Two‐Layered Immiscible Flows of Carreau and Carreau Nanofluid in an Inclined Channel With Nonlinear Boussinesq Approximation and Viscous Dissipation

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.