MST-Department of Mathematics

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Analysis of mass and heat transfer due to a stagnation point flow of casson fluid past a stretching/ shrinking sheet
(Kenyatta University, 2025-01) Nzomo, Francis Mutuku
Non-Newtonian nanofluid flow phenomena are predominant in various chemical and metal processing applications, featuring shear-stress-strain relationships distinct from Newtonian fluids. Casson nanofluid, a prominent non-Newtonian fluid, exhibits plastic flow with thinning characteristics, resembling rod-like solids. This study investigates the mass and heat transfer characteristics of Casson nanofluid in a stagnation point flow past a stretching/shrinking sheet. Casson fluid, known for its unique shear-thinning property and yield stress behaviour, finds applications in diverse industries, including polymer engineering and manufacturing. Investigating the boundary layer flow due to a shrinking/stretching plate is pertinent to numerous industrial processes such as polymer plate extraction, paper production, and glass-fiber manufacturing. The methodology involves non-dimensionalizing governing equations, resulting in a system of Ordinary Differential Equations (ODEs) solved using MATLAB bvp4c with the RK4 shooting method. Simulation results demonstrate the effects of varying parameters on fluid density, temperature, and concentration profiles. Analysis reveals that an increase in the Casson fluid parameter correlates with decreased concentration and temperature, reflecting the rheological properties of Casson fluids. Brownian motion enhances thermal mixing, raising temperature, while thermophoretic effects contribute to non-uniform concentration distribution. A higher Schmidt number strengthens the diffusive effect, leading to decreased concentration. These findings underscore the significant impact of Casson fluid parameter, Brownian parameter, thermophoretic parameter, and Schmidt number variations on concentration, temperature, and fluid velocity.
Mathematical Modelling Of Malaria Disease in Busia County, Kenya
(Kenyatta University, 2025-02) Mogambi, Nyasuguta Lucy
Malaria remains a leading global health challenge, causing millions of deaths annually, primarily through the bite of infected female Anopheles mosquitoes. In Kenya, Busia County records the highest malaria prevalence at 37%, yet it has often been excluded from mathematical modeling studies. Traditional SEIR models commonly used in malaria research fail to capture the persistence of asymptomatic Plasmodium parasites in individuals who have recovered from the disease. This study introduces an enhanced SIRSp model that incorporates this asymptomatic subpopulation to better understand malaria dynamics in Busia County. The model assumes a constant infection rate influenced by both susceptible and infected individuals, and its mathematical analysis yields reproduction numbers for humans and mosquitoes. Stability analysis of the disease-free equilibrium point indicates the feasibility of eradicating malaria in Busia County under certain conditions. Numerical simulations demonstrate that higher infection rates significantly amplify the prevalence of malaria, whereas improving recovery rates reduces infections among humans and mosquitoes while marginally increasing the pool of susceptible individuals. These results provide valuable insights into the dynamics of malaria transmission and emphasize the importance of tailored interventions for effective disease management in endemic regions.
A Study of MHD Fluid Flow Bounded by two Parallel Vertical Plates in A Porous Media with Heat Transfer
(Kenyatta University, 2025-05) Kariuki, John King’ori
The study investigated a Newtonian Magneto-hydrodynamic fluid flow bounded by two parallel vertical plates in a porous media with heat transfer. The fluid was considered to be flowing uniformly in the x-direction. The parallel vertical plates are impermeable and a transverse magnetic field is applied perpendicular to the plates in the positive y-direction. The plates are heated and kept at constant temperature 𝑇𝑇𝑤𝑤 and the distance between the two plates was varied. The fluid and the porous matrix are approximated to have the same temperature, 𝑇𝑇𝑓𝑓 . The effect of varying Darcy number, Hartmann number, Prandtl number, and Reynolds number on velocity and temperature profiles was discussed. The coupled non-linear PDE governing the fluid flow were non-dimensionalized to obtain a dimensionless equation. The resulting equation was discretized using the finite difference method to obtain non-linear algebraic equations which were solved using MATLAB. The obtained results were presented in graphs and then discussed. It was observed that velocity profile decreased when Hartmann number or Reynolds number was increased. On the other hand, velocity profile increased after increasing Prandtl number or Darcy number. It was also observed that temperature profile decreased when Hartmann number or Prandtl number was increased. On the other hand, temperature profile increased when Reynolds number or Darcy number was increased. These results have applications in aerodynamic heating and motor vehicle cooling.
