The unsteady magnetohydrodynamics (MHD) flow of nanofluid with variable fluid properties over an inclined stretching sheet in the presence of thermal radiation and chemical reaction is studied taking into account the effect of variable fluid properties in thermal conductivity and diffusion coefficient. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation. The numerical solutions of the problem are obtained by using the fourth order Runge-Kutta method in line with the shooting technique. It is found that the increase in both thermal conductivity and radiative heat flux decreases the heat transfer rate but increases the skin friction and mass transfer rates. It is further observed that the increase in porosity parameter and magnetic field reduces the skin friction, heat, and mass transfer rates.

Purpose The purpose of this paper is to review previous research studies on mathematical models for entropy generation in the magnetohydrodynamics (MHD) flow of nanofluids. In addition, the influence of various parameters on the velocity profiles, temperature profiles and entropy generation was studied. Furthermore, the numerical methods used to solve the model equations were summarized. The underlying purpose was to understand the research gap and develop a research agenda. Design/methodology/approach This paper reviews 141 journal articles published between 2010 and 2022 on topics related to mathematical models used to assess the impacts of various parameters on the entropy generation, heat transfer and velocity of the MHD flow of nanofluids. Findings This review clarifies the application of entropy generation mathematical models, identifies areas for future research and provides necessary information for future research in the development of efficient thermodynamic systems. It is hoped that this review paper can provide a basis for further research on the irreversibility of nanofluids flowing through different channels in the development of efficient thermodynamic systems. Originality/value Entropy generation analysis and minimization constitute effective approaches for improving the performance of thermodynamic systems. A comprehensive review of the effects of various parameters on entropy generation was performed in this study.

In 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.

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A 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.

Banana Xanthomonas Wilt disease (BXW) is a bacterial disease which highly threaten banana production in east and central Africa. It is caused by a bacteria known as Xanthomonas campestris pv. musacearum (Xcm). Mathematical modelling gives an insight on how to best understand the transmission dynamics and control of the disease. The existing mathematical models have not included contaminated soil in the dynamics of BXW. In this study we formulated a model which includes contaminated soil, calculated the basic reproduction number and carried out sensitivity analysis of some model parameters. We further conducted numerical simulation to validate the results. The simulations show that the infection rate by contaminated farming tools ( iand e β ), the infection rate by contaminated soil ( 2 ω ), vertical disease transmission rate (θ ), and the shedding rate of Xcm bacteria in the soil (φ ) are positively sensitive to the basic reproduction number. While, the most negative sensitive parameters are the clearance rate of Xcm bacteria from the soil ( h µ ), removal of infected plants from the farm ( r ), harvesting ( p α ), and banana plants disease induced death rate ( d ).The result also shows that contaminated soil contributes to the transmission and persistence of BXW disease.Therefore, we recommend that, along with the existing control measures scientist and technologist should carry out studies to find a way to reduce or avoid vertical disease transmission and increase the Xcm clearance rate in the soil. Furthermore, technology for early detection of infected plants should be brought down to the local farmers at affordable costs. This will help stakeholders to detect and remove the infected plants from the farm in time and hence reduce the number of secondary infections.

Water 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.