The study of gold nanoparticles (AuNPs) in the blood flow has emerged as an area of interest for numerous researchers, due to its many biomedical applications, such as cancer radiotherapy, DNA and antigens, drug and gene delivery, in vitro evaluation, optical bioimaging, radio sensitization and laser phototherapy of cancer cells and tumors. Gold nanoparticles can be amalgamated in various shapes and sizes. Due to this reason, gold nanoparticles can be diffused efficiently, target the diseased cells and destroy them. The current work studies the effect of gold nanoparticles of different shapes on the electro-magneto-hydrodynamic (EMHD) peristaltic propulsion of blood in a micro-channel under various effects, such as activation energy, bioconvection, radiation and gyrotactic microorganisms. Four kinds of nanoparticle shapes, namely bricks, cylinders and platelets, are considered. The governing equations are simplified under the approximations of low Reynolds number (LRN), long wavelength (LWL) and Debye–Hückel linearization (DHL). The numerical solutions for the non-dimensional equations are solved using the computational software MATLAB with the help of the bvp4c function. The influences of different physical parameters on the flow and thermal characteristics are computed through pictorial interpretations.

In this manuscript, we formulate a mathematical model of the deadly COVID-19 pandemic to understand the dynamic behavior of COVID-19. For the dynamic study, a new SEIAPHR fractional model was purposed in which infectious individuals were divided into three sub-compartments. The purpose is to construct a more reliable and realistic model for a complete mathematical and computational analysis and design of different control strategies for the proposed Caputo–Fabrizio fractional model. We prove the existence and uniqueness of solutions by employing well-known theorems of fractional calculus and functional analyses. The positivity and boundedness of the solutions are proved using the fractional-order properties of the Laplace transformation. The basic reproduction number for the model is computed using a next-generation technique to handle the future dynamics of the pandemic. The local–global stability of the model was also investigated at each equilibrium point. We propose basic fixed controls through manipulation of quarantine rates and formulate an optimal control problem to find the best controls (quarantine rates) employed on infected, asymptomatic, and “superspreader” humans, respectively, to restrict the spread of the disease. For the numerical solution of the fractional model, a computationally efficient Adams–Bashforth method is presented. A fractional-order optimal control problem and the associated optimality conditions of Pontryagin maximum principle are discussed in order to optimally reduce the number of infected, asymptomatic, and superspreader humans. The obtained numerical results are discussed and shown through graphs.

The combined effect of a magnetic baffle and a dimple turbulator on the heat transfer and pressure drop is investigated computationally in a mini channel. Fe₃O₄ magnetic nanofluid is used as a working fluid. The Reynolds number (Re) is varied from 150 to 210 and the magnetic field intensities range from 1200 G to 2000 G. Finite-volume based commercial computational fluid dynamics (CFD) solver ANSYS-Fluent 18.1 was used for the numerical simulations. A laminar viscous model is used with pressure-velocity coupling along with second-order upwind discretization and QUICK scheme for discretizing the momentum and energy equations. The results show that there is an increase of 3.53%, 10.77%, and 25.39% in the Nusselt numbers when the magnetic fields of 1200 G, 1500 G and 2000 G, respectively, are applied at x = 15 mm, as compared to the flow without a magnetic field when the pitch = 10 mm. These values change to 1.51%, 6.14% and 18.47% for a pitch = 5 mm and 0.85%, 4.33%, and 15.25% for a pitch = 2.5 mm, when compared to the flow without a magnetic field in the respective geometries. When the two sources are placed at x = 7.5 mm and 15 mm, there is an increase of 4.52%, 13.93%, and 33.08% in the Nusselt numbers when magnetic fields of 1200 G, 1500 G, and 2000 G are applied when the pitch = 10 mm. The increment changed to 1.82%, 8.16%, and 22.31% for a pitch = 5 mm and 1.01%, 5.96%, and 21.38% for a pitch = 2.5 mm. This clearly shows that the two sources at the front have a higher increment in the Nusselt numbers compared to one source, due to higher turbulence. In addition, there is a decrease in the pressure drop of 10.82%, 16.778%, and 26.75% when magnetic fields of 1200 G, 1500 G, and 2000 G, respectively, are applied at x = 15 mm, as compared to flow without magnetic field when the pitch = 10 mm. These values change to 2.46%, 4.98%, and 8.54% for a pitch = 5 mm and 1.62%, 3.52%, and 4.78% for a pitch = 2.5 mm, when compared to flow without magnetic field in the respective geometries. When two sources are placed at x = 7.5 mm and 15 mm, there is an decrease of 19.02%, 31.3%, and 50.34% in the pressure drop when the magnetic fields of 1200 G, 1500 G and 2000 G are applied when the pitch = 10 mm. These values change to 4.18%, 9.52%, and 16.52% for a pitch = 5 mm and 3.08%, 6.88%, and 14.88% for a pitch = 2.5 mm. Hence, with the increase in the magnetic field, there is a decrease in pressure drop for both the cases and the pitches. This trend is valid only at lower magnetic field strength, because the decrease in the pressure drop dominates over the increase in pressure drop due to turbulence.

This paper studies a nonlinear partial differential equation governing wave propagation in nonlinear low-pass electrical transmission. A travelling wave transformation is used to convert this equation into a 2D dynamical system which is proved to be a Hamiltonian system. Based on qualitative theory of the dynamical systems, a comprehensive qualitative study of bifurcation and phase portrait for this system is carried. We construct some new traveling wave solutions and they are graphically clarified.