Browsing by Author "Mureithi, Eunice"

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    Absolute-convective instability of a mixed forced-free convection boundary layer
    (Fluid Dynamics Research, 2010-08-18) Mureithi, Eunice; Denier, James
    A spatio-temporal inviscid instability of a mixed forced-free convection boundary layer is investigated. The base flow considered is the self-similar flow with free-stream velocity ue xn. Such a boundary-layer flow presents the unusual behaviour of generating a region of velocity overshoot, in which the streamwise velocity within the boundary layer exceeds the free-stream speed.A linear stability analysis has been carried out. Saddle points have been located and a critical value for the buoyancy parameter, G0c 3.6896, has been determined below which the flow is convectively unstable and above which the flow becomes absolutely unstable. Two spatial modes have been obtained, one mode being convective in nature and the other absolute. The convective-type spatial mode shows mode crossing behaviour at lower frequencies. Thermal buoyancy is shown to be destabilizing to the absolutely unstable spatial mode.
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    Absolute-convective instability of mixed forced-free convection boundary layers
    (2010-08) Mureithi, Eunice; Denier, James
    A spatio-temporal inviscid instability of a mixed forced-free convection boundary layer is investigated. The base flow considered is the self-similar flow with free-stream velocity ue ~ xn. Such a boundary-layer flow presents the unusual behaviour of generating a region of velocity overshoot, in which the streamwise velocity within the boundary layer exceeds the free-stream speed. A linear stability analysis has been carried out. Saddle points have been located and a critical value for the buoyancy parameter, G0c ≈ 3.6896, has been determined below which the flow is convectively unstable and above which the flow becomes absolutely unstable. Two spatial modes have been obtained, one mode being convective in nature and the other absolute. The convective-type spatial mode shows mode crossing behaviour at lower frequencies. Thermal buoyancy is shown to be destabilizing to the absolutely unstable spatial mode.
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    Analysis and Dynamically Consistent Numerical Schemes for the SIS Model and Related Reaction Diffusion Equation
    (2011-10) Lubuma, Jean M.S.; Mureithi, Eunice; Terefe, Yibeltal A.
    The classical SIS epidemiological model is extended in two directions: (a) The number of adequate contacts per infective in unit time is assumed to be a function of the total population in such a way that this number grows less rapidly as the total population increases; (b) A diffusion term is added to the SIS model and this leads to a reaction diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the model (a), with the disease-free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, traveling wave solutions are found for the model (b). Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous models are presented. In particular, for the model (a), a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided.
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    Analysis and dynamically consistent numerical schemes for the SIS model and related reaction diffusion equation
    (Proceedings of the 3rd International Conference on Applied Mathematics in Technical and Natural Sciences,(AMiTaNS’11), (Albena, Bulgaria), Institute of Physics-AIP Conf. Proc., 2011) Lubuma, Jean; Mureithi, Eunice; Terefe, Yibeltal
    The classical SIS epidemiological model is extended in two directions: (a) The number of adequate contacts per infective in unit time is assumed to be a function of the total population in such a way that this number grows less rapidly as the total population increases; (b) A diffusion term is added to the SIS model and this leads to a reaction diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the model (a), with the disease-free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, traveling wave solutions are found for the model (b). Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous models are presented. In particular, for the model (a), a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided.
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    Effects of buoyancy on the lower branch modes on a Blasius boundary layer
    (Journal of Discrete and Continuous Dynamical Systems series B, 2007-10) Mureithi, Eunice
    The effect of thermal buoyancy on the stability properties of lower branch Tollmein–Schlichting waves are investigated. At moderate values of thermal buoyancy the standard triple deck structure, which describes the evo- lution of such short wavelength instabilities in a buoyant boundary layer, is unaltered. The leading order eigenrelation is now a function of thermal buoy- ancy and from it we can derive the new dominant length- and time–scales for the instability in the case when the boundary layer is strongly buoyant. These new scales demonstrate that, in the case of strong wall cooling the lower branch structure is identical to the upper branch structure, thus suggesting that the curve of neutral stability may become closed at some large value of a Reynolds number. In the alternate limit of strong wall heating the evolution of a fixed frequency disturbance is governed by the linearized interactive boundary-layer equations; in this case wave–like disturbances cannot be described by any form of the quasi–parallel approximation theory.
