An investigation of Heat Transfer and Magnetohydrodynamics Flow of Fractional Oldroyd-B Nanofluid Suspended with Carbon Nanotubes

This study aims to investigate the heat transfer and magnetohydrodynamics flow of fractional Oldroyd-B nanofluid in a porous medium with radiation effect. The Caputo time-fractional derivative model is introduced to develop the Oldroyd-B fluid’s constitutive relationship, which describes both memory and elastic effects. Two kinds of carbon nanotubes, particularly single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with base fluid water are considered for the study. The presence of carbon nanotubes with fractional derivatives made the results advantageous for handling similar heat-regulating industrial and engineering problems like achieving heat transfer management in automobile engines, boiler, heat exchangers, grinders and refrigerators. Nonlinear coupled governing equations involving Caputo time-fractional derivatives are reduced to dimensionless form using suitable non-dimensional quantities. The obtained nonlinear governing equations are solved using finite difference approximation with the combined L1 algorithm. Influence of involved parameters on fluid motion and thermal distribution are presented via plots and discussed in detail. The comparison between two kinds of nanofluids, namely SWCNT Oldroyd-B nanofluid and MWCNT Oldroyd-B nanofluid are studied and noticed that MWCNT Oldroyd-B nanofluid provides higher velocity and lower temperature for all embedded parameters. Also, skin-friction and heat transfer rate are controlled by the flow parameters like relaxation and retardation times, relaxation and retardation fractional derivatives, nanoparticle volume fraction, porosity, Darcy number, magnetic and radiation parameters. Furthermore, it is observed that C_f_MWCNT Oldroyd-B nanofluid > C_f_SWCNT Oldroyd-B nanofluid and Nu_SWCNT Oldroyd-B nanofluid >Nu_MWCNT Oldroyd-B nanofluid .