Recently, novel coronavirus is a serious global issue and having a negative impact on the economy of the whole world. Like other countries, it also effected the economy and people of Pakistan. ...According to the publicly reported data, the first case of novel corona virus in Pakistan was reported on 27th February 2020. The aim of the present study is to describe the mathematical model and dynamics of COVID-19 in Pakistan. To investigate the spread of coronavirus in Pakistan, we develop the SEIR time fractional model with newly, developed fractional operator of Atangana-Baleanu. We present briefly the analysis of the given model and discuss its applications using world health organization (WHO) reported data for Pakistan. We consider the available infection cases from 19th March 2020, till 31st March 2020 and accordingly, various parameters are fitted or estimated. It is worth noting that we have calculated the basic reproduction number Formula: see text which shows that virus is spreading rapidly. Furthermore, stability analysis of the model at disease free equilibrium DFE and endemic equilibriums EE is performed to observe the dynamics and transmission of the model. Finally, the AB fractional model is solved numerically. To show the effect of the various embedded parameters like fractional parameter Formula: see text on the model, various graphs are plotted. It is worth noting that the base of our investigation, we have predicted the spread of disease for next 200 days.
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids, liquids, and gases. It has several subdisciplines, including aerodynamics (the ...study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modeling fission weapon detonation. In this book, we provide readers with the fundamentals of fluid flow problems. Specifically, Newtonian, non-Newtonian and nanofluids are discussed. Several methods exist to investigate such flow problems. This book introduces the applications of new, exact, numerical and semianalytical methods for such problems. The book also discusses different models for the simulation of fluid flow.
Gold nanoparticles are commonly used as a tracer in laboratories. They are biocompatible and can transport heat energy to tumor cells via a variety of clinical techniques. As cancer cells are tiny, ...properly sized nanoparticles were introduced into the circulation for invasion. As a result, gold nanoparticles are highly effective. Therefore, the current research investigates the magnetohydrodynamic free convection flow of Casson nanofluid in an inclined channel. The blood is considered as a base fluid, and gold nanoparticles are assumed to be uniformly dispersed in it. The above flow regime is formulated in terms of partial differential equations. The system of derived equations with imposed boundary conditions is non-dimensionalized using appropriate dimensionless variables. Fourier's and Fick's laws are used to fractionalize the classical dimensionless model. The Laplace and Fourier sine transformations with a new transformation are used for the closed-form solutions of the considered problem. Finally, the results are expressed in terms of a specific function known as the Mittag-Leffler function. Various figures and tables present the effect of various physical parameters on the achieved results. Graphical results conclude that the fractional Casson fluid model described a more realistic aspect of the fluid velocity profile, temperature, and concentration profile than the classical Casson fluid model. The heat transfer rate and Sherwood number are calculated and presented in tabular form. It is worth noting that increasing the volume percentage of gold nanoparticles from 0 to 0.04 percent resulted in an increase of up to 3.825% in the heat transfer rate.
Chemical kinetics is a branch of chemistry that is founded on understanding chemical reaction rates. Chemical kinetics relates many aspects of cosmology, geology, and even in some cases of, ...psychology. There is a need for mathematical modelling of these chemical reactions. Therefore, the present research is based on chemical kinetics-based modelling and dynamics of enzyme processes. This research looks at the two-step substrate-enzyme reversible response. In the two step-reversible reactions, substrate combines with enzymes which is further converted into products with two steps. The model is displayed through the flow chart, which is then transformed into ODEs. The Atangana-Baleanu time-fractional operator and the Mittag-Leffler kernel are used to convert the original set of highly nonlinear coupled integer order ordinary differential equations into a fractional-order model. Additionally, it is shown that the solution to the investigated fractional model is unique, limited, and may be represented by its response velocity. A numerical scheme, also known as the Atangana-Toufik method, based on Newton polynomial interpolation technique via MATLAB software, is adopted to find the graphical results. The dynamics of reaction against different reaction rates are presented through various figures. It is observed that the forward reaction rates increase the reaction speed while backward reaction rates reduce it.
Atangana and Baleanu (AB) in their recent work introduced a new version of fractional derivatives which uses the generalized Mittag-Leffler function as the non-singular and non-local kernel and ...accepts all properties of fractional derivatives. This articles aims to apply the AB fractional derivative to free convection flow of generalized Casson fluid due to the combined gradients of temperature and concentration with heat generation and first order chemical reaction. For the sake of comparison, this problem is also solved via Caputo-Fabrizio (CF) derivative technique. Exact solutions in both cases of AB and CF derivatives are obtained via Laplace transform and compared graphically as well as in tabular form. In the case of AB approach, the influence of pertinent parameters on velocity field is displayed in plots and discussed. It is found that for a unit time, the velocities obtained via AB and CF derivatives are identical. Velocities for the time less than 1 show little variation and for time bigger than 1, this variation increases.
Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. ...Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ 0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions.
