New idea of Atangana and Baleanu fractional derivatives to human blood flow in nanofluids.

ABSTRACT

Applications of fractional derivatives are rare for blood flow problems, more exactly in nanofluids. The old definitions published in the literature for fractional derivatives, such as Riemann-Liouville definition, are rarely used by the researchers now; instead, they like to use the new definition introduced by Atangana and Baleanu quite recently. Therefore, in this article, a new idea of Atangana and Baleanu for fractional derivatives possessing a non-local and non-singular kernel has been applied to blood of nanofluids. Blood is considered as a base fluid, and single-wall carbon nanotubes are suspended in blood as nanoparticles in order to make a nanofluid. The magnetic effect with Lorentz force is also taken. The modelled problem is first written in the dimensionless form and later on solved by using an integral transform of Laplace. The effects of embedded parameters are shown in various plots on blood flow and temperature. The heart transfer rate is computed numerically in a tabular form. The results showed that Atangana and Baleanu fractional parameter slow down the blood motion, whereas increasing nanoparticles' volume fraction causes a significant increase in the heat transfer rate.