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A fully developed mixed-convection nanofluid flow in a vertical channel with variable thermal and electrical wall conductivities in the presence of a uniform transverse magnetic field is studied. The working fluid is a homogeneous mixture of a base fluid (water) and metallic nanoparticles of three different kinds, namely, copper, alumina, and titanium dioxide. The fluid is also electrically conducting in the presence of an applied magnetic field. The flow is characterized by a moderate magnetic Reynolds number. An induced magnetic field is present. The effects of the pertinent parameters on the nanofluid temperature, velocity, and induced magnetic field strength, as well as on the shear stress and heat transfer rate at the channel wall, are shown. In the case of a negative vertical temperature gradient (heating from below), there exists a critical Rayleigh number at which the fluid becomes unstable. This number is also found as a function of the wall conductivities. [ABSTRACT FROM AUTHOR]

We study the velocity, thermal, and mass slips on chemically reacting magnetohydrodynamic boundary layer flow over a radiated stretching surface in the presence of suction. The governing momentum boundary layer and thermal boundary layer equations with boundary conditions are transformed into a system of nonlinear ordinary differential equations that are solved numerically using the Runge-Kutta-Fehlberg method. The involved differential systems are solved for velocity, temperature, and mass fraction. Graphical and numerical results are described for the analysis of various parameters of attention entering the modeled problems. Various tables are constructed to show rheological effects of different physical parameters. Combined effects of thermal and concentration jump are analyzed. We found that the slips have the propensity to control boundary layer flow. Velocity, temperature, and concentration show the increasing nature before and after a point, as the velocity slip increases and the momentum, thermal, and concentration boundary layer thickness become thinner for velocity slip. [ABSTRACT FROM AUTHOR]

Variable viscosity, activation energy and microgravity effects on Darcy nanofluid for the thermal performance improvement in thermal energy storage systems through stretching flat plate solar collector is the focus of this research. Thermal energy storage (TES) can be improved though solar collectors, phase change materials and photovoltaic cells using nanofluid in the base liquid. To increase the reaction rate in nanoparticles, the activation energy and solar radiations are used for the efficiency of TES. The viscosity of nanofluid improves the heat and mass transmission. Due to solar radiations, nanofluid plays prominent role in TES applications such as heat exchangers, electronic cooling devices and solar power generation through solar plate collector. Solar energy based mathematical model is developed to execute the frequency of oscillating heat transfer in TES numerically. Primitive and Stokes coefficients are used for feasible programming. Finite difference analysis is performed to display oscillatory thermal energy using Gaussian-elimination matrix scheme. Steady velocity, surface temperature and concentrations are plotted and utilized in oscillatory formula to perform oscillatory skin friction, oscillatory heat transfer and oscillatory mass transfer along π⁄4 angle. Fluid velocity enhances but temperature and concentration variation decreases as viscosity decreases. High amplitude in velocity, temperature and concentration is sketched as activation energy and microgravity increases. Steady heat and mass transmission enhances as thermophoretic and Brownian motion enhances. Amplitude and frequency of oscillations in heat transport, skin friction and mass transport enhances as Prandtl and Schmidt component enhances. In validation of results, the 0.00064% percentage error for heat transport and 0.00102% percentage error for mass transmission are deduced., (© 2024. The Author(s).)

This study proposes a non-linear mathematical model for analysing the effect of COVID-19 dynamics on the student population in higher education institutions. The theory of positivity and boundedness of solution is used to investigate the well-posedness of the model. The disease-free equilibrium solution is examined analytically. The next-generation operator method calculates the basic reproduction number ( R 0 ) . Sensitivity analyses are carried out to determine the relative importance of the model parameters in spreading COVID-19. In light of the sensitivity analysis results, the model is further extended to an optimal control problem by introducing four time-dependent control variables: personal protective measures, quarantine (or self-isolation), treatment, and management measures to mitigate the community spread of COVID-19 in the population. Simulations evaluate the effects of different combinations of the control variables in minimizing COVID-19 infection. Moreover, a cost-effectiveness analysis is conducted to ascertain the most effective and least expensive strategy for preventing and controlling the spread of COVID-19 with limited resources in the student population., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)

