Computational Fluid Dynamics of Manhole Overflow Due to Storm-water Inflow

This research article published by the Journal of Mathematics and Informatics, 2020In this study, the storm water overflow on manholes is numerically solved. To produce a real representation of storm overflow, the Navier-Stokes equations were used. Turbulence was modelled using the standard k-epsilon turbulence model together with the volume of fluid method for phase surface tracking. The open-source computational fluid dynamics (CFD) tool OpenFOAM 5.0 was used for solving the model while the visualization tool, paraview 5.4.0, was used for processing the solution data. The convergence test was performed at three different mesh sizes. The numerical solution established mesh independence by producing similar results at varied meshes sizes. The risen storm-water column inside the manhole exerts a non-uniform pressure on the manhole cover. The non-uniform pressure distribution leads to different uplifting forces at manhole cover areas. However, the global uplifting force remains constant as long as the storm water overflow is occurring on the manhole. The overflow intensity on the manhole is not the same, areas opposite to the outlet pipe provide the highest intensity of the leaking storm-water

The Effect of Navier Slip and Skin Friction on Nanofluid Flow in a Porous Pipe

This research article was published by Engineering, Technology and Applied Science Research, 2022The flow of nanofluids through a porous medium is considered the optimum method for convective heat transfer. In this study, nanofluid flow in a porous pipe with Navier slip is investigated. Two water-based nanofluids, Copper (Cu) and alumina (Al2O3), were considered. The governing equation is presented and non-dimensionalization has been done for momentum and energy equations, initial and boundary conditions, skin friction, and Nusselt number. The governing system was simplified to ordinary differential equations, which were numerically solved and a mathematical model of nanofluid flow was formulated. The results, with regard to variations in various parameters such as temperature, velocity, skin friction, and Nusselt number, are presented graphically and discussed. It was found that the velocity during the flow decreases with the increase of the Navier slip

Multi-Criteria Decision Making and Numerical Optimization Approaches for Optimizing Water Loss Management Strategies in Water Distribution System A case of Urban Water Supply and Sanitation Authorities in Tanzania

This research article published by Modern Education and Computer Science Press, 2019Water loss in water distribution systems (WDS) is a serious problem in Tanzania and the third world countries at large. A lot of water is lost on its way before reaching the consumers. This causes a shortage of water supply which leads to loss of revenues of the concerned water authorities. The control or reduction of water loss in the WDS is closely dependent on the commitment of the decision-makers and on the strategies and budget, they set for that purpose. This paper presents a combined model of Multi-Criteria Decision Making (MCDM) and Numerical optimization techniques which may help decision-makers to prioritize and select the best strategies to be used in the management of water loss in the WDS at Moshi Urban Water Supply and Sanitation Authority (MUWSA), Tanzania. The Multi-Criteria Decision Making family methods namely the Multi-Attribute Value Theory (MAVT), Simple Multi-Attribute Rating Technique Exploiting Ranks (SMARTER), and Complex Proportional Assessment (COPRAS) were used to evaluate and prioritize the strategies, whereas the Integer Linear Programming (ILP) technique a numerical optimization technique was used to select the best strategies or alternatives to be employed in water loss management. The results show that the most preferable alternative is replacement of dilapidated pipes while the least preferable alternative is network zoning. The model selects thirteen out of sixteen alternatives, which cost 97% (TZS 235.71 million) of the total budgets set by the water authority to form a portfolio of the best alternatives for water loss management. Furthermore, the model showed robustness as the selected portfolio of alternatives remained the same even when the weights of the evaluation criteria changed

Merton’s Jump Diffusion Model an Application to Stock Markets of East African Countries

