Dual Solutions of Stagnation Point of Carbon Nanotubes Across a Permeable Stretching/Shrinking Cylinder

Abstract

This study aims to investigate the presence of carbon nanotubes (CNTs) on the stagnation point flow and heat transfer over a stretching/shrinking cylinder with the effects of suction/injection. The findings highlight for understanding and optimizing flow and heat transfer with significant influence of suction and stagnation effects on the boundary layers in carbon nanotube-based nanofluids involving shrinking or stretching surfaces. Two types of carbon nanotubes are used which are single-walled (SWCNTs) and multi-walled (MWCNTs) with water or kerosene as the base fluid. The governing partial differential equations are converted into the ordinary differential equations by similarity transformation, which are then solved the equations numerically by using the bvp4c solver in MATLAB software. The effect on local skin friction and Nusselt numbers, velocity and temperature profile for nanoparticle volume fraction, curvature parameter, magnetic parameter and suction parameter are discussed and illustrated in graphical forms. The results indicate a range of parameters yielding dual solutions. It is determined that the curvature parameter and the suction effect could widen the range of solution due to it reduces the boundary layer separation. Furthermore, SWCNTs have a higher heat transfer rate compared to MWCNTs. Besides, kerosene exhibits a higher velocity and heat transfer rate than water as a base fluid.