Shirley Abelman

We formulate and analyze a deterministic mathematical model for the transmission dynamics of schistosomiasis with treatment of both humans and bovines and mollu-sciciding of the contaminated environment. The model effective reproduction number is derived and analytical results show that the disease-free and endemic equilibria are both locally and globally asymptotically stable. Pontryagin’s Maximum Principle which uses both Lagrangian and Hamiltonian principles with respect to a time-dependent constant is used to establish the existence of the optimal control problem and to derive the necessary conditions for optimal control of the disease. Mollusciciding of the contaminated environment has a major impact on disease control. However, combining it with treatment could help mitigate the spread of the disease compared to applying each control measure individually. Numerical simulations are performed to support theoretical results.

The purpose of this paper is to examine the effect of magnetic field on ferrofluid convective mode with radiation. Viscosity of Fe₃O₄ ferrofluid is considered as a function of magnetic field. Solutions of the governing equations are obtained by a powerful numerical method, namely, control volume finite element method (CVFEM). Roles of radiation parameter (Rd), number of undulations (N), Fe₃O₄–water volume fraction (ϕ), Hartmann (Ha) and Rayleigh numbers are illustrated graphically. A correlation for Nu_ave is extracted. The inner wall temperature decreases with increasing buoyancy forces, but increases with increasing Rd and Ha. Also increasing Rd results in increasing nanofluid motion. This influence is more evident when convection flow is dominant. As nanofluid temperature increases, the nanofluid begins moving from the warm surface to the outer one and dropping along the circular cylinder. At low Rayleigh number, conduction is more significant than convection. |Ψ_max| increases as buoyancy force increases and it decreases as the Lorentz force increases. As Hartmann number increases, the center of the vortices moves to x = 0. As Ra increases, convection becomes stronger. Thus, |Ψ_max| and temperature gradient increase with increasing Ra. As N increases, the distortion of isotherms reduces and vortices become weaker. Increasing Hartmann number results in a reduction in the thermal plume and the heat transfer mechanism changes from convection to conduction. Nusselt number decreases with increasing N. Nu decreases with increasing Lorentz force. At N = 5 , increasing the Lorentz force causes the main vortices to convert into three smaller ones. As the Lorentz force increases, the two upper vortices merge together and the thermal plume vanishes. The number of extrema in the Nu_loc profile matches the existence of the thermal plume and the number of undulations. Nu_ave increases with increasing Rd. As buoyancy forces increase, the temperature decreases and in turn Nu_ave increases with increasing Ra. Nanofluids are an innovative way to enhance radiation heat. In this paper, MHD Fe₃O₄–water nanofluid natural convection with radiation source term is examined. Magnetic field-dependent (MFD) viscosity is considered. Using the CVFEM, numerical simulations are carried out for various values of the radiation parameter (Rd = 0 to 0.8), volume fraction of Fe₃O₄–water (ϕ = 0 to 0.04), Rayleigh number (Ra = 10³, 10⁴ and 10⁵), number of undulations (N = 3,4 and 5) and Hartmann number (Ha = 0 to 40).

The problem of forced convection in a channel filled with a nanofluidsaturated porous medium is investigated, numerically. A finite difference Computational Fluid Dynamics (CFD) model with structured uniform grid system is employed to solve the momentum and energy equations. In modeling flow in the channel, the effects of flow inertia, variable porosity and Brinkman friction are taken into account. Studies are carried out for different nanoparticles with different volume fractions in the range 0%-4% and different nanoparticle diameters. Comparison made between our numerical and semi analytical Differential Transform Method (DTM) results with those in previous published research is found to be appropriate. Results show that increasing either nanoparticls volume fraction or pressure gradient parameter improves heat transfer. Further, for large quantities of nanoparticle concentration and pressure gradient, the channeling phenomenon is intensified.

Subcooled flow boiling has many industrial applications such as nuclear engineering and energy generation. Study of subcooled flow boiling provides copious information about vapor void fraction on the wall and also critical heat flux. In this paper, subcooled flow boiling in a vertical corrugated channel is investigated numerically. The two-fluid model and finite volume method are employed. Transport turbulence is also considered. To determine turbulence, we apply the transport shear stress model for the liquid phase and the laminar model for the vapor phase. Obtained results show that increasing nanoparticles in the base fluid reduces the vapor void fraction; however, wall temperature increases due to decreasing heat flux evaporation. When increasing wavy amplitude, then both wall temperature and vapor void fraction increase. Increasing water temperature on the wall decreases its density and fluid velocity increases in the vicinity of the wall since momentum of the flow is constant in the transverse cross section of the channel. In addition, variations of velocity due to variations of channel cross section result in increasing vapor void fraction in converging areas of the corrugated channel.

This research explores the impact of entropy generation on stagnation point flow of a non-Newtonian Williamson nanofluid over a moving plate with activation energy and binary chemical reaction. For energy activation a modifi ed Arrhenius function is invoked. Suitable transformation variables are used to simplify the governing flow problem to obtain self-similar solutions. Numerical solutions for temperature distribution, fluid velocity, concentration of nanoparticles, and entropy profile are established and examined using the shooting method. The results reveal that the velocity profile reduces due to an increasing Williamson parameter, whereas the temperature distribution and concentration of nanoparticles are enhanced with larger values of the Williamson parameter. It is also found that the concentration boundary layer increases due to the activation energy and decreases due to the reaction rate and temperature differences. Moreover, the entropy generation profile is higher for a non-Newtonian fluid compared to a Newtonian one. The results obtained from the present methodology are validated when compared with the data from articles in the existing literature. It gives excellent agreement with the predecessors. The expressions for the Nusselt and Sherwood numbers are also taken into consideration and presented in graphs and tables.

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An analytical investigation into compressible gas flow with slight rarefactions through the insect trachea and tracheoles during the closed spiracle phase is undertaken, and a complete set of asymptotic analytical solutions is presented. We first obtain estimates of the Reynolds and Mach numbers at the channel terminal ends where the tracheoles directly deliver respiratory gases to the cells, by comparing the magnitude of the different forces in the compressible gas flow. The 2D Navier–Stokes equations with a slip boundary condition are used to investigate compressibility and rarefied effects in the trachea and tracheoles. Expressions for the velocity components, pressure gradients and net flow inside the trachea are then presented. Numerical simulations of the tracheal compressible flow are performed to validate the analytical results from this study. This work extends previous work of Arkilic et al. (J Microelectromech Syst 6(2):167–178, 1997 ) on compressible flows through a microchannel. Novel devices for microfluidic compressible flow transport may be invented from results obtained in this study.

In this article, we introduce and investigate a new class of non-Bazilevič functions with respect to k-symmetric points defined by using fractional q-calculus operators and q-differentiation. Several interesting subordination results are derived for the functions belonging to this class in the open unit disc. Furthermore, we point out some new and known consequences of our main result.