This research article published by the International Journal of Advances in Scientific Research and Engineering (ijasre), Volume 5, Issue 8 August - 2019The stock price is characterized with a number of features which can only be captured by a best model. To investigate this the Merton’s jump diffusion model was applied to the selected stocks of three East African community countries’ stock markets. The daily closing stock prices of the Nairobi Securities Exchange (NSE), the Dar es Salaam Stock Exchange (DSE) and Uganda Securities Exchange (USE) over a period of 5 years from 01/07/2013 to 01/07/2018 were analyzed with the objective of investigating how best the model captures the stock price features at these three East African stock markets. The Merton’s jump diffusion model was considered as a stochastic differential equation and the Maximum Likelihood Estimation (MLE) method was used to estimate the optimal model parameters and implemented with MATLAB. The empirical results show that, the selected stocks from all the three markets exhibit a number of jumps as it was evidenced from non-zero values of jump intensities (lambda). Also, the log returns density of Merton reveals presence volatility and leptokurtosis features as evidenced by the presence of both negative and positive skewness and excessive kurtosis values

Application of Optimal Control Theory to Newcastle Disease Dynamics in Village Chicken by Considering Wild Birds as Reservoir of Disease Virus

This research article published by Hindawi, 2019In this study, an optimal control theory was applied to a nonautonomous model for Newcastle disease transmission in the village chicken population. A notable feature of this model is the inclusion of environment contamination and wild birds, which act as reservoirs of the disease virus. Vaccination, culling, and environmental hygiene and sanitation time dependent control strategies were adopted in the proposed model. This study proved the existence of an optimal control solution, and the necessary conditions for optimality were determined using Pontryagin’s Maximum Principle. The numerical simulations of the optimal control problem were performed using the forward–backward sweep method. The results showed that the use of only the environmental hygiene and sanitation control strategy has no significant effect on the transmission dynamics of the Newcastle disease. Additionally, the combination of vaccination and environmental hygiene and sanitation strategies reduces more number of infected chickens and the concentration of the Newcastle disease virus in the environment than any other combination of control strategies. Furthermore, a cost-effective analysis was performed using the incremental cost-effectiveness ratio method, and the results showed that the use of vaccination alone as the control measure is less costly compared to other control strategies. Hence, the most effective way to minimize the transmission rate of the Newcastle disease and the operational costs is concluded to be the timely vaccination of the entire population of the village chicken, improvement in the sanitation of facilities, and the maintenance of a hygienically clean environment

Identification of multiple unknown point sources occurring in the 2D transport equation: application to groundwater pollution source identification

This research article published by the Journal of Mathematical and Computational Science, 2020Water loss in the water distribution systems (WDS) is a challenge to many water authorities in the world but the problem is crucial in the less developed countries. The effect of water losses in the WDS includes the reduction in the revenue and availability of water, interruption in the quality of water, and inflation of the operation and maintenance cost of the water authorities. Using data from the Moshi Urban Water Supply and Sanitation Authority (MUWSA) Tanzania, an assessment of strategies used for water loss management (WLM) was carried out through an integrated model of MultiCriteria Decision Making (MCDM) and Integer Linear Programming (ILP) which is an optimisation technique. The family of MCDM methods, Multi-Attribute Value Theory (MAVT), Simple Multi-Attribute Rating Technique Exploiting Ranks (SMARTER), and Simple Additive Weighting (SAW) were employed to assess and prioritise the strategies while the ILP was used to formulate a decision model. The model was used to select a portfolio of the best strategies. Sixteen strategies were identified. The results show that the comparison between the bulk meter and customers’ meter on detecting the physical or apparent losses was ranked as the best strategy in managing the loss while the network zoning was ranked as the worst strategy. The model selected thirteen out of sixteen strategies to form the portfolio of the best strategies to be employed by the MUWSA for water loss management. Furthermore, the model was found to be robust as the selected portfolio of strategies remained the same even when the weights of the criteria were changed. The developed model in this study will assist the decision-makers to assess, prioritise and choose the best strategies for reducing or controlling water loss in the distribution system

Optimisation of Water Loss Management Strategies: Multi-Criteria Decision Analysis Approaches

