Fluid Dynamics Division, SAS

A SEIR mathematical model with multiple controls self-preven-tion, treatment and vaccination is formulated The properties of Pontryagin’s maximum principle were verified and found the optimal levels of controls Nu-merical simulations were shown to exhibit the flow of variables with or without control strategies © 2021, Advances in Mathematics: Scientific Journal All rights reserved

A SEIR mathematical model for COVID 19 with a single control vaccination was formulated to analysis the flow of state variables. Properties of Pontryagin’s maximum principle is verified and found the optimal levels of control variable. Optimal values of S, E, I, R were derived by equilibrium analysis. Numerical simulations were carried out to exhibit the Susceptible, Exposed, Infectious and Recovery class with and without vaccination which directs that when the susceptible is vaccinated the flow of disease will drop eventually.

The article concentrates on the role of fluctuating parameters for removable population from the incubated class in a susceptible-incubated-infected model. The discrete analogous of this model is also investigated. Conditions for local asymptotic stability are derived for both the disease free and endemic cases. Numerical simulations are performed to validate the theoretical results.

The main objective of this paper is to study the homogeneous-heterogeneous reactions in magnetohydrodynamic flow due to a nonlinear stretching sheet. Analysis for single wall carbon nanotubes with water and pure blood are taken as the base fluids. The governing non-linear partial differential equations are transformed into ordinary which are solved numerically by utilizing the fourth order Runge-Kutta method with shooting technique. Graphical results have been presented for velocity profile, temperature, concentration, local skin friction coefficient and local Nusselt number profiles for various physical parameters of interest. Comparisons with previously published data are performed and the results are found to be excellent agreement.

The problem of unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible, electrically conducting and heat-absorbing fluid along a semi-infinite vertical permeable moving plate in the presence of a uniform transverse magnetic field and thermal and concentration buoyancy effects is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. The obtained analytical results reduce to previously published results on a special case of the problem. Numerical evaluation of the analytical results is performed and some graphical results for the velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and the Sherwood number are presented and discussed.

In this paper, we present a study for the steady two dimensional radiative MHD boundary layer flow of an incompressible, viscous, electrically conducting fluid caused by a non-isothermal linearly stretching sheet placed at the bottom of fluid saturated porous medium. The governing system of partial differential equations is converted to ordinary differential equations by using the similarity transformations, which are then solved by shooting method. The dimensionless velocity, temperature and concentration are computed for different thermo physical parameters viz the magnetic parameter, permeability parameter, radiation parameter, wall temperature parameter, Prandtl number and Schmidt number.

In this paper, the prediction of the magnetohydrodynamic boundary layer slip flow over a permeable stretched cylinder with chemical reaction is investigated by using some mathematical techniques, namely Runge-Kutta fourth order method along with shooting technique and artificial neural network (ANN). A numerical method is implemented to approximate the flow of heat and mass transfer characteristics as a function of some input parameters, explicitly the curvature parameter, magnetic parameter, permeability parameter, velocity slip, Grashof number, solutal Grashof number, Prandtl number, temperature exponent, Schmidt number, concentration exponent and chemical reaction parameter. The non-linear partial differential equations of the governing flow are converted into a system of highly non-linear ordinary differential equations by using the suitable similarity transformations, which are then solved numerically by a Runge-Kutta fourth order along with shooting technique and then ANN is applied to them. The Back Propagation Neural Network is applied for forecasting the desired outputs. The reported numerical values and the ANN values are in good agreement than those published works on various special cases. According to the findings of this study, the ANN approach is reliable, effective and easily applicable for simulating heat and mass transfer flow over a stretched cylinder.

An analysis is carried out to investigate the steady two-dimensional magnetohydrodynamic boundary layer flow of a Casson fluid over an exponentially stretching surface in the presence of thermal radiation and chemical reaction. Velocity, thermal and solutal slips are considered instead of no-slip conditions at the boundary. Stretching velocity, wall temperature and wall concentration are considered in the exponential forms. The non-linear partial differential equations are converted into a system of non-linear ordinary differential equations by similarity transformations. The resultant non-linear ordinary differential equations are solved numerically by fourth order Runge-Kutta method along with shooting technique. The influence of various parameters on the fluid velocity, temperature, concentration, wall skin friction coefficient, the heat transfer coefficient and the Sherwood number have been computed and the results are presented graphically and discussed quantitatively. Comparisons with previously published works are performed on various special cases and are found to be in excellent agreement.