Thermal Applications of Carbon Nanotubes in Polyethylene Glycol in The Presence of Magnetic Field on Electronic Devices
(Kenyatta University, 2025-06) Muteti, Winfred Wandia
In this study, the thermal management of electronic devices, specifically Central Processing Units (CPUs), using carbon nanotubes (CNT) dispersed in polyethylene glycol (PEG-400) under the influence of a magnetic field was studied. The research optimized cooling performance by enhancing efficiency, extending the operating temperature range, and improving the reliability of such systems. The study modeled impingement cooling using a Darcy-Brinkman-Forchheimer approach and considered the effects of viscous dissipation. The governing nonlinear partial differential equations were converted into nonlinear ordinary differential equations (ODEs) by utilizing similarity variables and solved using MATLAB’s bvp4c. CNT-PEG-400 nanofluid flowing via a porous metal foam CPU cooler with a fan and a heated CPU surface was simulated. The investigation of key parameters like Hartmann number, Reynolds number, Darcy number, and porosity revealed that increasing the Darcy number significantly enhances heat transfer. The Hartmann number’s effect varies with porosity, where stronger magnetic fields are advantageous for highly porous metal foams, ultimately improving cooling efficiency. CNTs increase both the density and viscosity of PEG-400, leading to enhanced heat transfer characteristics, which improve overall cooling performance. These findings contribute to optimizing cooling strategies for CPUs and other electronic devices, especially when using CNT-PEG-400 nanofluids in the presence of magnetic fields.
A prey predator conservation model for a fishery with a reserve area and prey refuge: a study of Lake Victoria
(Kenyatta University, 2024-09) Wasike, Silas Were
Overfishing and predation are causing loss of species in most fisheries worldwide and now most endemic fish species are on the brink of extinction. This threatens biodiversity and sustainability of these fisheries. Despite the many mitigation measures by the Kenyan government to address the decline of fish species in Lake Victoria, the decline continues unabated. A major decline has been observed in haplochromines (fulu) due to predation by Nile perch (mbuta) and the species is now in danger of extinction. There is need for research to enrich conservation practices for the fishery. To understand the preypredator dynamic system of the Nile perch and haplochromines, we have formulated and analyzed a two species prey-predator conservation model with a reserve area and prey refuge. The model is formulated using a logistic nonlinear differential equation which describes a self-limiting growth of a biological population and incorporates Holling type II functional response of the predator towards the prey. The fishery ecosystem is divided into two zones, the protected reserved area and the unreserved area. Scaling down the parameters of the equations was done to reduce the number of parameters for easier analysis of equilibrium points. The study aims to determine the positivity and boundedness of the model, the stability of equilibrium points, conditions for their existence and the effect of a reserve area on the stability of the system. Analysis of the model has been done, equilibrium points and conditions for their existence determined. The stability of equilibrium points both locally and globally has been established. To assess the effect of a reserve area on stability of the population of the system, numerical simulations in MATLAB using known parameters was done. This was done by variation of some parameters and the time series solutions drawn. The results showed that the reserved area has a stabilizing effect on the prey-predator dynamic system
A Quantile Regression Approach to Modeling and Predicting Geothermal Well Drilling Costs
(Kenyatta University, 2025-06) Kizambo, Eric Kachila
Several factors influence cost of drilling a geothermal well. The most common ones consist drilled depth, type of drilling method used, drilling time, non-productive time among others. Accurate cost estimation is critical for a project’s planning and financial viability. In current practice, most drilling cost models estimate cost solely as a function of drilled depth. However, these models often overlook other critical factors such as drilling time and non-productive time that significantly influence drilling costs. Consequently, the models relied on do not explain the full range of variation in cost. Ordinary Least Squares (OLS) regression has been a widely used method for modeling drilling cost as a function of explanatory variables. However, the estimators derived from OLS are highly sensitive to outliers, which can significantly distort predictions and reduce the model’s robustness in the presence of non-normal error distributions. The objective of this study was to develop a robust model for estimating geothermal well drilling costs by incorporating key predictors that were previously overlooked using a quantile regression approach. The study accounted for the varying impact of predictors across different points of the cost distribution. This method offered a more comprehensive understanding of cost drivers and provided robust estimates that are less sensitive to outliers compared to traditional mean-based regression techniques like Ordinary Least Squares (OLS). Data from