RP-Department of Mathematics
http://ir-library.ku.ac.ke/handle/123456789/1384
Mon, 05 Jun 2023 13:58:54 GMT2023-06-05T13:58:54ZDynamics of Williamson Fluid over an Inclined Surface Subject To Coriolis and Lorentz Forces
http://ir-library.ku.ac.ke/handle/123456789/25136
Dynamics of Williamson Fluid over an Inclined Surface Subject To Coriolis and Lorentz Forces
Juma, Belindar A; Oke, Abayomi S.; Mutuku, Winifred N; Ariwayo, Afolabi G; Ouru, Olum J
: Enhancement of heat and mass transfer heat over rotating plates in industrial processes is a major
area of research recently due to several attempts to find cost-effective means. In this study, the flow of
Williamson fluid is considered because of its ability to exhibit pseudo-plastic and shear-thinning properties. A
theoretical analysis of the effect of Coriolis force and the angle inclination on the magnetohydrodynamic flow
of Williamson fluid is considered. The flow is modelled by including Coriolis force and angle of inclination
in the Navier-Stokes equation. By adopting a suitable similarity transformation, the system of governing
partial differential equations is reduced to a system of ordinary differential equations which are solved using
bvp4c solver in MATLAB. The simulations are depicted as graphs and it is found that velocity increases with
increasing Coriolis force while it decreases as the magnetic field strength and inclination angle increases.
Also, the local skin friction reduces as the rotation increases. Hence, to boost heat and mass transfer in the
flow of fluid over a rotating inclined plate in a magnetic field, it is recommended that rotation should be
increased and magnetic field strength should be reduced.
Article
Sat, 01 Jan 2022 00:00:00 GMThttp://ir-library.ku.ac.ke/handle/123456789/251362022-01-01T00:00:00ZModelling Turbulence Using the Staggered Grid and Simplec Method
http://ir-library.ku.ac.ke/handle/123456789/22697
Modelling Turbulence Using the Staggered Grid and Simplec Method
Kimunguyi, J. K.; Gatheri, F. K.; Awuor, K. O.
In a natural convection, local density
differences and a resulting pressure gradient accelerate
the fluid. In this paper a numerical study of a turbulent,
natural convection problem is performed with an
incompressible fluid in a rectangular enclosure. At the
heated wall, the temperature distribution is a function
of temperature gradients. The objective of this study is
to conduct a numerical investigation of turbulent
natural convection in a 3-D cavity using the staggered
grid and the SIMPLEC method. The statisticalaveraging process of the mass, momentum and energy
governing equations introduces unknown turbulent
correlations into the mean flow equations which
represent the turbulent transport of momentum, heat
and mass, namely Reynolds stress () and heat flux (),
which are modeled using k- SST model. The ReynoldsAveraged Navier-stokes (RANS), energy and k- SST
turbulent equations are first non-dimensionalized and
the resulting equations are discretized using a staggered
and solved using SIMPLEC. From the results, both the
experimental data and simulation using the staggered
grid and SIMPLEC return a non-dimensional
temperature of 0.5 at the core of the cavity and almost
zero towards the cold and the natural turbulence flow is
responsible for temperature distribution. Further,
convective mass exchange is dominant in the centre of
the enclosure. The investigated Rayleigh number of this
study lies at Ra = 1.58.
A research article published in International Journal of Innovative Science and Research Technology
Wed, 01 Jan 2020 00:00:00 GMThttp://ir-library.ku.ac.ke/handle/123456789/226972020-01-01T00:00:00ZMathematical Analysis of the Dynamics of COVID-19 in Africa under the Influence of Asymptomatic Cases Andre-Infection
http://ir-library.ku.ac.ke/handle/123456789/22506
Mathematical Analysis of the Dynamics of COVID-19 in Africa under the Influence of Asymptomatic Cases Andre-Infection
Abayomi, Samuel Oke; Oluwafemi, Isaac Bada; Ganiyu, Rasaq; Adodo, Victoria
Coronavirus pandemic (COVID-19) hit the world in December 2019, and only less than 5% of the
15 million cases were recorded in Africa. A major call for concern was the significant rise from 2%
in May 2020 to 4.67% by the end of July 15, 2020. This drastic increase calls for quick intervention
in the transmission and control strategy of COVID-19 in Africa. A mathematical model to
theoretically investigate the consequence of ignoring asymptomatic cases on COVID-19 spread
in Africa is proposed in this study. A qualitative analysis of the model is carried out with and
without re-infection, and the reproduction number is obtained under re-infection. The results
indicate that increasing case detection to detect asymptomatically infected individuals will be
very effective in containing and reducing the burden of COVID-19 in Africa. In addition, the fact
that it has not been confirmed whether a recovered individual can be re-infected or not, then
enforcing a living condition where recovered individuals are not allowed to mix with the
susceptible or exposed individuals will help in containing the spread of COVID-19
A research article published in Mathematical Methods in the Applied Sciences
Fri, 01 Jan 2021 00:00:00 GMThttp://ir-library.ku.ac.ke/handle/123456789/225062021-01-01T00:00:00ZTowards Understanding Crime Dynamics in a Heterogeneous Environment: A Mathematical Approach
http://ir-library.ku.ac.ke/handle/123456789/22305
Towards Understanding Crime Dynamics in a Heterogeneous Environment: A Mathematical Approach
White, Jane K. A.; Campillo-Funollet, Eduard; Nyabadza, Farai; Cusseddu, Davide; Kasumo, Christian; Imbusi, Nancy Matendechere; Juma, Victor Ogesa; Meir, A. J.; Marijani, Theresia
Crime data provides information on the nature and location of the crime but, in
general, does not include information on the number of criminals operating in a region. By
contrast, many approaches to crime reduction necessarily involve working with criminals
or individuals at risk of engaging in criminal activity and so the dynamics of the criminal
population is important. With this in mind, we develop a mechanistic, mathematical model
which combines the number of crimes and number of criminals to create a dynamical system.
Analysis of the model highlights a threshold for criminal efficiency, below which criminal
numbers will settle to an equilibrium level that can be exploited to reduce crime through
prevention. This efficiency measure arises from the initiation of new criminals in response
to observation of criminal activity; other initiation routes - via opportunism or peer pressure
- do not exhibit such thresholds although they do impact on the level of criminal activity
observed. We used data from Cape Town, South Africa, to obtain parameter estimates and
predicted that the number of criminals in the region is tending towards an equilibrium
point but in a heterogeneous manner - a drop in the number of criminals from low crime
neighbourhoods is being offset by an increase from high crime neighbourhoods.
An Article Published in Journal of Interdisciplinary Mathematics
Fri, 01 Jan 2021 00:00:00 GMThttp://ir-library.ku.ac.ke/handle/123456789/223052021-01-01T00:00:00Z