This paper focuses on a theoretical analysis of a steady two-dimensional magnetohydrodynamic boundary layer flow of a Maxwell fluid over an exponentially stretching surface in the presence of velocity slip and convective boundary condition. This model is used for a nanofluid, which incorporates the effects of Brownian motion and thermophoresis. The resulting non-linear partial differential equations of the governing flow field are converted into a system of coupled non-linear ordinary differential equations by using suitable similarity transformations, and the resultant equations are then solved numerically by using Runge-Kutta fourth order method along with shooting technique. A parametric study is conducted to illustrate the behavior of the velocity, temperature and concentration. The influence of significant parameters on velocity, temperature, concentration, skin friction coefficient and Nusselt number has been studied and numerical results are presented graphically and in tabular form. The reported numerical results are compared with previously published works on various special cases and are found to be an in excellent agreement. It is found that momentum boundary layer thickness decreases with the increase of magnetic http://ppr.buaa.edu.cn/ www.sciencedirect.com

This work concentrates on the effects of homogeneous-heterogeneous chemical reactions on MHD boundary layer flow of Casson fluid over a stretching surface. Cattaneo-Christov heat flux model is considered instead of classical Fourier's law to explore the heat transfer phenomena. Appropriate similarity transformations are used to convert the governing partial differential equations into a system of coupled non-linear differential equations. The resulting coupled non-linear differential equations are solved numerically by using the fourth order Runge-Kutta method with shooting technique. The impact of significant parameters on velocity, temperature, concentration, skin friction coefficient and the Nusselt number are presented graphically and in tabular form. Our computations disclose that fluid temperature has inverse relationship with the thermal relaxation time. Also, the strength of homogeneous and heterogeneous parameters has no effect on the skin friction coefficient and Nusselt number.

The present study investigates the effects of Soret and Dufour on MHD non-Darcy convective flow of a viscous incompressible radiating micropolar fluid past an inclined permeable plate with non-uniform heat source or sink and chemical reaction. The flow field with partial differential equations are converted to a system of nonlinear coupled ordinary differential equations by similarity transformations and solved employing shooting method. Swiftness in the momentum of the fluid is observed as the Darcian and fluid parameter ascends. Speed of the fluid in angular rotation ascends as the material parameter or sheet inclination or magnetic parameter increases. Molecular diffusion rate is more as the microparticles undergo chemical reactions. While the thermal distribution rate reduces because of the reactions. Rest of the results are interpreted graphically. A good agreement is observed with the previous publications. The presence of chemical reaction makes the problem industrially applicable taking the case of heterogeneous reactions.

This paper presents a numerical exploration on the unsteady three-dimensional hydromagnetic flow of Carreau nanofluid over a slendering stretchable sheet in the presence of thermal radiation and chemical reaction. Furthermore, the effects of velocity slip, thermal slip, solutal slip, Soret and Dufour are taken into account. The prevailing time-dependent partial differential equations are metamorphosed into a system of coupled nonlinear ordinary differential equations by using the appropriate similarity transformations. The resultant nonlinear coupled differential equations are solved numerically by using the Runge–Kutta fourth-order method along with shooting scheme. The sway of sundry parameters on velocity, temperature, concentration, shear stress, temperature gradient and concentration gradient has been premeditated, and numerical results are presented graphically and in tabular form. Comparison amid the previously published results, and the current numerical results are made for...

The main object of this paper is to steady the Bio-mathematical analysis for the stagnation point flow over a non-linear stretching sheet with the velocity slip and Casson fluid model. Analysis for the both titanium and titanium alloy within the pure blood as taken as the base fluid. The governing non-linear partial differential equations are transformed into ordinary which are solved numerically by utilizing the fourth order Runge-Kutta method with shooting technique. Graphical results have been presented for dimensionless stream function, velocity profile, shear stress, temperature profile for various physical parameters of interest. It was found that the velocity profile of the nanofluids decreases and increases with the increasing the first-order and second-order slips respectively. Comparisons with previously published work are performed and the results are found to be excellent agreement.

