Micropolar Nanofluid Flow in a Stagnation Region of a Shrinking Sheet with Fe 3 O 4 Nanoparticles

Conventional liquids have poor thermal conductivity, thus limiting their use in engineering. Therefore, scientists and researchers have created nanofluids, which consist of nanoparticles dispersed in a base fluid, to improve heat transfer properties in various fields, such as electronics, medicine, and molten metals. In this study, we examine the micropolar nanofluid flow in a stagnation region of a stretching/shrinking sheet by employing the modified Buongiorno nanofluid model. The nanofluid consists of magnetite (Fe 3 O 4 ) nanoparticles. The similarity equations are solved numerically using MATLAB software. The solution is unique for the shrinking strength λ ≥ − 1 . Two solutions are found for the limited range of λ when λ c < λ < − 1 . The solutions terminate at λ = λ c in the shrinking region. The rise in micropolar parameter K contributes to the increment in the skin friction coefficient Re x 1 / 2 C f and the couple stress Re x M w , but the Nusselt number Re x − 1 / 2 N u x and the Sherwood number Re x − 1 / 2 S h x decrease. These physical quantities intensify with the rise in the magnetic parameter M . Finally, we investigated the stability of the solutions over time. This work contributes to the dual solution and time stability analysis of the current problem. In addition, critical values of the main physical parameters are also presented. These critical values are usually known as the separation values from laminar to turbulent boundary layer flows. In this case, once the critical value is achieved, the process for the specific product can be planned according to the desired output to optimize the productivity.