Application of Atangana-Baleanu Fractional Derivative to Carbon Nanotubes Based Non-Newtonian Nanofluid: Applications in Nanotechnology

Abstract

Single and multi-walled carbon nanotubes (SWCNTs & MWCNTs) comprise a large group of nanometer-thin hollow fibrous nanomaterials having physico-chemical characteristics like atomic configuration, length to diameter ratios, defects, impurities and functionalization. This manuscript is devoted for the analysis of carbon nanotubes based non-Newtonian nanofluid suspended in ethylene glycol taken as base fluid. The problem is modeled through modern method of fractional calculus namely Atangana-Baleanu fractional derivative and then solved analytically by invoking Laplace transform. The analytic solutions are established for the temperature and velocity distribution and expressed in terms of special function. The graphical results are depicted through computational software Mathcad and discussed for carbon nanotubes with various embedded parameters. An interesting comparison is explored graphically between single and multi-walled carbon nanotubes subject to the single and multi-walled carbon nanotubes are suspended in ethylene glycol. The several similarities and differences suggested that carbon nanotubes are accelerated and decelerated, while for unit time t = 1s, carbon nanotubes have identical velocities with and without fractional approach.