This research article published by the Journal of Mathematics and Informatics, 2020Water loss in the water distribution systems (WDS) is a challenge to many water authorities in the world but the problem is crucial in the less developed countries. The effect of water losses in the WDS includes the reduction in the revenue and availability of water, interruption in the quality of water, and inflation of the operation and maintenance cost of the water authorities. Using data from the Moshi Urban Water Supply and Sanitation Authority (MUWSA) Tanzania, an assessment of strategies used for water loss management (WLM) was carried out through an integrated model of Multi- Criteria Decision Making (MCDM) and Integer Linear Programming (ILP) which is an optimisation technique. The family of MCDM methods, Multi-Attribute Value Theory (MAVT), Simple Multi-Attribute Rating Technique Exploiting Ranks (SMARTER), and Simple Additive Weighting (SAW) were employed to assess and prioritise the strategies while the ILP was used to formulate a decision model. The model was used to select a portfolio of the best strategies. Sixteen strategies were identified. The results show that the comparison between the bulk meter and customers’ meter on detecting the physical or apparent losses was ranked as the best strategy in managing the loss while the network zoning was ranked as the worst strategy. The model selected thirteen out of sixteen strategies to form the portfolio of the best strategies to be employed by the MUWSA for water loss management. Furthermore, the model was found to be robust as the selected portfolio of strategies remained the same even when the weights of the criteria were changed. The developed model in this study will assist the decision-makers to assess, prioritise and choose the best strategies for reducing or controlling water loss in the distribution system

Sensitivity and Uncertainty Analysis of Variable-Volume Deterministic Model for Endothermic Continuously Stirred Tank Reactor

This research article published by the Journal of Mathematics and Informatics, Vol. 20, 2021This paper deals with the formulation and the identifiability of the variablevolume deterministic model for the endothermic continuously stirred tank reactor (CSTR). The identifiability of physical parameters of the formulated model is done by using the least squares and the delayed rejection adaptive algorithm version of the Markov chain Monte Carlo (MCMC) method. The least square estimates are used as prior information for the MCMC method. To measure the model output associated with the perturbed model parameters, we use global sensitivity analysis implemented in Latin Hypercube Sampling method. The obtained results from partial rank correlation coefficients show that six parameters are very sensitive and correlated with the model outputs. Finally, we show that the least square and the MCMC numerical results impart the model to be realistic, reliable and worthwhile to describe the dynamics of CSTR processes as physical parameters of the model are well identified and their uncertainties in the model response are analysed and quantified

Identification of the Time-Dependent Point Source in a System of two Coupled Two Dimension Diffusion-Advection-Reaction Equations: Application to Groundwater Pollution Source Identification

This research article published by Global Journal of Pure and Applied Mathematics, Volume 16, Number 3, 2020This paper addresses the inverse source problem in a system of two-dimension advection-dispersion reaction equation with an emphasis on groundwater pollution source identification. We develop an inverse source problem method for identifying the unknown groundwater point sources utilizing only the boundary and interior measurements. We develop an identifiability criterion of the point sources from recording the oxygen deficit concentration relative to the biochemical oxygen demand concentration. We have also established an identification method that uses the records of oxygen deficit concentration and biochemical oxygen demand concentration to identify the source position as a solution to nonlinear dispersion current equations. We recover the source intensity function using the multi-dimension inverse Laplace transform of the de-convolution function without any need of an iterative process. The inverse Laplace transforms are approximated by shifted Legendre Polynomials. The results show that the proposed inverse problem method is accurate

MHD Arterial Blood Flow and Mass Transfer under the Presence of Stenosis, Body Acceleration and Chemical Reaction: A Case of Magnetic Therapy

This research article published by the Journal of Mathematics and Informatics, 2020A mathematical model has been developed and used to study pulsatile blood flow and mass transfer through a stenosed artery in the presence of body acceleration and magnetic fields. An explicit Finite Difference Method (FDM) has been used to discretize the formulated mathematical model. The discretized model equations were solved in MATLAB software to produce simulations. The effect of Hartman number, Reynolds number, Schmidt number, stenotic height, body acceleration and chemical reactions have been investigated. It has been observed that, the velocity, concentration and skin friction, decrease with increasing stenotic height. Velocity on the other hand increases, as body acceleration increases. It has further been observed that as the Hartman number increases, both the radial and axial velocities diminish. Increase of the Reynolds number results in the increase of the velocity profiles. The higher the chemical reaction parameter is, the lower are the concentration profiles