Fractional Simulations of Casson nanofluid and hybrid nanofluid flow over a vertical plate with radiation and vibration conditions.

Abstract

This thesis investigates the dynamics of blood nanofluid and hybrid nanofluid flow over a vertical plate using fractional calculus, with radiation and vibration conditions. Two models are presented for the simulations, using two different fractional definitions. In the first model the Prabhakar fractional derivative is applied with blood as the base fluid and Single-wall carbon nanotube (SWCNT) and Multi-wall carbon nanotubes (MWCNT) as the nanoparticles to form the nanofluids. The second model applies the Atangana-Baleanu fractional derivative, with Copper (Cu) and Aluminium Oxide (Al2O3) nanoparticles being used to form the hybrid nanofluid. The governing equations for the blood nanofluid and hybrid nanofluid are derived and solved using the Laplace transform technique. Numerical computation of the inverse Laplace transform was performed using the Tzou’s and Zakian’s algorithms. The effects of various parameters, such as the fractional orders, and nanoparticle volume fraction, on the velocity and temperature profiles are analyzed. The results show that the Prabhakar and Atangana-Baleanu fractional derivatives can effectively model the behavior of the blood nanofluid and hybrid nanofluid, and that the nanoparticle volume fraction has a significant impact on the fluid dynamics. Furthermore, the research investigates and discusses the effects of additional fluid parameters such as the Prandtl number, Grashof number, Nusselt number, and Skin friction. The effects of applied radiation and vibration is also analysed and discussed. The study concludes that the use of fractional derivatives provides a valuable tool for analyzing complex fluid dynamics problems and can be applied to a wide range of practical applications in engineering and medicine.