Comsolic solution of an elliptic cylindrical compressible fluid flow.

In this article, the primary focus is to investigate the heat transfer effects with viscous compressible laminar flow in the permeable elliptic cylinder. The Reynolds number is kept 100 for flow to be laminar. The physics of heat transfer is selected to be coupled with the laminar flow. The results for particular step-size time for Velocity distribution, pressure profile, temperature profile, isothermal temperature contours, and drag coefficient have been analyzed. Mesh has been generated through COMSOL, mesh entities have been elaborated statistically. The maximum and minimum velocity profile is observed at the elliptical cylinder's walls and upper, lower boundary respectively. The maximum velocity observed is 2.22 m/s. Pressure profile around elliptic corners is found maximum, distinct patterns are observed even under the influence of applied heat. Temperature is observed maximum at walls but it gradually increases as moving from the upper boundary towards the lower boundary. The isothermal contour patterns are observed maximum near the walls, drag coefficient of gradual decrease is observed. COMSOL multi-physics is utilized for mathematical modeling of problems and the Backward-Differentiation-Formula has been exploited to handle problems numerically. The results will help greatly to understand the characterizations of viscous fluids and in industries like air furnaces and automobile cooling systems.

A fractional-order model of COVID-19 considering the fear effect of the media and social networks on the community.

Since December 2019, the world has experienced from a virus, known as Covid-19, that is highly transmittable and is now spread worldwide. Many mathematical models and studies have been implemented to work on the infection and transmission risks. Besides the virus's transmission effect, another discussion appears in the community: the fear effect. People who have never heard about coronavirus, face every day uncertain and different information regarding the effect of the virus and the daily death rates from sources like the media, the medical institutions or organizations. Thus, the fear of the virus in the community can possibly reach the point that people become scared and confused about information polluted from different networks with long-term trend discussions. In this work, we use the Routh-Hurwitz Criteria to analyze the local stability of two essential critical points: the disease-free and the co-existing critical point. Using the discretization process, our analysis have shown that one should distinguish between the spread of "awareness" or "fear" in the community through the media and others to control the virus's transmission. Finally, we conclude our theoretical findings with numerical simulations.