Rheological impact of nanoparticles in two immiscible fluids through a heated curved pipe with continuous axial pressure gradient

Abstract The current article scrutinizes the flow and heat transfer characteristics of two immiscible fluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is distributed into two regions, the first being filled with a nanofluid (NF) such as Copper (Cu), and the second with a transparent viscous fluid. The flow governing equations are meticulously considered, incorporating all curvature ratio terms, and are resolved analytically using the perturbation technique. The analytical solution takes into account the continuity of velocities and shear stresses at the fluid–fluid interface, while also adhering to no‐slip, symmetric, and regularity conditions. The effect of various fluid parameters, such as curvature ratio, Reynolds number, viscosity ratio, Prandtl number, heat source/sink parameter, and density ratio, is studied through two‐dimensional graphs and contour plots. The results show that the axial velocity of immiscible fluid flow decreases with an increase in the concentration of nanomaterials. Heat transport characteristics of NF are increased by the addition of nanomaterials.