A nonlinear differential equation model is proposed to study the dynamics of HIV/AIDS and its effects on workforce productivity. The disease-free equilibrium point of the model is shown to be locally asymptotically stable when the associated basic reproduction number [Formula: see text] is less than unity. The model is also shown to exhibit multiple endemic states for some parameter values when [Formula: see text] and [Formula: see text]. Global asymptotic stability of the disease-free equilibrium is guaranteed only when the fractions of the Susceptible subclass populations are within some bounds. Optimal control analysis of the model revealed that the most cost effective strategy that should be adopted in the fight against HIV/AIDS spread within the workforce is one that seeks to prevent infections and the treatment of infected individuals., (© 2021. Springer Nature B.V.)

Background: The present work provides important insights regarding three dimensional unsteady magnetohydrodynamic flow and entropy generation of micropolar Casson Cross nanofluid subject to nonlinear thermal radiation and chemical reaction. The Buongiorno's nanofluid model featured with Brownian movement and thermophoresis is considered. Realistic aspects namely convective boundary condition, viscous dissipation and joule heating are introduced. The present problem is modeled by momentum, temperature, microrotation and nanoparticles concentration equations., Method: The non-dimensional highly nonlinear differential equations are solved numerically via shooting iteration technique together with 4th order Runge-Kutta integration scheme., Results: The current study imparts a reasonable, pragmatic and realistic approach to a good absorber of solar energy. In addition, strong and visionary profiles of velocity, microrotation, temperature, nanoparticles concentration, entropy generation rate and Bejan number for concern nanofluids are presented. Besides, intensive physical interpretation of the involved thermophycal parameters has been well-addressed., Conclusions: The present investigation shows that strengthening of Weissenberg number uplifts the axial as well transverse fluid velocities while that of Hartmann number turns out to be a reverse trend. Furthermore, heat and mass transfer rates exhibit ascending and descending trends for intensified Brownian motion and thermophoresis respectively. Improved thermal boundary layer due to the upgrading temperature ratio parameter is another outcome of the current analysis., Competing Interests: Declaration of Competing Interest None., (Copyright © 2019. Published by Elsevier B.V.)

In this paper we formulate a mathematical model for malaria-cholera co-infection in order to investigate their synergistic relationship in the presence of treatments. We first analyze the single infection steady states, calculate the basic reproduction number and then investigate the existence and stability of equilibria. We then analyze the co-infection model, which is found to exhibit backward bifurcation. The impact of malaria and its treatment on the dynamics of cholera is further investigated. Secondly, we incorporate time dependent controls, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. We found that malaria infection may be associated with an increased risk of cholera but however, cholera infection is not associated with an increased risk for malaria. Therefore, to effectively control malaria, the malaria intervention strategies by policy makers must at the same time also include cholera control., (Copyright © 2014 Elsevier Inc. All rights reserved.)

The thermodynamic second law analysis is utilized to investigate the inherent irreversibility in an unsteady hydromagnetic generalized Couette flow with variable electrical conductivity in the presence of induced electric field. Based on some simplified assumption, the model nonlinear governing equations are obtained and solved numerically using semidiscretization finite difference techniques. Effects of various thermophysical parameters on the fluid velocity, temperature, current density, skin friction, the Nusselt number, entropy generation number, and the Bejan number are presented graphically and discussed quantitatively.

We derived and analyzed rigorously a mathematical model that describes the dynamics of malaria infection with the recruitment of infected immigrants, treatment of infectives and spray of insecticides against mosquitoes in the population. Both qualitative and quantitative analysis of the deterministic model are performed with respect to stability of the disease free and endemic equilibria. It is found that in the absence of infected immigrants disease-free equilibrium is achievable and is locally asymptotically stable. Using Pontryagin's Maximum Principle, the optimal strategies for disease control are established. Finally, numerical simulations are performed to illustrate the analytical results., (Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.)