In this paper, based on the magnetohydrodynamics approach, the blood flow along with magnetic particles through a circular cylinder is studied. The fluid is acted by an oscillating pressure gradient ...and an external magnetic field. The study is based on a mathematical model with Caputo fractional derivatives. The model of ordinary fluid, corresponding to time-derivatives of integer order, is obtained as a particular case. Closed forms of the fluid velocity and magnetic particles velocity are obtained by means of the Laplace and finite Hankel transforms. Effects of the order of Caputo's time-fractional derivatives and of the external magnetic field on flow parameters of both blood and magnetic particles are studied. Numerical simulations and graphical illustrations are used in order to study the influence of the fractional parameter α, Reynolds number and Hartmann number on the fluid and particles velocity. The results highlights that, models with fractional derivatives bring significant differences compared to the ordinary model. This fact can be an important advantage for some practical problems. It also results that the blood velocity, as well as that of magnetic particles, is reduced under influence of the exterior magnetic field.
•The flow of blood with magnetic particles in cylindrical domains is studied using the fractional governing equation.•The closed forms for fluid velocity and velocity of particles are determined with Laplace and Hankel transforms.•The effects of the order of Caputo's time fractional derivative and of the external magnetic field on flow parameters are analyzed.•The velocity profiles for the fractional case are different by the profiles corresponding to the ordinary case.
Thermal radiation and thermophoretic particle deposition have important applications in research and engineering. These two principles are employed in practical applications such as electrical fuel, ...projectiles, thermal transportation, renewable energy, nuclear power plants, gas turbines, and aerospace engineering. In light of the aforementioned applications, the current study investigates the stagnation point hybrid CNTs movement around a rotating sphere in the existence of thermal radiation and thermophoretic particle deposition. Using appropriate similarity factors, nonlinear governing equations are converted into ordinary differential equations. The Runge Kutta Fehlberg 45 (RKF-45) order and a shooting approach are used to find the numerical results of the simplified equations and boundary conditions. The numerical findings are presented graphically. It is explored how different limitations impact their individual profiles. According to the research, primary velocity increases with acceleration parameter but decreases with secondary velocity. As the radiation parameter value increases, so does the thermal distribution. Concentration decreases as both the Schmidt number and the thermophoretic parameter decrease. The heat dispersion rate heightens as the percentage of volume fraction of solid and the radiation parameter increase. Mano CNTs have a higher primary velocity than hybrid CNTs.
Abstract
In the present work, the magnetohydrodynamic flow and heat transfer of a micropolar tri-hybrid nanofluid between two porous surfaces inside a rotating system has been examined. A tri-hybrid ...nanofluid is a new idea in the research area, which gives a better heat transfer rate as compared to hybrid nanofluid and nanofluid. We also incorporated the thermal radiation effects and Hall current in this article. The similarity techniques are used to reduce the governing nonlinear PDEs to a set of ODEs. For the numerical solution of the considered problem, we have used the MATLAB-based Bvp4c method. The results are presented for tri-hybrid Fe
3
O
4
-Al
2
O
3
-TiO
2
/H
2
O nanofluid. The main focus of this study is to examine the magnetohydrodynamic heat transfer and tri-hybrid nanofluid flow in a rotating system between two orthogonal permeable plates by taking into account the Hall current and thermal radiation effects. The obtained results have been explained with the help of graphical illustrations and tables. It is observed that the heat transfer rate of tri-hybrid nanofluid is greater than as compared to hybrid nanofluid and nanofluid. The increasing behavior is also noticed in micro rotational velocity for augmented values of
$${R}_{0}$$
R
0
,
$$Ha,$$
H
a
,
and
$$\beta$$
β
. The larger values of
$${\phi }_{1}$$
ϕ
1
,
$${\phi }_{2}$$
ϕ
2
, and
$${\phi }_{3}$$
ϕ
3
result in the decrement of SFC and increment in Nusselt number in both (suction and injection) cases.
A stable colloid called ferrofluid is made up of tiny magnetic particles, often magnetite (Fe 3 O 4 ), that have been bonded with an amphiphilic dispersion layer and are then suspended in a suitable ...liquid solvent carrier. Current industrial uses for ferrofluid include dynamic sealing, inertial and viscous damping, magnetic drug targeting, liquid microrobots, etc. In this article, we studied the heat transfer and MHD micropolar ferrofluid flow caused by non-linearly stretching surface. The results are presented for hybrid alumina- copper/ethylene glycol (${Al}_2 {O}_3$-Cu/EG) nanofluid. The governing non-linear equations describing flow are transformed into a system of ordinary differential equations using similarity transformations. Using the BVp4c method, the microstructure and inertial properties of a magnetite ferrofluid across a non-linear stretched sheet are studied. The influence of relevant parameters on stream function, velocity, micro-rotation velocity, and temperature are obtained and represented graphically. The computed results are original, and it has been observed that if we increase the magnetic parameter, the stream function and the velocity decrease, while the temperature and micro-rotation velocity increase. As the Prandtl number increases, the temperature profile decreases. It has been observed that the Nusselt number or heat transfer rate of hybrid nanofluid is better as compared to nanofluid flow.