the Menengai geothermal project in Nakuru county was used in the study. The data comprised drilling data of 52 wells drilled between 2011 and 2019. The findings reveal significant correlations between drilling cost and both drilling time and non-productive time. Quantile regression analysis demonstrated that the impact of these covariates varies across the 0.25, 0.5, and 0.75 quantiles, with non-productive time exerting a more substantial influence on higher-cost wells. Compared to traditional Ordinary Least Squares (OLS) regression, quantile regression provides a more detailed understanding of the cost drivers. The model's coefficients for drilling time and non-productive time at different quantiles indicate that Drilling cost sensitivity varies, underscoring the importance of using quantile regression for more accurate and tailored cost estimations in geothermal drilling. The proposed model outperforms the traditional Ordinary Least Squares (OLS) approach, offering improved predictive power and more nuanced insights into cost determinants.
Analysis of Double Stratification on Magneto-Hydrodynamic Boundary Layer Flow and Heat Transfer of an Eyring-Powell Fluid
(Kenyatta University, 2022-03) Wekesa, Waswa Simon
Eyring-Powell fluids play important roles in many industrial and engineering applications. As technology advances, the demand for efficient and effective heat transfer systems,minimally available, increases.Fluids are being improved time after time to increase the efficiency of heat dissipation systems.Eyring-Powell, one of the fluid on advancement, has numerous applications in life such as coolant in diesel engines, heat exchangers, electronic circuits, nuclear reactors, manufacture of syrups, gels ,liquid medicines , yoghurt and the design of shapes of aircrafts and cars in that order. Among the non-Newtonian’s possessing varying characteristics is EyringPowel fluid.Due to the demand, mathematicians have formulated unlike models to describe fluid by appropriate substitution into Navier-Stokes equations. The complexity and nature of the equations attract numerous investigations. The current work aims at filling the demand gap by numerically analysing the effect of double stratification of magneto-hydro-dynamic boundary layer flow and heat transfer of a steady Eyring Powell fluid flow. The nonlinear differential equations governing the flux with appropriate boundary conditions were formulated, transformed to linear differential equations by appropriate similarity transformations. The simulation of predictor-corrector method in MATLAB odel13 function invoked with bvpSc call numerically solved the equations. The impacts of various parameters on the fluid velocity and temperature were illustrated graphically. Increasing the magnetic field strength, thermo-phoresis, thermal stratification, and solutal stratification leads to speed, temperature, Sherwood number, Nusselt number, and skin friction decrease. An increase in the magnetic field strength, thermal stratification, solutal stratification, and thermo-phoresis increases the fluid concentration. It is clear that an increase in mangetic,thermal stratification and solutal stratification reduces the velocity and temperature of the fluid under the study.
Analysis of Double Stratification on Magneto-Hydrodynamic Boundary Layer Flow and Heat Transfer of an Eyring-Powell Fluid
(Kenyatta University, 2022-03) Wekesa, Waswa Simon
Eyring-Powell fluids play important roles in many industrial and engineering applications. As technology advances, the demand for efficient and effective heat transfer systems,minimally available, increases.Fluids are being improved time after time to increase the efficiency of heat dissipation systems.Eyring-Powell, one of the fluid on advancement, has numerous applications in life such as coolant in diesel engines, heat exchangers, electronic circuits, nuclear reactors, manufacture of syrups, gels ,liquid medicines , yoghurt and the design of shapes of aircrafts and cars in that order. Among the non-Newtonian’s possessing varying characteristics is EyringPowel fluid.Due to the demand, mathematicians have formulated unlike models to describe fluid by appropriate substitution into Navier-Stokes equations. The complexity and nature of the equations attract numerous investigations. The current work aims at filling the demand gap by numerically analysing the effect of double stratification of magneto-hydro-dynamic boundary layer flow and heat transfer of a steady Eyring Powell fluid flow. The nonlinear differential equations governing the flux with appropriate boundary conditions were formulated, transformed to linear differential equations by appropriate similarity transformations. The simulation of predictor-corrector method in MATLAB odel13 function invoked with bvpSc call numerically solved the equations. The impacts of various parameters on the fluid velocity and temperature were illustrated graphically. Increasing the magnetic field strength, thermo-phoresis, thermal stratification, and solutal stratification leads to speed, temperature, Sherwood number, Nusselt number, and skin friction decrease. An increase in the magnetic field strength, thermal stratification, solutal stratification, and thermo-phoresis increases the fluid concentration. It is clear that an increase in mangetic,thermal stratification and solutal stratification reduces the velocity and temperature of the fluid under the study.
