energies Article Numerical Simulation of the Thermally Developed Pulsatile Flow of a Hybrid Nanofluid in a Constricted Channel Amjad Ali 1 , Zainab Bukhari 1 , Gullnaz Shahzadi 2, *, Zaheer Abbas 3 and Muhammad Umar 1   Citation: Ali, A.; Bukhari, Z.; Shahzadi, G.; Abbas, Z.; Umar, M. Numerical Simulation of the Thermally Developed Pulsatile Flow of a Hybrid Nanofluid in a Constricted Channel. Energies 2021, 14, 2410. https://doi.org/10.3390/ en14092410 Academic Editor: Guido Marseglia Received: 18 March 2021 Accepted: 19 April 2021 Published: 23 April 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan; amjadali@bzu.edu.pk (A.A.); zainabbukhari398@gmail.com (Z.B.); muhammadumar@bzu.edu.pk (M.U.) 2 Department of Mechanical Engineering, École de Technologie Supérieure ÉTS, 1100 Notre-Dame W, Montreal, QC H3C 1K3, Canada 3 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan; zaheer.abbas@iub.edu.pk * Correspondence: gullnaz.shahzadi.1@ens.etsmtl.ca Abstract: Heat transfer analysis of the pulsatile flow of a hybrid nanofluid through a constricted channel under the impact of a magnetic field and thermal radiation is presented. Hybrid nanofluids form a new class of nanofluids, distinguished by the thermal properties and functional utilities for improving the heat transfer rate. The behaviors of a water-based copper nanofluid and water-based copper plus a single-wall carbon nanotube, i.e., (Cu–SWCNT/water), hybrid nanofluid over each of velocity, wall shear stress, and temperature profiles, are visualized graphically. The time-dependent governing equations of the incompressible fluid flow are transformed to the vorticity-stream function formulation and solved numerically using the finite difference method. The laminar flow simulations are carried out in 2D for simplicity as the flow profiles are assumed to vary only in the 2D plane represented by the 2D Cartesian geometry. The streamlines and vorticity contours are also shown to demonstrate the flow behviour along the channel. For comparison of the flow characteristics and heat transfer rate, the impacts of variations in Hartmann number, Strouhal number, Prandtl number, and the thermal radiation parameter are analyzed. The effects of the emerging parameters on the skin friction coefficient and Nusselt number are also examined. The hybrid nanofluid is demonstrated to have better thermal characteristics than the traditional one. Keywords: constricted channel; pulsatile flow; heat transfer analysis; hybrid nanofluid; single-wall carbon nanotube 1. Introduction Blood flow (pulsatile flow) in the arteries exhibits a periodically echoing time scale that affects the flow-induced mass transfer. This makes the modeling of the physiological processes challenging because the time scales of the characteristics are larger than the pulse period. To address the challenge, researchers look at performing time-averaging over the period to reduce the flow variations within the time period so as to capture a characteristic flow profile. In addition, for discussing the blood flow characteristics in arteries, researchers used constricted channels instead of straight channels because of their geometrical advantages. The phenomena of blood flow through arteries have been associated as an essential factor in hemostasis. For example, many events such as atherogenesis, platelet adhesion, thrombosis, and red blood cell lysis have been connected to various hemodynamic factors. A nanofluid (NF) is formed by an engineered suspension of nanoparticles (NPs) of a highly conducting substance (such as copper, aluminum, carbon nanotubes, etc.) in a base fluid such as water. The nanofluids are used extensively for their higher thermal conductivity than the base fluids alone. NPs can be categorized into various types by scale, Energies 2021, 14, 2410. https://doi.org/10.3390/en14092410 https://www.mdpi.com/journal/energies