MHD flow of a Newtonian fluid in symmetric channel with ABC fractional model containing hybrid nanoparticles

Introduction: The nanofluid is novelty of nanotechnology to overcome the difficulties of heat transfer in several manufacturing and engineering areas. Fractional calculus has many applications in nearly all fields of science and engineering which comprises electrochemistry, dispersion and viscoelasticity. Objectives: This paper focused on the heat transfer of hybrid nanofluid in two vertical parallel plates and presented a comparison between fractional operators. Methods: The fractional viscous fluid model is considered with physical initial and boundary conditions for the movement occurrences. The analytical solutions were obtained via Laplace transform method for the concentration, temperature and velocity fields. After that we presented a comparison between Atangana-Baleanu (ABC), Caputo (C) and Caputo-Fabrizio (CF) fractional operators. Results: The comparison of different base fluids (Water, kerosene, Engine Oil) is discussed graphically for temperature and velocity. It is resulted that due to high thermal conductivity in water, temperature and velocity are high. While engine oil has maximum viscosity than water and kerosene, so temperature and velocity are very low. Due to the thermal conductivity improving with the enrichment of hybrid nanoparticles, so the Temperature is increased and since viscosity increased, so the velocity is reduced. Conclusion: Atangana-Baleanu (ABC) fractional operator gives better memory effect of concentration, temperature and velocity fields than Caputo (C) and Caputo-Fabrizio (CF). Temperature and velocity of water with hybridized nanoparticles is high in comparison with kerosene and engine oil.

The Effect of Draft Ratio of Side-By-Side Barges on Fluid Oscillation in Narrow Gap

In the present study, the effects of the draft ratio of the floating body on the fluid oscillation in the gap are investigated by using the viscous fluid model. Numerical simulations are implemented by coupling wave2Foam and OpenFOAM. The Volume of Fluid (VOF) model is used to capture the free surface waves. It is verified that the numerical results agree well with the experimental and other results. It is firstly found that, within the water depth range investigated in the present study, the depth of the wave tank has a significant effect on the numerical results. As the depth of the wave tank increases, the oscillation amplitude of the narrow-gap fluid largely decreases and the resonant frequency of the fluid oscillation in the narrow gap increases. The results also reveal that the draft ratio of floating bodies has a significant nonlinear influence on the resonant frequency and on the oscillation amplitude of the fluid in the narrow gap. With an increase in the draft of either the floating body on the wave side or the one on the back wave side, the resonant frequency decreases. The increase in the draft of the floating body on the wave side causes an increase in the reflection wave coefficient and leads to a drop in the fluid oscillation amplitude, and the increase in the draft of the floating body on the back wave side triggers a decrease in the reflection wave coefficient and results in an increase in the fluid oscillation amplitude. Meanwhile, the viscous dissipation induced by the fluid viscosity synchronously increases with the oscillation amplitude of the fluid in the increasing gap. Moreover, it is found that the draft ratio mainly affects the horizontal force of the floating body on the back wave side and that the highest calculated force increases with the draft ratio.

Theoretical Analysis of the Induction of Forced Resonance Mechanical Oscillations to Virus Particles by Microwave Irradiation:Prospects as an Anti-virus Modality

The induction of acoustic-mechanical oscillations to virus particles by illuminating them with microwave signals is analyzed theoretically. Assuming the virus particle being of spherical shape, its capsid consisting primarily of glycoproteins, a viscous fluid model is adopted while the outside medium of the sphere is taken to be ideal fluid. The electrical charge distribution of virus particle is assumed to be spherically symmetric with a variation along the radius. The generated acoustic-mechanical oscillations are computed by solving a boundary value problem analytically, making use of the Green’s function approach. Resonance conditions to achieve maximum energy transfer from microwave radiation to acoustic oscillation to the particle is investigated. Estimation of the feasibility of the technique to compete virus epidemics either for sterilization of spaces and/or use for future therapeutic applications is examined briefly.

On the correct use of mathematical constructions in physical models

The physical limitations of the mathematical constructions used in developing or modifying mathematical models are discussed. All reasonings are illustrated by examples from fluid mechanics. The following topics are considered: means of description; correct approach to model modification and the physical meaning of model development stages. In the first case, the method of describing physical objects using numbers as well as corresponding restrictions are investigated, followed by developing general recommendations on procedures for modifying mathematical models of fluid dynamics. The well-known procedure of averaging the viscous fluid model equations to obtain the turbulent fluid model is used as an illustration. Since we are considering the models of physical phenomena, it is natural to provide physical interpretation for each stage of model development. Unfortunately, some of the transformations used are often treated as purely technical tricks, therefore denoting the lack of the physical meaning in such cases, which does not make a mathematical procedure unacceptable, but does mark out the model's place which requires reasonable interpretation. In this paper, we are considering two variants of this kind of interpretation, namely the case of using imaginary quantities, and the case of applying integral transformations. Meanwhile, all the above-mentioned restrictions are not always given due attention. Sometimes this leads to various undesirable consequences, including excessive task complication, implicit substitution of a declared problem with another one, or, finally, lack of solution to the formulated problem.

Influence of magnetic field on double convection problem of fractional viscous fluid over an exponentially moving vertical plate: New trends of Caputo time-fractional derivative model

In this article, the influence of a magnetic field is studied on a generalized viscous fluid model with double convection, due to simultaneous effects of heat and mass transfer induced by temperature and concentration gradients. The fluid is considered over an exponentially accelerated vertical plate with time-dependent boundary conditions. Additional effects of heat generation and chemical reaction are also considered. A generalized viscous fluid model consists of three partial differential equations of momentum, heat, and mass transfer with corresponding initial and boundary condition. The idea of non-integer order Caputo time-fractional derivatives is used, and exact solutions for velocity, temperature, and concentration in terms of Wright function and function of Lorenzo–Hartley are developed for ordinary cases. Graphical analysis of flow and fractional parameters is made by using computational software MathCad, and discussed. The results obtained are also in good agreement with the published results from the literature. As a result, it is found that temperature and fluid velocity can be enhanced for smaller values of fractional parameters.

MECHANICS OF BIOLOGICAL BLOOD FLOW ANALYSIS THROUGH CURVED ARTERY WITH STENOSIS

The viscous fluid model is considered in this article for the study of blood flow through an axis-symmetric stenosis with the effect of three distinct types of arteries i.e., diverging tapering arteries, converging tapering arteries and nontapered arteries. The Cauchy–Euler method has been used for the solution to velocity profile, resistance impedance to flow and the pressure gradient. The characteristics of viscous blood flow on velocity profile, impedance resistance to flow and pressure gradient have been discussed by plotting the graphs of various flow parameters and finally it is found that stenosis dominantes the curvature of curved artery.