Several scientists are interested in recent developments in nanotechnology and nanoscience. Grease is an essential component of many machines and engines because it helps keep them cool by reducing ...friction between their various elements. In sealed life applications including centralized lubrication systems, electrical motors, bearings, logging and mining machinery, truck wheel hubs, construction, landscaping, and gearboxes, greases are also utilized. Nanoparticles are added to convectional grease to improve its cooling and lubricating properties. More specifically, the current study goal is to investigate open channel flow while taking grease into account as a Maxwell fluid with MoS
nanoparticles suspended in it. The Caputo-Fabrizio time-fractional derivative is used to convert the issue from a linked classical order PDE to a local fractional model. To determine the precise solutions for the velocity, temperature, and concentration distributions, two integral transform techniques the finite Fourier sine and the Laplace transform technique are jointly utilized. The resultant answers are physically explored and displayed using various graphs. It is important to note that the fractional model, which offers a variety of integral curves, more accurately depicts the flow behavior than the classical model. Skin friction, the Nusselt number, and the Sherwood number are engineering-related numbers that are quantitatively determined and displayed in tabular form. It is determined that adding MoS
nanoparticles to grease causes a 19.1146% increase in heat transmission and a 2.5122% decrease in mass transfer. The results obtained in this work are compared with published literature for the accuracy purpose.
The paper aims to investigate the channel flow of second grade visco-elastic fluid generated due to an oscillating wall. The effect of heat and mass transfer has been taken into account. The ...phenomenon has been modelled in terms of PDEs. The constitutive equations are fractionalized by using the definition of the Caputo fractional operator with Fick's and Fourier's Laws. The system of fractional PDEs is non-dimensionalized by using appropriate dimensionless variables. The closed-form solutions of thermal and concentration boundary layers are obtained by using the Laplace and finite Fourier-Sine transforms, while the momentum equation is solved by a numerical approach by Zakian using Formula: see text. Furthermore, the parametric influence of various embedded physical parameters on momentum, temperature, and concentration distributions is depicted through various graphs. It is observed that the fractional approach is more convenient and realistic as compared to the classical approach. It is worth noting that the increasing values of Formula: see text, Formula: see text and Formula: see text retard the boundary layer profile. For instance, this behaviour of Formula: see text is significant where boundary control is necessary. That is, in the case of resonance, the physical solution may be obtained by adding the effect of MHD. The Reynolds number is useful in characterising the transport properties of a fluid or a particle travelling through a fluid. The Reynolds number is one of the main controlling parameters in all viscous flow. It determines whether the fluid flow is laminar or turbulent. The evolution of the rate of heat, mass transfer, and skin friction on the left plate with various physical parameters are presented in tables. These quantities are of high interest for engineers. Keeping in mind the effect of various parameters on these engineering quantities, they make their feasibility reports.
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Herein, we present a green, economic and ecofriendly protocol for synthesis of cobalt oxide (Co3O4-NPs) and magnesium oxide nanoparticles (MgO-NPs) for multifaceted biomedical ...applications. In the study, a simple aqueous leaf extract of Hibiscus rosa sinensis, was employed for the facile one pot synthesis of Co3O4-NPs and MgO-NPs. The well characterized NPs were explored for multiple biomedical applications including bactericidal activity against urinary tract infection (UTI) isolates, leishmaniasis, larvicidal, antidiabetic antioxidant and biocompatibility studies. Our results showed that both the NPs were highly active against multidrug resistant UTI isolates as compared to traditional antibiotics and induced significant zone of inhibition against Proteus Vulgaris, Pseudomonas Aurigenosa and E.coli. The NPs, in particular Co3O4-NPs also showed significant larvicidal activity against the Aedes Aegypti, the mosquitoes involve in the transmission of Dengue fever. Similarly, excellent leishmanicidal activity was also observed against both the promastigote and amastigote forms of the parasite. Furthermore, the particles also exhibited considerable antidiabetic activity by inhibiting α-amylase and α-glucosidase enzymes. The biosynthesized NPs were found to be excellent antioxidant and biocompatible nanomaterials. Owing to ecofriendly synthesis, non-toxic and biocompatible nature, the Hibiscus rosa sinensis synthesized Co3O4-NPs and MgO-NPs can be exploited as potential candidates for multiple biomedical applications.
This article aims to investigate the combined effects of the heat transfer and magnetic field on the electrically conducting magnetohydrodynamic two-phase free convective flow of dusty Casson fluid ...between parallel plates. The flow is caused by buoyancy force with heat transfer due to free convection. Moreover, the left plate moves at uniform velocity while the right plate is stationary, and all dust particles with spherical forms are scattered evenly throughout the fluid. Mathematically, the flow is described as partial differential equations. A newly introduced fractional derivative, namely Caputo-Fabrizio fractional derivative, is used to generalize the given derived system of PDEs. The problem is solved using joint applications of finite sine Fourier and Laplace transforms. Exact solutions of velocity and temperature profile are obtained. Moreover, the impact of different parameters like a magnetic parameter, Grashof number, Dusty fluid parameter, Casson parameter, Peclet number, Reynold number, and particle's mass parameter on temperature, and dust particle and Casson fluid velocity have been discussed. The graphical results for Casson fluid, dusty fluid, and temperature profiles are plotted through Mathcad-15. The behavior of Casson fluid and dusty fluid is matching for different embedded parameters. Moreover, the Nusselt number and skin friction are also determined. It is shown in Table 1 that by increasing the value of the peclet number, the rate of heat transfer decreases. Furthermore, Table 2 shows that by increasing the magnetic parameter, the skin friction decreases. Graphical results conclude that fractional Casson fluid model described a more realistic aspect of the both (Fliud and dust particle) velocities profile, temperature profile, rate of heat transfer and skin friction than the classical Casson fluid model.
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