The paper carries out an analysis on the momentum, heat and mass transfer characteristics in an incompressible magnetohydrodynamic non-Newtonian boundary flow of a viscoelastic fluid over a stretching sheet in the presence of thermal diffusion and chemical reaction. The partial differential equations governing the flow as well as heat and mass transfer features are converted into highly non-linear coupled ordinary differential equations by similarity transformations. The resulting differential equations are solved by using a shooting technique with fifth-order Runge-Kutta-Fehlberg integration scheme. The influence of magnetic interaction, variable thermal conductivity, viscoelastic, variable fluid viscosity, heat source/sink rate of chemical reaction, themal radiation and thermal diffusion parameters as well as Prandtl and Schmidt numbers are analyzed for velocity, temperature and concentration profiles. The wall shear stress, wall temperature and concentration gradients are also investigated for the problem. The fluid viscosity varies as an inverse function of velocity while the thermal conductivity assumes a linear and an inverse function of temperature and concentration respectively. The study shows that the thermal diffusion and thermal radiation parameters have opposite effects on the skin friction coefficient and wall concentration gradient. However, the rate of chemical reaction has similar influence on the skin friction coefficient and wall temperature gradient.

Abstract This research attempted to investigate the effects of double dose vaccination in a non-linear mathematical model of Covid-19 infections with special compartments class termed first and second dose vaccination. The basic reproduction number was obtained, the stability of the model was analyzed, and the sensitivity analysis was also carried out. Of interest is the numerical simulation of the model where the impacts of contact rate, first and second dose vaccination were studied. The obtained results recommended how to control the corona virus keeping in mind the contact rate and vaccination. Keywords:   Covid-19, Double dose Vaccination, Basic Reproduction Number, Global Stability

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Abstract:We consider the self-similar solution of non-linear diffusion equation with convection term. We examine the existence and uniqueness of solution of the problem. The numerical result is presented as concentration profile for various values of m, the diffusion index.

This paper investigates a chemically reactive Magnetohydrodynamic fluid flow with heat and mass transfer over a permeable surface taking into consideration the buoyancy force, injection suction, heat source sink and thermal radiation. The governing momentum, energy and concentration balance equations are transformed into a set of ordinary differential equations by method of similarity transformation and solved numerically by Runge-Kutta method based on shooting technique. The influence of various pertinent parameters on the velocity, temperature, concentration fields are discussed graphically. Comparison of this work with previously published work on special cases of the problem was carried out and the results are in excellent agreement. Results also show that the thermo physical parameters in the momentum boundary layer equations increase the skin friction coefficient but decrease the momentum boundary layer. Fluid suction/injection and Prandtl number increase the rate of heat transfer. The order of chemical reaction is quite significant and there is a faster rate of mass transfer when the reaction rate and Schmidth number are increased.