In many environments, predators have significantly longer lives and meet several generations of prey, or the prey population reproduces rapidly. The slow-fast effect can best describe such ...predator-prey interactions. The slow-fast effect ε can be considered as the ratio between the predator's linear death rate and the prey's linear growth rate. This paper examines a slow-fast, discrete predator-prey interaction with prey refuge and herd behavior to reveal its complex dynamics. Our methodology employs the eigenvalues of the Jacobian matrix to examine the existence and local stability of fixed points in the model. Through the utilization of bifurcation theory and center manifold theory, it is demonstrated that the system undergoes period-doubling bifurcation and Neimark-Sacker bifurcation at the positive fixed point. The hybrid control method is utilized as a means of controlling the chaotic behavior that arises from these bifurcations. Moreover, numerical simulations are performed to demonstrate that they are consistent with analytical conclusions and to display the complexity of the model. At the interior fixed point, it is shown that the model undergoes a Neimark-Sacker bifurcation for larger values of the slow-fast effect parameter by using the slow-fast effect parameter ε as the bifurcation parameter. This is reasonable since a large ε implies an approximate equality in the predator's death rate and the prey's growth rate, automatically leading to the instability of the positive fixed point due to the slow-fast impact on the predator and the presence of prey refuge.
In this paper, a hybrid method called variational iteration transform method has been implemented to solve fractional-order Navier–Stokes equation. Caputo operator describes fractional-order ...derivatives. The solutions of three examples are presented to show the validity of the current method without using Adomian and He’s polynomials. The results of the proposed method are shown and analyzed with the help of figures. It is shown that the proposed method is found to be efficient, reliable, and easy to implement for various related problems of science and engineering.
Unsteady natural convection flow of viscous fluids in a circular cylinder, due to a generalized fractional thermal transport is analytically studied. The considered mathematical model is based on a ...new fractional differential constitutive equation of the thermal flux suitable to describe the thermal memory effects. To develop the mathematical model, the time-fractional Caputo-Fabrizio derivative is used. The generalized constitutive equation becomes equivalent to the classical Fourier's law for the zero value of the fractional order of derivative. Analytical solutions for the fluid temperature and velocity are determined using the Laplace and finite Hankel transforms. The influence of the memory parameter on heat transfer and fluid motion is discussed by numerical simulations and graphical illustrations.
The effects of the Riga plate flow of Williamson fluid with a Darcy-Forchheimer medium and suction/injection are explained in this study. Convective heat and mass circumstances are considered. The ...energy and concentration equations are developed using Catteneo-Christov dual theory. The heat transfer attributes are analyzed via heat consumption/generation. To estimate total entropy creation, the second law of thermodynamics is applied. The governed mathematical models are transmuted into an ODE model by adopting befitting variables. The MATLAB bvp4c algorithm and the HAM scheme are used to solve these problems numerically and analytically. Novel attributes of various physical parameters are debated through graphs, charts and tables. The fluid flow speed decelerates when enlarging the Weissenberg number and porosity parameters. The fluid temperature enriches when enhancing the radiation parameter. The chemical reaction parameter leads to suppresses the fluid concentration. The higher quantity of heat consumption/generation parameter enriches the heat transfer gradient. The mass transfer gradient accelerates due to more presence of the chemical reaction parameter. We also compared numerical and analytical results and found them in good agreement. When the values of the radiation parameter, Brinkman number, and Reynolds number are increased, the entropy generation increases. The Bejan number downturns when enlarging the modified Hartmann number.
The present research article is related to the analytical investigation of some nonlinear fractional-order Fisher’s equations. The homotopy perturbation technique and Shehu transformation are ...implemented to discuss the fractional view analysis of Fisher’s equations. For a better understanding of the proposed procedure, some examples related to Fisher’s equations are presented. The identical behavior of the derived and actual solutions is observed. The solutions at different fractional are calculated, which describe some useful dynamics of the given problems. The proposed technique can be modified to study the fractional view analysis of other problems in various areas of applied sciences.
We have investigated the two-dimensional mixed convective Maxwell hybrid nanofluid boundary layer mass and heat flows over a linearly stretching porous surface with the applied external magnetic ...flux. Thermal radiations along with the Dufour and Soret effects are also incorporated. The governing model of partial differential equations (PDE) is altered into ordinary differential equations (ODE) with an appropriate similarity transformation. The finite difference-based numerical method BVP4c is applied to solve the system of nonlinear ODEs. The flow features and the heat transfer characteristics have been illustrated with graphical representations and a numerical table. For varied values of the flow-related variables, organized and graphical data for the Nusselt number and skin friction coefficient are indicated. In most cases, spherical-shaped nanoparticles have a better influence on stream function, velocity and temperature distributions. This behavior is the opposite of the mass concentration profile. It has been observed that stream function decreases as increase the value of the magnetic field but opposite for mass concentration distribution and temperature profile. The temperature gradient is enhanced as a result of stronger convective flow when Soret number Sr values increase, which causes the boundary layer thickness to grow. A comparative study of hybrid nanofluid and nanofluid showed that the hybrid nanofluid has superior shear stress/skin friction and Sherwood number/surface mass flux than nanofluid flow.
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