This article addresses the dynamic of three-dimensional rotating flow of Maxwell nanofluid across a linearly stretched sheet subject to a water-based fluid containing copper nanoparticles. Nanoparticles are used due to their fascinating features, such as exceptional thermal conductivity, which is crucial in modern nanotechnology and electronics. The primary goal of this comprehensive study is to examine the nanoparticles size and shape factors effect on the base fluid temperature. The mathematical model contains the governing equations in three dimensional partial differential equations form, and these equations transformed into dimensionless ordinary dimensional equations via suitable similarity transformation. The bvp4c technique is harnessed and coded in Matlab script to obtain a numerical solution of the coupled non-linear ordinary differential problem. It is observed that the greater input of rotating, Deborah number, and magnetic parameters caused a decline in the fluid primary and secondary velocities, but the nanoparticles concentration enhanced the fluid temperature. Further, a substantial increment in the nanofluid temperature is achieved for the higher nanoparticle’s diameter and shape factors.

The current research article discusses the two-dimensional, laminar, steady, and incompressible third-grade viscoelastic micropolar fluid flow along with thermal radiation caused by an exponentially stretched sheet. The primary goal of this extensive study is to improve thermal transportation. Thermophoresis and Brownian motion are two key causes of nanoparticle migration in nanofluids, and their impacts on the thermophysical properties of nanofluids are significant. Micropolar fluids are investigated due to their micro-motions that are significant in convective thermal and mass transport polymer formation, nanotechnology, and electronics. The consequences of third-grade fluid parameters, thermophoresis and Brownian motion, induced magnetic field, micro-polarity, and micro-inertia density on the stream of an electrically conductive fluid are analyzed. A homogeneous magnetic field is supplied perpendicularly to the surface, and the liquid is believed to be electrically conducting. As the flow has a significant magnetic Reynolds number, the contribution of the evoked magnetic field is properly accounted in the governing equations. A mathematical model in the form of partial differential equations (PDEs) is built under certain assumptions. By invoking the suitable similarity transformation, the non-linear PDEs are modified into dimensionless coupled ordinary differential equations (ODEs). The MATLAB numerical technique bvp4c is employed to settle the subsequent ODEs together with the boundary constraints. The consequences of numerous physical parameters on the non-dimensional concentration, temperature, micropolar, velocity, and induced magnetic field profiles are portrayed in graphs. It is found that the concentration boundary layer, thermal boundary layer, and micropolar boundary layer thickness decelerate with the increment in the micro-polarity of the fluid.

The heat transmission process is a prominent issue in current technology. It occurs when there is a temperature variation between physical processes. It has several uses in advanced industry and engineering, including power generation and nuclear reactor cooling. This study addresses Maxwell fluid’s steady, two-dimensional boundary layer stream across a linearly stretched sheet. The primary objective of this research is to investigate the impact of the non-Newtonian fluid parameter (Deborah number) on flow behavior. The secondary objective is to investigate the effect of linear and quadratic convection to check which model gives higher heat transfer. The flow is caused by the surface stretching. The mathematical model containing the underlying partial differential equations (PDEs) is built using the boundary layer estimations. The governing boundary layer equations are modified to a set of nonlinear ordinary differential equations (ODEs) using similarity variables. The bvp4c approach is employed to tackle the transformed system mathematically. The impacts of numerous physical parameters like stretching coefficient, mixed convective parameter, heat source/sink coefficient, magnetic coefficient, variable thermal conductance, Prandtl number, and Deborah number over the dimensionless velocity and temperature curves are analyzed via graphs and calculated via tables. After confirming the similarity of the present findings with several earlier studies, a great symmetry is shown. The findings show that the linear convection model gains more heat transport rate than the quadratic convection model, ultimately giving a larger thermal boundary layer thickness. Some numeric impacts illustrate that boosting the magnetic coefficient elevates the fluid’s boundary layer motion, causing an opposite phenomenon of Lorentz force because the free stream velocity exceeds the stretched surface velocity.

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