Mathematical modelling on impact of interventions in the spread of covid-19 in Kenya
(Kenyatta University, 2022-06) Mwangi, Lucas Muiruri
Magnetohydrodynamic Bioconvection Flow of Walter’s – B Nanofluid Over an Exponentially Stretching Surface
(Kenyatta University, 2024-05) Kipolelo, Aziz Mohamed
Abstract
Ratio Estimator of Population Mean in Simple Random Sampli
(Kenyatta University, 2022-11-02) sheryl, Kosgey Chebet
This study considers the problem of estimating the population mean in Simple Random Sampling. One key objective of any statistical estimation process is to find estimates of parameter of interest with more efficiency. Incorporating additional information in the estimation procedure yields enhanced estimators. Ratio estimation improves accuracy of the estimate of the population mean by incorporating prior information of a supporting variable that is highly associated with the main variable. This study incorporates non-conventional measure (Tri-mean) with quartile deviation as they are not affected by outliers together with kurtosis coefficients and information on the sample size to develop an estimator with more precision. Using Taylor series expansion, the properties of the estimator are evaluated to first degree order. Further, the estimator's properties are assessed by bias and mean squared error. Efficiency conditions are derived theoretically whereby the suggested estimator performs better than the prevailing estimators. To support the theoretical results, simulation and numerical studies are undertaken to assess efficiency of the suggested estimator over the existing estimators. Percentage relative efficiency indicate the suggested estimator performs better compared to the existing estimators. It is concluded that the suggested estimator is more efficient than the existing estimators.
Turbulent natural modeling of fluid in a 3-d enclosure using k- model and simple method.
(Kenyatta University, 2022-11) Mutua, Benson Ndolo
Modeling optimal strategies for effective control of the spread of malaria in Bubanza Province
(Kenyatta University, 2023-05) Venant Niyonkuru
Analysis of Boundary Layer Flow Second-Grade Hybrid Nanofluid Subject to Lorentz Force
(Kenyatta University, 2024-11) Chege, Stephen Njoroge
Fluids are non-solids that usually change shape under the action of shear stress. Over the past two decades, fluid thermophysical properties have been refined by the use of nanoparticles in the field of nanotechnology. The addition of nanoparticles has been a sure way of steadily improving fluid behaviour. Hybrid nanofluids have been of major interest to researchers. This is because more advancement in fluid behaviour has been achieved by the use of two dissimilar nanoparticles in a base fluid compared to the use of just one nanoparticle. Since major progress has been achieved, a variety of issues have also arisen like what would happen to the fluid properties when the stress tensor to strain tensor relationship is up to derivatives of order two. Multiple studies have been done on first-grade hybrid nanofluid flow (a subclass of Newtonian fluids) with little emphasis on second-grade hybrid nanofluids (a subclass of non-Newtonian fluids) research. So far, no researcher has considered the influence of Lorentz force on a second-grade hybrid nanofluid flow. To bridge this gap, this study analyses the boundary layer flow of second-grade hybrid nanofluid subject to Lorentz force. The nanoparticles used are TiO_2 and MoS_2 due to their great lubricating and efficient heat transfer properties. This study’s outcome will provide theoretical information to industries dealing with electronic and automotive cooling systems on how to improve their heat transfer efficiency. This will be done by indicating how to adjust the parameters of interest for maximum yield at the end of this study. The flow is on a surface of uniform thickness. The surface is linearly stretching horizontally and the fluid flow is experiencing perpendicular magnetic influence. The governing non-linear equations are formulated and rendered dimensionless via similarity variables. The resulting boundary condition equations are transformed to initial condition equations by use of shooting technique in MATLAB bvp4c. The IVP is then numerically solved by Runge Kutta (4) method in MATLAB bvp4c. The parameters of interest in the study are the second-grade fluid and magnetic strength parameters. These parameters are simulated and the results are presented graphically. Fluid’s velocity profile rises with increasing volume fraction and fluctuates with increasing fluid parameters and magnetic strength. The temperature profile grows with the Prandtl number and magnetic field and decreases with the increase in volume fraction and the second-grade fluid parameter.
