping this in mind, the present research project addresses the utilization of nanoparticles in a steady three-dimensional rotating flow of magnetohydrodynamic water-based hybrid fluid over an extending sheet. Nanoparticles of aluminum oxide (Al 2 O 3 ) and silver (Ag) are being used with water (H 2 O) as base fluid. The velocity of nanoparticles is being captured under the influence of an inclined magnetic field and the transport of heat is scrutinized through thermal radiation. The physical model generates partial differential equations and then transported into an equivalent set of a nonlinear ordinary differential equations. The purpose of numerical computation is made by the Lobatto IIIA method, which is

Fluid viscosity manages several engineering processes and keeps its leading role in lubrication models, biological models, polymer processes, melt solutions, colloidal suspensions, and mayonnaise. The cross viscosity model is the most appropriate model, which interprets the key features of non-Newtonian fluids in the region of shear-thinning/thickening when very high and very low shear rates are applied. This article focuses on the mathematical model of threedimensional Cross nanofluid and interprets its aspect of infinite shear rate of viscosity over the expanding sheet. Velocity is studied through placing inclined magnetic dipole effect, transportation phenomenon is brought by considering the radiation effects, heat generation and chemical process is engaged for concentration of nanoparticles. The geometry of this mathematical model is expanding the stretching sheet with velocity slip, and convective heat conditions are associated. Similarity variables are being utilized for conversion dimensional mathematical model into nondimensional one. For the pursuit of numerical solution of the system of nondimensional

Researchers across the world have tried to explore the impact of non-Newtonian liquid flowing via an extendable surface with the inclusion of various effects due to its industrial and engineering applications like polymer production, paper production, filament extrusion from a dye, etc. This study investigates the behavior of stagnation point flow of Carreau liquid attached with inclined magnetic effect and spectral relaxation approach is utilized here for the numerical outcome. In this study, a few other vital features are attached like the quadratic multiple regression model for Nusselt number evaluation, passive control of nanoparticles, viscus heating thermophoresis, Brownian motion, and mixed convection, etc. Velocity disbursement visibility is analyzed by placing an inclined magnetic field. Physical model generates collection of partial differential equations (PDEs) and these PDEs are moved into ordinary differential equations by a similarity transformations scheme. Further for numerical process, spectral relaxation method is used. Growth in K causes a reduction in velocity because this parameter K creates the impedance to flowing resulting in confines the movement of liquid in restricted the plate. Direct relation is found between $$Ec$$ Ec and the energy file. In the case of S > 1, physically it is a representation of Joule and viscous dissipations. This article is novel in its sense that the influence of oblique magnetic force and second order velocity slippage on Carreau nano liquid and its numerical computation with help of the spectral relaxation method has never been done before. Furthermore, the quadratic multiple regression model has been employed to find the heat transition rate in the status of the Nusselt number.

Cross nanofluid possesses an extraordinary quality among the various fluidic models to explore the key characteristics of flowing fluid during very low and very high shear rates and its viscosity models depend upon shear rate. The current study establishes the numerical treatment regarding variable viscosity-based mixed convective inclined magnetized Cross nanofluid with varying thermal conductivities over the moving permeable surface. Along with variable thermal conductivities, we considered thermal radiation, thermophoresis, and the Brownian motion effect. An inclined magnetic field was launched for velocity scrutiny and the heat transfer fact was numerically seen by mixed convective conditions. Similarity variables were actioned on generated PDEs of the physical model and conversion was performed into ODEs. Numerical results showed that the frictional force and Nusselt quantity considerably influence the skinning heat transfer processes over the geometry of a moving permeable surface. Furthermore, less velocity was noticed for the greater suction parameter and the Brownian motion parameter corresponds to lower mass transport.

Solar energy is the basic source of renewable energy, and it is being used for controlling global pollution/warming. As the Cross nanofluid is very useful for cooling solar devices, in this paper analysis of the global warming effect is investigated by incorporating the nonlinear thermal radiation over the exponentially extendable surface because it plays a major role related to solar energy absorption of nanofluid. Furthermore, the mathematical modeling of Cross nanofluid involving magnetic effect and diffusion is discussed by using the fact of chemical reaction. Chemical reaction finds astonishing applications in pollution studies, chemical processing equipment, and polymer production. As a result of this study, it is noticed that more magnetized conducting fluid controls the motion of fluids for both cases of shear thinning and shear thickening. Brownian motion parameter Nb affects the rate of the random motion of nanoparticles. Increased Nb temperature also increases due to these random movements of nanoparticles. That is the reason why pollutant nanoparticles spread in air as a result of global warming increase.

No abstract

Cross nanofluidic model yields extraordinary results and describes the behaviour of nanofluid at very high and very low shear rate. In this paper infinite shear rate viscosity model of cross nanofluid flow containing nanoparticles and motile gyrotactic microorganisms over three dimensional horizontal cylinder is taken. In this attempt simultaneous utilization of nanoparticles along with motile microorganisms attached mathematical model of cross fluid and three-dimensional geometry of cylinder has been carried out as an innovation. For the inspection of velocity profile of cross nanofluid inclined magnetic field is scrutinized. Temperature of Cross nanofluid and its concentration is also carried out with several facts. Mass flux and heat flux values for motile microorganisms and nanoparticles are calculated through statistical graphs. This attempt reveals that small variation of Brownian motion parameter gives lower concentration of nanoparticle about 80.21% and 78.44% reduction is found in concentration of motile microorganisms.