With efficient thermal activities, nanofluids have a novel role in different scientific engineering fields due to their unique and numerous applications. For example, these fluids can be used in magnetic resonance imaging (MRI), magnetic refrigeration (MR), cancer treatment (hyperthermia), and drug delivery. By inspiriting these applications and the significance of electrically conducting nanofluids, in this article, we have studied blood-based nanofluid containing carbon nanotubes (CNTs). The Brinkman type nanofluid modal is established in terms of an efficient mathematical fractional technique namely Prabhakar fractional derivative with ramped temperature and sinusoidal oscillations conditions and for the generalized solutions of temperature and velocity profile, Laplace transformation scheme is utilized. For the heat transfer of nanofluids, the Prabhakar fractional derivative which is based on generalized Fourier’s law of thermal flux is determined. The physical behavior of different parameters is examined by graphical illustrations. As a result, we have concluded that the velocity profile is a bit higher for multi-walled carbon nanotubes (MWCNTs) as compared to single-walled carbon nanotubes (SWCNTs). Furthermore, velocity and temperature fields represent decaying behavior by varying the values of fractional parameters.
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