Analysis of a 3D Heat Transfer of Magnetohydrodynamics Cu-H_2 O and Al_2 O_3-H_2 O Nanofluid over an Exponentially Stretching Plate
(Kenyatta University, 2024-11) Rutto, Celestine C.
Biomedical sensors, such as eye-imaging systems, and drug delivery mechanisms, heavily rely on magnetohydrodynamic (MHD) flow for effective operation. This study investigates the heat transfer characteristics in MHD nanofluid flow over an exponentially stretching surface, focusing on copper (Cu) and alumina (Al_2 O_3) nanoparticles suspended in water as the base fluid. The governing equations, which include the continuity, momentum, and energy equations, are formulated under the assumptions of steady, incompressible, and laminar flow. These equations are then made dimensionless using a Similarity Transformation, which reduces the partial differential equations (PDEs) to a system of ordinary differential equations (ODEs). The resulting system is numerically solved using the MATLAB package bvp4c, which is designed for solving boundary value problems. The study emphasises the impact of varying the nanoparticle volume fraction on the rate of heat transfer and skin friction. The results reveal that the Cu-water nanofluid exhibits higher heat transfer rates and lower skin friction compared to the Al_2 O_3-water nanofluid, highlighting its potential for enhanced thermal management in biomedical applications.
Numerical Investigation of Turbulent Convection Flow in a Rectangular Closed Cavity
(Kenyatta University, 2024-11) Manoti, Geofrey Moturi
Natural turbulent convection in closed cavities has many practical applications in the field of engineering such as the design of electronic computer chips, atomic installation and industrial cooling among others. In particular, it enables in achieving a desired micro-climate and efficient ventilation in a building. Recent studies show that turbulent flow is affected by variations in Rayleigh numbers, aspect ratio and heater position among others. Temperature is kept constant in all these studies hence inadequate literature on the effects of temperature on a turbulent flow. In this study, aspect ratio and Rayleigh numbers are kept constant at 2 and 1012 respectively and natural turbulent convection flow in a closed rectangular cavity is investigated numerically as the operating temperature is varied from 285.5K to 293K. The rectangular cavity’s lower wall was heated and cooling done at the top face wall while the rest of the vertical walls were kept in adiabatic condition. Material properties such as density of the fluid kept on changing at any given temperature. The thermal profile data generated influenced the nature of the turbulent flow. The non-linear averaged continuity, momentum, and energy equation terms were modeled by the SST k-ω model to generate streamlines, isotherms and velocity magnitude for a different operating temperature and presented graphically. The finite difference method and FLUENT were used to solve two SST k-ω model equations, vortices and energy with boundary conditions. It was discovered that, as the operating temperature increased turbulence decreased due to a decrease in the velocity of the elements and vortices became more parallel and smaller.
