Impact of fractional derivatives on unsteady flows of brinkman type nanofluids, hybrid nanofluids and blood

Abstract

The boundary layer flows of nanofluids, hybrid nanofluids, and blood are usually studied in terms of classical partial differential equations instead of fractional partial differential equations to avoid complexities in the exact solutions. Fractional partial differential equations offer immense unconventional features to the research, making them potential mathematical tools for describing the complex behaviour of boundary layer flow. Therefore, the main objective of this thesis is to study unsteady convection flows of nanofluids, hybrid nanofluids, and magnetohydrodynamic blood based on the generalized fractional Brinkman type fluid model. The mixed convection boundary layer flows of water-based carbon nanotubes nanofluids and Ferro nanofluid with shape effect past a vertical plate are considered. The effects of thermal radiation, heat generation with ramped, and isothermal heating are studied. The natural convection boundary layer flows of water-based hybrid nanofluids in a channel and magnetohydrodynamic blood flow in a cylindrical tube are also examined. The dimensional boundary layer flow models are transformed into dimensional forms by using appropriate dimensionless variables. Then, the obtained dimensionless models are transformed into the fractional form by using Caputo and Caputo-Fabrizio fractional derivatives. The exact solutions are obtained by using the Laplace transform and joint Henkel and Laplace transform methods. The impacts of the fractional parameter, the volume concentration of nanoparticles, Brinkman type fluid parameter, magnetic parameter, thermal radiation, heat generation, and thermal Grashof number are studied graphically with physical interpretations. The empirical results reveal that for a shorter time, the temperature field, velocity field, blood velocity, and magnetic particles velocity are decreasing with increasing fractional parameters due to variations in temperature and velocity boundary layers. However, this trend revises for a longer time. Meanwhile, it is noticed that the temperature field is increasing with the increasing volume concentration of nanoparticles and hybrid nanoparticles due to the advanced thermal conductivity, but the velocity field behaves oppositely because of effective density. Besides this, the velocity field is decreasing with increasing Brinkman type fluid parameter due to resistive forces. Finally, in a limiting case, the general fractional solutions are reduced to the published classical solutions for the sake of correctness and validation.