a b s t r a c tThe industrial prilling process is a common technique to produce small pellets which are generated from the break-up of rotating liquid jets. In many cases the fluids used are molten liquid and/or contain small quantities of polymers and thus typically can be modelled as non-Newtonian liquids. Industrial scale set-ups are costly to run and thus mathematical modelling provides an opportunity to assess methods of improving efficiency and introduces greater levels of precision. In order to understand this process, we will consider a mathematical model to capture the essential physics related to a cylindrical drum, which is rotated about its axis. In this paper, we will model the viscoelastic nature of the fluid using the Oldroyd-B model. An asymptotic approach is used to simplify the governing equations into 1D equations. Moreover, a linear instability analysis is examined and the most unstable modes are found to grow along the jet. Furthermore, the non-linear instability is investigated by using a finite difference scheme to find break-up lengths and droplet formation.

Droplet generated from the rupture of a compound liquid jet can be used to produce encapsulated droplets which have applications in a wide variety of industrial processes. In this paper, we examine the instability of a two dimensional axisymmetric inviscid compound jet falling vertically downwards in a surrounding gas under the influence of gravity. The steady state equations are derived using an asymptotic method and the linear instability, including temporal and spatial instability, is determined using a multiple scales approach. The results are analysed to investigate how the gas-to-shell density ratio affects key features of the jet including theoretical breakup lengths.

No abstract

No abstract

No abstract

No abstract

The numerical solution of reaction diffusion systems may require more computational efforts if the change in concentrations occurs extremely rapid. This is because more time points are needed to resolve the reaction diffusion process accurately. In this paper, three finite difference implicit schemes are used which are unconditionally stable in order to enhance consistency. Novelty is reported by compact finite difference implicit scheme on a reaction diffusion system with higher accuracy measured by L 2 , L ∞ , and Relative error norms. Efficiency is observed by reducing grid space along small temporal steps. CPU performance, transmission capacity along comparison of three schemes shows excellent agreement with the analytical solution.INDEX TERMS Reaction diffusion systems, alternating direction implicit, Douglas scheme, higher order compact scheme, Thomas algorithm.

Purpose: This paper studies a simple SVIR (susceptible, vaccinated, infected, recovered) type of model to investigate the coronavirus’s dynamics in Saudi Arabia with the recent cases of the coronavirus. Our purpose is to investigate coronavirus cases in Saudi Arabia and to predict the early eliminations as well as future case predictions. The impact of vaccinations on COVID-19 is also analyzed. Methods: We consider the recently introduced fractional derivative known as the generalized Hattaf fractional derivative to extend our COVID-19 model. To obtain the fitted and estimated values of the parameters, we consider the nonlinear least square fitting method. We present the numerical scheme using the newly introduced fractional operator for the graphical solution of the generalized fractional differential equation in the sense of the Hattaf fractional derivative. Mathematical as well as numerical aspects of the model are investigated. Results: The local stability of the model at disease-free equilibrium is shown. Further, we consider real cases from Saudi Arabia since 1 May–4 August 2022, to parameterize the model and obtain the basic reproduction number R0v≈2.92. Further, we find the equilibrium point of the endemic state and observe the possibility of the backward bifurcation for the model and present their results. We present the global stability of the model at the endemic case, which we found to be globally asymptotically stable when R0v>1. Conclusion: The simulation results using the recently introduced scheme are obtained and discussed in detail. We present graphical results with different fractional orders and found that when the order is decreased, the number of cases decreases. The sensitive parameters indicate that future infected cases decrease faster if face masks, social distancing, vaccination, etc., are effective.