Boundary layers at the interface of thermally radiative nanofluid and Ree–Eyring fluid with different shear strength

Purpose The boundary layer flow of immiscible fluids plays a crucial role across various industries, influencing advancements in industrial processes, environmental systems, healthcare and more. This study explores the thermally radiative boundary layer flow of a shear-driven Ree–Eyring fluid over a nanofluid. The investigation offers valuable insights into the intricate dynamics and heat transfer behavior that arise when a nanofluid, affected by thermal radiation, interacts with a non-Newtonian Ree–Eyring fluid. This analysis contributes to a deeper understanding of the complex interactions governing such systems, which is essential for enhancing efficiency and innovation in multiple applications. Design/methodology/approach The simulation investigates the convergence of boundary layers under varying shear strengths. A comparative analysis is conducted using <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>γ</m:mi><m:mi>A</m:mi><m:msub><m:mi>l</m:mi><m:mn>2</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>3</m:mn></m:msub></m:mrow></m:math> and Al 2 O 3 nanoparticles, with water as the base fluid. The model’s numerical outcomes are derived using the bvp4c method through the application of appropriate similarity transformations. The resulting numerical data are then used to produce graphical representations, offering valuable insights into the influence of key parameters on flow behavior and patterns. Findings The temperature of the Al 2 O 3 nanoparticles is always higher than the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>γ</m:mi><m:mi>A</m:mi><m:msub><m:mi>l</m:mi><m:mn>2</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>3</m:mn></m:msub></m:mrow></m:math> nanoparticles, and hence, Al 2 O 3 nanoparticles become more significant in the cooling process then <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>γ</m:mi><m:mi>A</m:mi><m:msub><m:mi>l</m:mi><m:mn>2</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>3</m:mn></m:msub></m:mrow></m:math> nanoparticles. It is also observed that the fluid velocity for both regions is enhanced by increasing values of the Ree–Eyring fluid parameter. Originality/value The results stated are original and new with the thermal radiative boundary layer flow of two immiscible Ree–Eyring fluid and Al 2 O 3 / <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>γ</m:mi><m:mi>A</m:mi><m:msub><m:mi>l</m:mi><m:mn>2</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>3</m:mn></m:msub></m:mrow></m:math> nanofluid.