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    Effects of buoyancy on the lower branch modes on a Blasius boundary layer
    (2007-09) Mureithi, Eunice
    The effect of thermal buoyancy on the stability properties of lower branch Tollmien-Schlichting waves are investigated. At moderate values of thermal buoyancy the standard triple deck structure, which describes the evolution of such short wavelength instabilities in a buoyant boundary layer, is unaltered. The leading order eigenrelation is now a function of thermal buoyancy and from it we can derive the new dominant length-and time-scales for the instability in the case when the boundary layer is strongly buoyant. These new scales demonstrate that, in the case of strong wall cooling the lower branch structure is identical to the upper branch structure, thus suggesting that the curve of neutral stability may become closed at some large value of a Reynolds number. In the alternate limit of strong wall heating the evolution of a fixed frequency disturbance is governed by the linearized interactive boundary-layer equations; in this case wave-like disturbances cannot be described by any form of the quasi-parallel approximation theory
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    Effects of buoyancy on the lower branch modes on a Blasius boundary layer
    (2007-10) Mureithi, Eunice
    The effect of thermal buoyancy on the stability properties of lower branch Tollmien-Schlichting waves are investigated. At moderate values of thermal buoyancy the standard triple deck structure, which describes the evolution of such short wavelength instabilities in a buoyant boundary layer, is unaltered. The leading order eigenrelation is now a function of thermal buoyancy and from it we can derive the new dominant length-and time-scales for the instability in the case when the boundary layer is strongly buoyant. These new scales demonstrate that, in the case of strong wall cooling the lower branch structure is identical to the upper branch structure, thus suggesting that the curve of neutral stability may become closed at some large value of a Reynolds number. In the alternate limit of strong wall heating the evolution of a fixed frequency disturbance is governed by the linearized interactive boundary-layer equations; in this case wave-like disturbances cannot be described by any form of the quasi-parallel approximation theory.
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    Effects of magnetic fields on an unsteady mixed convective boundary layer flow of an electrically conducting fluid with temperature dependent properties
    (Tanzania Journal of Science, 2018-07) Kitengeso, Raymond; Mureithi, Eunice; James, Makungu; Mango, John
    A mixed convective boundary layer flow of an electrically conducting fluid with temperature dependent properties over an inclined plate is investigated. The magnetohydrodynamic boundary layer governing equations are derived by using Boussinesq and boundary layer approximations. The equations are transformed to similarity form using a similarity transformation variable and the resulting boundary value problem is solved numerically. The effects of magnetic fields, unsteadiness, mixed convection and variable fluid properties on velocity and temperature in the boundary layer are analysed. The effects of pertinent parameters on skin friction and heat transfer are also analysed
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    Effects of over-harvesting and drought on a predator-prey system with optimal control
    (Open Journal of Ecology, 2018-08-31) Mapunda, Alanus; Mureithi, Eunice; Nyimvua, Shaban; Sagamiko, Thadei
    In this paper, a two species predator-prey model is developed where prey is affected by over-harvesting and drought and predator is affected by drought. The intention is to investigate the impact of over-harvesting and drought on predator-prey system, and suggest control strategies to alleviate the problem of loss of prey and predator species due to over-harvesting and drought. The control strategies suggested are creation of reserve areas with restriction of harvesting for controlling over-harvesting and construction of dams for mitigating drought effects. The results obtained from theoretical and numerical simulation of the predator-prey model with harvesting and drought without control strategies showed that, both harvesting and drought affect the predator- prey population negatively. However, the results obtained from numerical simulations of the model with control measures showed that, the use of control strategies one at a time encourages the increase of the prey and predator species to the optimal population size. Furthermore, the best result is obtained when control strategies, creation of reserve areas with restriction of harvesting and construction of dams are applied simultaneously.
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    Exact and numerical solutions of a fully developed generalized second-grade incompressible fluid with power-law temperature-dependent viscosity
    (2006-03) Soh, C. Wafo; Mureithi, Eunice
    We compute exact and numerical solutions of a fully developed flow of a generalized second-grade fluid, with power-law temperature-dependent viscosity (μ=θ-M), down an inclined plane. Analytical solutions are found for the case when M=m+1, m≠1, m being a constant that models shear thinning (m<0) or shear thickening (m>0). The exact solutions are given in terms of Bessel functions. The numerical solutions indicate that both the velocity and the temperature increase with decreasing Froude number and that there is a critical value of Fr below which temperature “overshoots” its free surface value of unity. This phenomena is not reported in the work of Massoudi and Phuoc [Fully developed flow of a modified second grade fluid with temperature dependent viscosity, Acta Mech. 150 (2001) 23–37.] for viscosity that depends exponentially on temperature.
