Abstract:The magnetohydrodynamic thin film nanofluid sprayed on a stretching cylinder with heat transfer is explored. The spray rate is a function of film size. Constant reference temperature is used for the motion past an expanding cylinder. The sundry behavior of the magnetic nano liquid thin film is carefully noticed which results in to bring changes in the flow pattern and heat transfer. Water-based nanofluids like Al 2 O 3 -H 2 O and CuO-H 2 O are investigated under the consideration of thin film. The basic constitutive equations for the motion and transfer of heat of the nanofluid with the boundary conditions have been converted to nonlinear coupled differential equations with physical conditions by employing appropriate similarity transformations. The modeled equations have been computed by using HAM (Homotopy Analysis Method) and lead to detailed expressions for the velocity profile and temperature distribution. The pressure distribution and spray rate are also calculated. The comparison of HAM solution predicts the close agreement with the numerical method solution. The residual errors show the authentication of the present work. The CuO-H 2 O nanofluid results from this study are compared with the experimental results reported in the literature showing high accuracy especially, in investigating skin friction coefficient and Nusselt number. The present work discusses the salient features of all the indispensable parameters of spray rate, velocity profile, temperature and pressure distributions which have been displayed graphically and illustrated.
The present article deals to study heat transfer analysis due to convection occurs in a fractionalized H2O-based CNTs nanofluids flowing through a vertical channel. The problem is modeled in terms of fractional partial differential equations using a modern trend of the fractional derivative of Atangana and Baleanu. The governing equation (momentum and energy equations) are subjected to physical initial and boundary conditions. The fractional Laplace transformation is used to obtain solutions in the transform domain. To obtain semi-analytical solutions for velocity and temperature distributions, the Zakian's algorithm is utilized for the Laplace inversions. For validation, the obtained solutions are compared in tabular form using Tzou's and Stehfest's numerical methods for Laplace inversion. The influence of fractional parameter is studied and presented in graphs and discussed.
Chemical processes are constantly occurring in all existing creatures, and most of them contain proteins that are enzymes and perform as catalysts. To understand the dynamics of such phenomena, mathematical modeling is a powerful tool of study. This study is carried out for the dynamics of cooperative phenomenon based on chemical kinetics. Observations indicate that fractional models are more practical to describe complex systems’ dynamics, such as recording the memory in partial and full domains of particular operations. Therefore, this model is modeled in terms of classical-order-coupled nonlinear ODEs. Then the classical model is generalized with two different fractional operators of Caputo and Atangana–Baleanu in a Caputo sense. Some fundamental theoretical analysis for both the fractional models is also made. Reaction speeds for the extreme cases of positive/negative and no cooperation are also calculated. The graphical solutions are achieved via numerical schemes, and the simulations for both the models are carried out through the computational software MATLAB. It is observed that both the fractional models of Caputo and Atangana–Baleanu give identical results for integer order, i.e. [Formula: see text]. By decreasing the fractional parameters, the concentration profile of the substrate [Formula: see text] takes more time to vanish. Moreover, binding of first substrate increases the reaction rate at another binding site in the case of extreme positive cooperation, while the opposite effect is noticed for the case of negative cooperativity. Furthermore, the effects of other parameters on concentration profiles of different species are shown graphically and discussed physically.
This paper introduces a mathematical model of a convection flow of magnetohydrodynamic (MHD) nanofluid in a channel embedded in a porous medium. The flow along the walls, characterized by a non-uniform temperature, is under the effect of the uniform magnetic field acting transversely to the flow direction. The walls of the channel are permeable. The flow is due to convection combined with uniform suction/injection at the boundary. The model is formulated in terms of unsteady, one-dimensional partial differential equations (PDEs) with imposed physical conditions. The cluster effect of nanoparticles is demonstrated in the C 2 H 6 O 2 , and H 2 O base fluids. The perturbation technique is used to obtain a closed-form solution for the velocity and temperature distributions. Based on numerical experiments, it is concluded that both the velocity and temperature profiles are significantly affected by φ. Moreover, the magnetic parameter retards the nanofluid motion whereas porosity accelerates it. Each H 2 O-based and C 2 H 6 O 2 -based nanofluid in the suction case have a higher magnitude of velocity as compared to the injections case.
In this research article, a new mathematical model of delayed differential equations is developed which discusses the interaction among CD4 T cells, human immunodeficiency virus (HIV), and recombinant virus with cure rate. The model has two distributed intracellular delays. These delays denote the time needed for the infection of a cell. The dynamics of the model are completely described by the basic reproduction numbers represented by R0, R1, and R2. It is shown that if R0 < 1, then the infection-free equilibrium is locally as well as globally stable. Similarly, it is proved that the recombinant absent equilibrium is locally as well as globally asymptotically stable if 1 < R0 < R1. Finally, numerical simulations are presented to illustrate our theoretical results. Our obtained results show that intracellular delay and cure rate have a positive role in the reduction of infected cells and the increasing of uninfected cells due to which the infection is reduced.
Abstract:This investigation aims at analyzing the thin film flow passed over an inclined moving plate. The differential type non-Newtonian fluid of Williamson has been used as a base fluid in its unsteady state. The physical configuration of the oscillatory flow pattern has been demonstrated and especial attention has been paid to the oscillatory phenomena. The shear stresses have been combined with the energy equation. The uniform magnetic field has been applied perpendicularly to the flow field. The principal equations for fluid motion and temperature profiles have been modeled and simplified in the form of non-linear partial differential equations. The non-linear differential equations have been solved with the help of a powerful analytical technique known as Optimal Homotopy Asymptotic Method (OHAM). This method contains unknown convergence controlling parameters C 1 , C 2 , C 3 , ... which results in more efficient and fast convergence as compared to other analytical techniques. The OHAM results have been verified by using a second method known as Adomian Decomposition Method (ADM). The closed agreement of these two methods and the fast convergence of OHAM has been shown graphically and numerically. The comparison of the present work and published work has also been equated graphically and tabulated with absolute error. Moreover, the effect of important physical parameters like magnetic parameter M, gravitational parameter m, Oscillating parameter ω, Eckert number Ec and Williamson number We have also been derived and discussed in this article.
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