Mathematical Modelling of the Impact of Misinformation on the Spread of Covid-19
(Kenyatta University, 2024-08) Thiong’o, John
COVID-19, which is caused by SARS-CoV-2 is a viral disease of the respiratory system that emerged in 2019 and spread across all continents. The virus swiftly spread because of the unprecedented speed at which information, particularly false information, has spread in this century. This study established a mathematical model to analyze how misinformation influenced the transmission rate of COVID-19. The study employs SEIR mathematical model that integrates misinformation factor to analyze its impact on transmission rates. The obtained basic reproductive number (R0), which is the average number of new infections caused by infected person was used to assess the illiness contagiousness. The study also derived stability conditions for the equilibrium points of the model and discussed the long-term dynamics of the disease. The model was then solved numerically using the fourth-order Runge-Kutta method to investigate the effects of changing parameters as well as the simulation of various scenarios. The Results demonstrated that elevating the rates of misinformation had a positive correlation with both infected and recovered compartmet. The susceptible population first declined and then rose with the increase in the rate of misinformation. These findings pointed out understanding how misinformation affects the spread of COVID-19 will help researchers develop strategies that will effectively combat misinformation and limit the disease’s spread, thereby reducing the overall impact of the disease.
Effects of Thermal Radiation on Darcy Forchheimmer Flow of a Casson Nanofluid
(Kenyatta University, 2024-11) Loco, Valerie Sasha
Fluids are non-solid states of matter which deform continuously when an external force is subjected to them. They can be classified as either Newtonian or non-Newtonian fluids. Since most fluids fall within the category of non-Newtonian fluids, models like the Casson fluid model have been developed. Owing to Casson nanofluids’ enhanced thermophysical properties, it has a wide range of applications in the fields of mining, drilling operations, material science, metallurgy, food manufacturing, and nanotechnology and bio-engineering. Casson fluid is frequently modelled since the model agrees with the rheological evidence about human blood. Some of its applications in technological, industrial, mechanical, and scientific disciplines include; grain storage, geothermal energy production, designing warm protectors, artificial dialysis, catalytic converters, circulation of water in reservoirs and fermentation processes. On the other hand, radiation heat transfer mechanism has an immense impact in industries, engineering, technological fields where apparatus operate at extremely high temperatures. This study aims to investigate the effects of thermal radiation on Darcy Forchheimer flow of a two- dimensional, steady, incompressible flow of Casson Nanofluid over a linear stretching surface. The equations governing the fluid flow are formulated, then transformed to a system of ordinary differential equations using similarity variables. The resulting ordinary differential equations are solved using the fourth order Runge- Kutta Method. The model is simulated using MATLAB bvp4c to demonstrate the impact of pertinent parameters on the temperature, velocity, and concentration of the fluid. It was observed that an increase in the thermophoretic parameter leads to an increase of the temperature at the boundary. The concentration of the fluid decreases with an increase in porosity parameter value. Increasing the Brownian Motion parameter leads to an increase in concentration. An increase in Schmidt number leads to a decrease in temperature. Schmidt number increases with a decrease in concentration. The velocity and temperature profiles decrease with an increase in porosity parameter and an increase in thermal radiation leads to an increase of heat energy on the surrounding system leading to a decrease in fluid’s flow temperature.
A Model for the Dengue Virus Transmission Incorporating Educational Campaigning and Quarantining in Mombasa County, Kenya
(Kenyatta University, 2024-09) Munene, Antony Murimi
Mathematical Modelling of Tuberculosis-Covid-19 Co-Infection
(Kenyatta University, 2024-07) Githinji, Mary Ng’endo
It was noted that the spread of tuberculosis reduced significantly during the COVID-19 pandemic. This reduction has been associated with the preventive measures placed to combat the spread of COVID-19. Research showed a strong correlation between the spread of COVID-19 and the spread of tuberculosis in any population. It is worth noting that tuberculosis and COVID 19 are among the leading most deadly communicable diseases in the world today. The correlation in their spread also leaves us to believe that the spread of one can enhance the spread of the other. Hence, we proposed a situation where a population was co-infected with both COVID-19 and tuberculosis. By employing the conservative laws, the mathematical model was formulated, and the resulting model analysed both qualitatively and numerically. The equilibrium points of the model were obtained and the reproduction number calculated. The condition for stability of the co-infection at the equilibrium point was determined as R0<1. The non-negativity conditions for the solution were established. A numerical simulation was carried out for the model and the dynamics of the diseases studied as the parameters vary. It was found that the rate of contracting tuberculosis posessed a more significant impact on the possibility of coinfection than COVID-19 and the effects of migration from the tuberculosis sub-population were more significant than migration from COVID-19.

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