The current study discusses the laminar, incompressible steady flows of Carreau fluid and Carreau nanofluid in an inclined channel with two regions. In Region‐I, Carreau fluid is considered, whereas in Region‐II, Carreau nanofluid is deliberated. Both regions are considered porous, with a constant pressure gradient. Carreau fluids are characterized by shear‐thickening features and possess applications in varied industries, including petroleum, food, and polymer processing. Higher temperature variations are taken into account, leading to the incorporation of nonlinear thermal radiation and quadratic thermal convection. Nonlinear thermal radiation plays a key role in various real‐life applications, including solar energy systems, high‐temperature operations, and aerospace engineering. Similarly, quadratic thermal convection is relevant to geothermal energy, crystal growth and solidification, as well as microfluidic technologies. The uniqueness of the proposed model is further strengthened by incorporating viscous dissipation and a heat source/sink. Numerical solutions are obtained using the NDSolve technique. Graphs illustrate velocity, temperature, concentration, surface drag coefficient, and heat transmission rate against various parameters. It is deduced that the porosity parameter has a decreasing effect on both regions, and the Brownian motion parameter has an increasing effect on nanoparticle volume fraction, whereas a reverse impact is observed for the thermophoresis parameter. This insight can be applied to the design of porous media‐based cooling mechanisms and nanofluid‐driven heat exchangers, where optimized porosity and Nanoparticle mobility (via Brownian motion and thermophoresis) are crucial for controlling particle distribution and enhancing thermal performance in layered or multiphase systems. Moreover, for higher values of the Eckert number, the thermal distribution is more pronounced in the second region of the channel containing non‐Newtonian nanoliquid. This result is valuable for designing thermal systems involving high‐speed or high‐viscosity flows, such as microchannel heat sinks, polymer processing units, or energy storage systems, where viscous dissipation (high Eckert number) significantly impacts temperature profiles, especially in non‐Newtonian nanofluid layers that require efficient heat management. The validation of the anticipated model is also a part of this exploration.

Let $(M,F)$ be a Finsler surface with the isotropic main scalar $\mathcal{I}=\mathcal{I}\left(x\right)$. The well-known Berwald’s theorem states that F is a Berwald metric if and only if it has a constant main scalar $\mathcal{I}=constant$. This ensures a kind of equality of two non-Riemannian quantities for Finsler surfaces. In this paper, we consider a positively curved Finsler surface and show that $\mathbf{H}=0$ if and only if $\mathcal{I}=0$. This provides an extension of Berwald’s theorem. It follows that F has an isotropic scalar flag curvature if and only if it is Riemannian. Our results yield an infrastructural development of some equalities for two-dimensional Finsler manifolds.

This study looks at how an electrically conducting Sutterby nanofluid flow due to a horizontal stationary sheet behaves under the influence of the Darcy–Forchheimer effect in a porous medium. Flows across a permeable medium possess interesting applications, including environmental and biological systems like soils, bones, and tissues. Heat and mass transmissions are enriched by viscous and ohmic dissipations, radiative heat flux, and chemical reaction. A thermal convective condition is imposed on the boundary of the surface. The governing fluid model of a nonlinear system is modeled using boundary layer approximations. Further, the transformed ordinary differential equations (ODEs) are obtained via a nonsimilarity procedure up to the second level of truncation and are numerically evaluated by using the bvp4c approach. The velocity, thermal, and concentration distributions are demonstrated graphically against the pertinent factors. Quantities of engineering, such as wall heat flux, wall drag coefficient, and surface mass flux, are tabulated numerically. The outcomes depict that the Eckert number diminishes the wall heat transmission rate while the wall mass transfer rate grows for the upsurging estimates of the chemical reaction parameter. Furthermore, the Lorentz force promotes wall heat transmission and lowers the mass transfer rate. The intended model is verified against the published work using a comparison table. An excellent correlation is noted between the values in percentage of the present and the published work, substantiating its truthfulness.