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    Free convection flow past a impermeable wedge embedded in nanoflluid saturated porous medium with variable viscosity base fluid
    (Engineering Mathematics Letters, 2014-08) James, Makungu; Mureithi, Eunice; Kuznetsov, Dmitry
    The paper investigates a free convection flow past an impermeable wedge embedded in nanofluid saturated porous medium. The governing partial differential equations are transformed into a set of non-linear ordinary differential equations with the help of self-similarity technique and solved using standard numerical techniques. The numerical results for the dimensionless velocity, temperature and nanoparticles volume fraction as well as the reduced Nusselt and Sherwood numbers have been analyzed and presented for various parameters, namely, viscous dissipation parameter s, buoyancy ratio Nr, variable viscosity parameter qe, Brownian motion parameter Nb, thermophoresis parameter Nt , Lewis number Le and the angle of the wedge W. The results obtained shows that the Brownian motion, thermophoresis effects, buoyancy ratio and Lewis number significantly enhance the heat and mass transfer properties from the wall of the wedge to the fluid saturated porous medium.
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    The Impact of Human Mobility on HIV Transmission in Kenya
    (Plos One, 2015-11-24) Isdory, Augustino; Mureithi, Eunice; Sumpter, David
    Disease spreads as a result of people moving and coming in contact with each other. Thus the mobility patterns of individuals are crucial in understanding disease dynamics. Here we study the impact of human mobility on HIV transmission in different parts of Kenya. We build an SIR metapopulation model that incorporates the different regions within the country.We parameterise the model using census data, HIV data and mobile phone data adopted to track human mobility. We found that movement between different regions appears to have a relatively small overall effect on the total increase in HIV cases in Kenya. However, the most important consequence of movement patterns was transmission of the disease from high infection to low prevalence areas. Mobility slightly increases HIV incidence rates in regions with initially low HIV prevalences and slightly decreases incidences in regions with initially high HIV prevalence. We discuss how regional HIV models could be used in public-health planning. This paper is a first attempt to model spread of HIV using mobile phone data, and we also discuss limitations to the approach.
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    Local Non-Similarity Solutions for a Forced-Free Boundary Layer Flow with Viscous Dissipation
    (2010-11) Mureithi, Eunice; Mason, D. P.
    The boundary layer flow over a horizontal plate with power law vari-ations in the freestream velocity and wall temperature of the form U e ∼ x n and T w − T ∞ ∼ x m and with viscous dissipation, is studied. The boundary layer equa-tions are transformed to a dimensionless system of equations using a non–similarity variable ξ(x) and a pseudo-similarity variable η(x, y). The effects of the various pa-rameters of the flow on velocity and temperature distribution in the boundary layer, on the local skin friction and local heat transfer coefficients and on the non–similar terms, are investigated.
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    Local Non-similaritysolutions for a forced-free boundary layer flow with viscous dissipation
    (Mathematical and Computational Applications, 2010) Mureithi, Eunice; Mason, David
    The boundary layer flow over a horizontal plate with power law variations in the freestream velocity and wall temperature of the form Ue ∼ xn and Tw − T∞ ∼ xm and with viscous dissipation, is studied. The boundary layer equations are transformed to a dimensionless system of equations using a non–similarity variable (x) and a pseudo-similarity variable (x; y). The effects of the various parameters of the flow on velocity and temperature distribution in the boundary layer, on the local skin friction and local heat transfer coefficients and on the non–similar terms, are investigated.
