Micropolar fluids had many industrial applications such as polymer solutions, lubricant fluids, and biological structures. However, the present study deals with the drug delivery in the cardiovascular system where the blood particles are considered as microparticles included their self-rotation (mainly red blood cells) and interaction. The nanoparticles may be used as drug carrier particles. In the present problem, nanoparticles are considered as metallic oxides, e.g., Alumina (Al 2O 3), Titania (TiO 2), and Magnetite (Fe 3O 4) with water as base fluid. The magnetohydrodynamic micropolar fluid flow between two parallel squeezing plates is considered. Further, the analysis is carried out in the presence of viscous dissipation and Joule heating effects. With the aid of a similarity transformation, the flow governing Navier–Stokes equations is transformed into a system of coupled nonlinear ordinary differential equations. Fourth-order Runge–Kutta method with shooting approach is used to solve the nonlinear coupled boundary value problem. The profiles of flow field variables are acquired for key parameters arising in the present problem. It is noticed that, when the plates are fixed, the viscous drag of the base fluid is the same as that of nanofluid. Further, it is observed that increasing volume fraction results a decrement in microrotation and thereby causing an increase in temperature of Titania–water nanofluid which is in contrast to the behavior of other nanofluids. © 2021, Indian Association for the Cultivation of Science.