In this study, we investigate the flow of electrically conducting hybrid nanofluid (Ag+Cu/H2O), due to rotating disks, along with thermal slip, heat generation, and viscous dissipation. The nonlinear differential system is modelled and transformed into dimensionless partial differential equations using suitable dimensionless variables. To obtain solutions for the considered model, a finite difference toolkit is implemented, and numerical solutions are achieved. Graphical results are presented to display the influences of different dimensionless variables on flow velocity and temperature. This research contributes to a better understanding of hybrid nanofluid flows and can inform the design of cooling systems and other practical applications.
The stretched surface's convective heat transfer capability can be improved by using nanoparticles. There is a significant role of the Prandtl number in determining the thermal and momentum stretching layer surfaces. It is proposed in this study that an effective Prandtl number model be used to explore the two-dimensional oblique stagnation point flow of γ A l 2 O 3 - H 2 O and γ A l 2 O 3 - C 2 H 6 O 2 nanofluids moving over a convective stretching surface. The fluid in question is subjected to a thorough investigation. It is necessary to apply non-linear ordinary differential equations in order to connect the controlling partial differential equations with the boundary conditions. To solve these equations, an efficient and reliable numerical technique is used. Shooting Method with Runge Kutta-IV in Mathematica software. Visual representations of normal and tangential velocity and temperature as well as streamlines as a function of many physical parameters are shown. The results show that as the volume fraction of nanoparticles increases, the fluid flow f ( y ) , h ( y ) and velocity f ' ( y ) , h ' ( y ) all increase, whereas the flow f ( y ) and velocity f ' ( y ) both increase against the stretching ratio parameter, while the flow h ( y ) and velocity h ' ( y ) both decrease. When the volume percentage of nanoparticles and the Biot number are both increased, the temperature rises. However, when the stretching ratio parameter is increased, the temperature falls. Physical attributes like the local skin friction coefficient and the heat flow may be characterized in many ways. A nanofluid comprised of γ A l 2 O 3 - C 2 H 6 O 2 outperformed a γ A l 2 O 3 - H 2 O nanofluid in terms of heat transfer rate. The source of zero skin friction may be observed to move to the left or right depending on the balance of obliqueness and straining motion at point x s . The computed numerical results of the current research correspond well with those accessible in the literature for the limiting scenario.
In the present work, we investigated the transmission dynamics of fractional order SARS-CoV-2 mathematical model with the help of Susceptible S ( t ) , Exposed E ( t ) , Infected I ( t ) , Quarantine Q ( t ) , and Recovered R ( t ) . The aims of this work is to investigate the stability and optimal control of the concerned mathematical model for both local and global stability by third additive compound matrix approach and we also obtained threshold value by the next generation approach. The author's visualized the desired results graphically. We also control each of the population of underlying model with control variables by optimal control strategies with Pontryagin's maximum Principle and obtained the desired numerical results by using the homotopy perturbation method. The proposed model is locally asymptotically unstable, while stable globally asymptotically on endemic equilibrium. We also explored the results graphically in numerical section for better understanding of transmission dynamics.
It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.