Present work aims to investigate the blood stream in a permeable vessel in the presence of an external magnetic field with heat and mass transfer. The instability in the coupled flow and temperature fields is considered to be produced due to the time-dependent extending velocity and the surface temperature of the vessel. The non-uniform heat source/sink effects on a chemically responded blood stream and heat viscous. This study is of potential value in the clinical healing of cardiovascular disorders accompanied by accelerated circulation. The problem is treated mathematically by reducing it to a system of joined non-linear differential equations, which have been solved by utilizing similarity transformation and boundary layer approximation. The resultant non-linear coupled ordinary differential equations are solved numerically by utilizing the fourth order Runge-Kutta method with shooting technique. Computational results are gotten for the velocity, temperature, the skin-friction coefficient, the rate of heat transfer and rate of mass transfer in the vessel. The evaluated results are compared with another analytical study reported earlier in scientific literatures. The present investigation exposes that the heat transfer rate is upgraded as the value of the unsteadiness parameter increases, but it decreases for the increment of the space reliance parameter for heat source/sink.

This paper presents a numerical analysis of the magnetohydrodynamic (MHD) flow of Carbon nanotube (CNT) nanofluid over a non-linear inclined stretching/shrinking sheet with heat generation and viscous dissipation. In this model, we used SWCNT-H2O and MWCNT- H2O as Nano liquids. By using the self-similar numerical solutions, the governing non-linear momentum and thermal boundary layer equations rehabilitated to ordinary differential equations. The resultant mathematical model is numerically solved with the assistance of R-K fourth order with shooting technique. Numerical exploration is completed by inspecting the various values of a magnetic field parameter, non-linear stretching/shrinking parameter, Richardson number, Eckert number, effective Prandtl number and a suction parameter for the flow and heat transfer which are obtainable through graphs. It is found that SWCNT-H2O nano liquid produce high heat transfer compared to MWCNT- H2O nano liquid. The validity of calculated results ...

In this paper, a mathematical model has been developed to analyze the double diffusive convective flow of Casson fluid over an inclined stretching sheet with Cattaneo-Christov Heat Flux model. The velocity slip is considered over the surface of the stretching sheet as well. The governing equations for the pertinent model are transformed into non-dimensional highly coupled nonlinear differential equations using similarity transformations. The implicit finite difference method is used to carry out the numerical results and presented the graphs for different values of the physical parameter, Casson fluid parameter, and thermal relation time parameter, chemical reaction parameter for the cases of assisting flow, opposing flow and blowing. The present results are compared with earlier existing results and found to be very good agreement. Increasing Casson fluid parameter retards the flow velocity and temperature fields and skin friction coefficient while enhance the concentration field, rate of heat and mass transfer. The fluid velocity and temperature fields, skin friction coefficients, heat and mass transfer rates are decreased with increase in thermal relation time while concentration profile enhanced. This type of study finds applications in industry and engineering fields like condensation processes, artificial fibers and heart valves and heat conduction in tissues etc. Increasing Casson fluid parameter causes to decelerates fluid velocity while accelerates temperature and concentration, skin friction coefficient, Nusselt number and Sherwood number as well. Increasing velocity slip parameter leads to reduce the fluid velocity and Nusselt & Sherwood number while increases temperature and concentration distribution and skin friction coefficient values.

A theoretical model is drafted to inspect the hydromagnetic flow of carbon nanotubes (CNT's) suspended in a Maxwell nanofluid by means of activation energy with binary chemical reaction over a stretching sheet. Modified Arrhenius function is measured instead of the energy activation. Heat transport phenomena are explored in energy expression through a nonlinear thermal radiation and viscous dissipation, which is incorporated with a novel theory specifically Cattaneo-Christov model of heat diffusion-a sophisticated form of Fourier's heat flux formula. The flow analysis is reported in attendance of convective slip and suction. Two different kinds of CNT's (i.e. single and multiple walls) are consistently dispersed in the base fluid (engine oil) to illustrate the fine points of the flow. The governing system of mathematical expressions for the locally similar flow is tackled numerically by Runge-Kutta-based MATLAB bvp4c package. The procured solutions are drawn for different values of pertinent parameters of interest. The temperature of the fluid escalates with the nonlinear thermal radiation. Activation energy boosts up the concentration, and a negative trend is observed for rate of chemical reaction.