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    mixed convection boundary layer flow over a vertical wall in a porous medium with exponentially varying fluid viscosity
    (Journal of Applied Mathematics and Physics, 2014-07) Mureithi, Eunice
    highly porous medium. The fluid viscosity is assumed to decrease exponentially with temperature.The boundary layer equations are transformed into a non-similar form using an appropriate nonsimilar variable ξ and a pseudo-similar variable η . The non-similar equations are solved using an efficient local non-similarity method. The effect of viscosity variation parameter on the heat transfer, skin friction and the velocity and temperature distribution within the boundary layer is investigated. The viscosity variation parameter, the viscous dissipation parameter and non-similarity variable are shown to have a significant effect on velocity and thermal boundary layer and also on the skin friction coefficient and heat transfer at the wall.
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    A mixed convection boundary layer flow over a vertical wall in a porous medium, with exponentially varying fluid viscosity
    (Scientific Research, 2014-07-03) Mureithi, Eunice;
    study investigates a mixed convection boundary layer flow over a vertical wall embedded in a highly porous medium. The fluid viscosity is assumed to decrease exponentially with temperature.The boundary layer equations are transformed into a non-similar form using an appropriate non-similar variable ξ and a pseudo-similar variable η . The non-similar equations are solved using an efficient local non-similarity method. The effect of viscosity variation parameter on the heat transfer, skin friction and the velocity and temperature distribution within the boundary layer is investigated. The viscosity variation parameter, the viscous dissipation parameter and non-similarity variable are shown to have a significant effect on velocity and thermal boundary layer andalso on the skin friction coefficient and heat transfer at the wall
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    A Mixed Convection Boundary Layer Flow over a Vertical Wall in a Porous Medium, with Exponentially Varying Fluid Viscosity
    (2013-12) Mureithi, Eunice
    This study investigates a mixed convection boundary layer flow over a vertical wall embedded in a highly porous medium. The fluid viscosity is assumed to decrease exponentially with temperature. The boundary layer equations are transformed into a non-similar form using an appropriate non- similar variable ξ and a pseudo-similar variable η. The non-similar equations are solved using an efficient local non-similarity method. The effect of viscosity variation parameter on the heat transfer, skin friction and the velocity and temperature distribution within the boundary layer is investigated. The viscosity variation parameter, the viscous dissipation parameter and non-simi- larity variable are shown to have a significant effect on velocity and thermal boundary layer and also on the skin friction coefficient and heat transfer at the wall
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    Non-standard discretizations of SIS epidemiological model with or without diffusion
    (Contemporary Mathematics, Mathematics of Continuous and Discrete Dynamical System, 2014) Lubuma, Jean; Mureithi, Eunice; Terefe, Yibeltal
    We design and investigate the reliability of various nonstandard finite difference (NSFD) schemes for SIS-type epidemiological models. The success of the study is due to an innovative use of Mickens’ rules of complex denominator functions and nonlocal approximation of nonlinear terms. For the classical SIS-ODE model, we construct for the first time a nonstandard Runge- Kutta method, which is shown to be of order four. We also consider two new NSFD schemes which faithfully replicate the property of the continuous model of having the value R0 = 1 of the basic reproduction parameter as a forward bifurcation: the disease-free equilibrium is globally asymptotically stable when R0 < 1; it is unstable when R0 > 1 and there appears a unique locally asymptotically stable endemic equilibrium in this case. The latter schemes are further used to derive NSFD schemes that are dynamically consistent with the positivity and boundedness properties of the SIS-diffusion model for the spatial spread of disease. Numerical simulations that support the theory are provided.
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    Nonstandard Discretizations of the SIS Epidemiological Model with and without Diffusion
    (2013-12) Lubuma, Jean M.S.; Mureithi, Eunice; Terefe, Yibeltal
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    On the Boundary Layer Flow over a Moving Surface in a Fluid with Temperature-Dependent Viscosity
    (2012-12) Mureithi, Eunice; Mwaonanji, J. J.; Makinde, Oluwole D.
    This paper examines a boundary layer flow over a continuously moving heated flat surface with velocity in a streaming flow with velocity and with temperature dependent viscosity,. The momentum and the energy equations are coupled through the viscous dissipation term. The coupled boundary layer equations are transformed into a self-similar form using an appropriate similarity variable. An efficient numerical technique is used to solve the self-similar boundary layer equations. It is shown that at low enough values for the velocity ratio, an increase in viscous dissipation enhances greatly the local heat transfer leading to temperature overshoots adjacent to the wall. The viscosity variation parameter is shown to have significant effects on the temperature dependent viscosity and the velocity and temperature distribution within the boundary layer.