Hybrid carbon nanotubes flow and heat transfer over a vertical thin needle with suction effect: A numerical and optimisation analysis

Abstract

The present study aims to provide a numerical and optimisation analysis of the hybrid carbon nanotubes flow over a vertical thin needle under the suction effect. The thin needle is suspended in water-based hybrid nanofluids containing a combination of single- and multi-walled carbon nanotubes. The heat is transported using the mixed convection flow. A mathematical model of partial differential equations (PDEs) is developed subject to boundary conditions. The PDEs system is converted to non-dimensional ordinal differential equations (ODEs) by using the similarity solution method. Then, the first order of the ODEs system is solved in a MATLAB bvp4c function. We innovatively carry out an optimisation process using response surface methodology (RSM) to enhance the efficiency of the numerical experiment data and fill a gap in the optimised analysis. To observe the variation solutions for the reduced skin friction and heat transfer coefficients, several parameters, such as the mixed convection and suction parameters, are altered into several values. The solutions are essential for accurately forecasting the occurrence of boundary layer separation, particularly in the case of dual solutions. Our analysis reveals that the model generates multiple solutions for the opposing flow, and the boundary layer separates slowly due to the suction effect. To complete the research, RSM reveals that the highest value of the nanoparticle volume fraction and suction parameters, as well as the smallest value of the needle size, generate the maximum transmitting heat through the slender needle. Furthermore, both the numerical and RSM results show that hybrid carbon nanotubes perform better than mono‑carbon nanotubes for better practical reference.