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.

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.

No abstract