Duality Solutions in Boundary Layer Flow and Heat Transfer of SWCNTs-MWCNTs/Water Hybrid Nanofluids over a Vertical Thin Needle with Effect of Suction

The flow, considering the influence of gravity past a vertical thin needle, is studied analytically and numerically under the suction effect. The thin needle is presumed to be submerged in a combination of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs), and then they are incorporated together with water. The investigation was launched by assembling the thermal boundary layer equation within a system of partial differential equations (PDEs) and bringing together this system with a number of boundary conditions. To reduce the complexity of computation, the PDEs system was conversed to non-dimensional ordinal differential equations (ODEs) by using similarity variables. Then, the ODEs system was successfully solved in a MATLAB build-in function, called bvp4c. Several parameters, such as the suction parameter, the nanoparticles volume fraction parameter, and the assisting/opposing flow parameter, were shown graphically to show how they affected the computational results and physical quantity solutions. Based on our analysis, there existed multiple solutions for the opposing flow, and boundary layer was separated slowly due to the suction effect. Besides, it was revealed that carbon nanotubes (CNTs) hybrid nanofluid contributed a higher rate of heat transfer than CNTs nanofluids.