iosr-Jm   Volume-9 ~ Issue-2

Abstract: The surface instability of Kelvin-Helmholtz type in a couple stress fluid layers bounded above by a porous layer and below by a rigid surface is investigated using linear stability analysis. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of KHI in presence of couple stress fluid. In order to observe the effect of boundary layer applying the Beavers-Joseph (BJ) slip condition. The dispersion relation is derived using suitable boundary and surface conditions and the results are discussed through graphically. The couple stress fluid is found to be stabilizing effect and the influence of the various parameters of the problem on the interface stability is thoroughly analyzed.

Key Words: Couple-stress fluid, KHI, B-J Condition, dispersion relation, porous media.

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Abstract: In this paper we study an epidemic model with immigration and non-monotone incidence rate under limited resources for treatment is proposed to understand the effect of the capacity for treatment. It is assumed that the treatment rate is proportional to the number of patients as long as this number is below a certain capacity and it becomes constant when that number of patients exceeds this capacity. Global analysis is used to study the stability of the disease free equilibrium and endemic equilibrium. It is shown that this kind of treatment rate leads to the existence of multiple endemic equilibria where the basic reproduction number plays a big role in determining this stability.

Keywords: Endemic, Global Stability, Non-monotone incidence rate, Reproduction number, Treatment rate.

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Abstract: This paper is concerned with the development of non-polynomial spline function approximation method to obtain numerical solution of ordinary and partial differential equations. The parametric spline function which depends on a parameter p  0, is discussed which reduced to the ordinary cubic spline [1] when the parameter p  0. The numerical method is tested by considering an example. Keywords : Cubic spline function, Parametric spline function, finite difference method

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Abstract: We considered the equation of population dynamics and interacting growth of Clarias glariepinus (catfish) in a concrete pond. We proposed a logistic model using a combination of Euler and Runge- Kutta methods as the "best" approach in approximating the increases in the yield of the fish according to time. The results obtained showed that it allowed a choice of optimal regimes of aeration, feeding and fertilization of the fish for different climatic conditions in order to maximize the yield. We concluded that these approaches were the best in determining maximum yields of the fish in a concrete pond when tested for growth, stocking densities and harvesting processes.

Keywords: Population Dynamics and Growth, Clarias glariepinus, Runge- Kutta method, Euler's method, Logistic model.

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