Duality of similarity solutions for angular momentum equation in thermo-micropolar aqua-base Al₂O₃–Cu flow

The flow and heat transfer characteristics of a thermo-micropolar hybrid nanofluid (TMPHN) over a shrinking perpendicular surface are studied and analyzed in this paper. The TMPHN contains alumina and copper nanoparticles suspended in an aqua-base fluid. The adopted approach involves taking into account the masses of the base fluid and nanoparticles instead of relying on the first and second nanoparticles’ volume fractions. This method aligns with the single-phase approach known as the Tiwari–Das model. The complicated basic PDEs are converted to nondimensional forms utilizing the process of similarity transformation. Moreover, the MATLAB software’s bvp4c routine is used for problem analysis. The computational procedure is reliable since it complies well with earlier reports. The analysis shows that the present boundary value problem can have more than one unique solution. The solutions (first and second) have been obtained for important parameters such as the second nanoparticle mass, the shrinking parameter, the micropolar heat conduction parameter and the suction parameter. A stability analysis was done to explore and separate stable and unstable solutions. In-plane wall movement, classified as “shrinking”, leads to a reduction in boundary layer thickness, increasing fluid velocity and temperature near the wall. These changes collectively contribute to a higher wall shear stress and an enhanced wall heat flux. In specific conditions, for a thermo-micropolar hybrid nanofluid with a mass of 15[Formula: see text]g for each type of nanoparticle and of 100[Formula: see text]g for the aqua-base fluid, incorporating an additional 15[Formula: see text]g of the second nanoparticle into the base fluid results in a 3.3% improvement in heat transfer. These results can be attractive in both mathematical and physical aspects.