Magnetohydrodynamic flow of carbon nanotubes and heat transfer over a moving thin Needle: A numerical and research surface methodology

A steady flow of carbon nanotubes (CNTs) nanofluids and heat transfer past a horizontally moving thin needle are investigated under the influence of magnetohydrodynamic (MHD). Single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs) are the two main nanoparticles that represent CNTs. The slender needle moves relative to the flow with parallel velocity in either the same or opposite direction. Using the similarity method, a system of partial differential equations (PDEs) subject to boundary conditions is converted into nondimensional ordinary equations (ODEs). The ODEs are then reduced to a first-order ODEs system and solved using the MATLAB R2022b bvp4c solver. On a numerical scale, the impacts of varying potential parameters, such as the magnetic, CNTs’ volume fraction, and moving parameters, on the velocity and temperature profiles, the skin friction, and heat transfer coefficients are investigated. Utilising response surface methodology (RSM), the optimisation of the response based on numerical experimentation of physical quantities is performed. The outcomes are depicted using tables and a graphical approach. Results indicate the existence of dual solutions when the needle travels in the opposite direction. Moreover, the increase in the magnetic parameter by 100% in the flow will increase both the skin friction and heat transfer coefficients by nearly 30% and 4%, respectively. Furthermore, when the value of the CNTs volume fraction increases by 100%, the heat transfer rate increases substantially by almost 33%.However, doubling the size of the thin needle cansignificantly reduce the skin friction coefficient by nearly 32%. RSM results demonstrate that the maximal heat transfer coefficient is generated at the highest values of the magnetic and CNTs’ volume friction parameters and the lowest value of the needle size parameter. Findings also show that SWCTNs are superior to MWCNTs both in the skin friction and heat transfer coefficients. When comparing the performance of water and kerosene, we find that water is less effective as a base fluid than kerosene.