This work investigates the effects of combined variable viscosity and thermal conductivity, nonlinear radiation and non-Darcian porous medium on a boundary layer MHD Casson nanofluid flow over a vertical flat plate with convective heating and velocity slip boundary conditions. The governing transport nonlinear partial differential equations and the boundary conditions are non-dimensionalized. The resulting system of coupled partial differential equations is then reduced to a set of coupled nonlinear ordinary differential equations using similarity transformation. Galerkin weighted residual method (GWRM) is then employed to solve the resulting set of equations. Numerical results are obtained for dimensionless velocity, temperature and nanoparticle volume fraction (nanoparticle concentration). It is found that the velocity increases, while both temperature and nanoparticle volume fraction decrease with increased values of variable thermal conductivity and viscosity. Comparisons are carried out with published data in the literature thereby validating the numerical results. An excellent agreement is observed. Furthermore, this present study can find applications in the process involving nanofluid operations.
The formulation of mathematical models using differential equations has become crucial in predicting the evolution of viral diseases in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China, which causes a severe and potentially fatal respiratory syndrome. Since then, it has been declared a pandemic by the World Health Organization and has spread around the globe. A reaction–diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process, in which different substances are transformed, and a diffusion process, which causes their distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic using the bias of reaction–diffusion equations. Both local and global asymptotic stability conditions for the equilibria were determined using a Lyapunov function, and the nature of the stability was determined using the Routh–Hurwitz criterion. Furthermore, we consider the conditions for the existence and uniqueness of the model solution and show the spatial distribution of the model compartments when the basic reproduction rate R0<1 and R0>1. Thereafter, we conducted a sensitivity analysis to determine the most sensitive parameters in the proposed model. We demonstrate the model’s effectiveness by performing numerical simulations and investigating the impact of vaccination, together with the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. Therefore, we offer to the public health policymakers a better understanding of COVID-19 management.
The present study concerns the natural convective heat generating/absorbing, radiative magnetohydrodynamic, oscillatory fluid flow through a vertical porous channel with slip and temperature jump. The effect of Joule dissipation is taken into consideration while it is assumed that the flow is fully developed. The differential transforms method(DTM) is employed to solve the system of non-linear ordinary differential equations that is obtained from the non-linear partial differential equations governing the flow. Semi analytical solutions of the steady and unsteady part of the flow in the slip flow regime through a vertical porous channel are obtained. The effects of various flow parameters on the velocity and temperature profiles as well as Nusselt and skin friction are presented graphically and discussed. An excellent agreement between the results of this article and those available in the literature validated the presented approach.
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