Rotating MHD Williamson nanofluid flow in 3D over exponentially stretching sheet with variable thermal conductivity and diffusivity.

Nanofluids are a topic of great interest for researchers due to their remarkable performance in most heat transport applications. Williamson fluids have also gained importance due to their numerous uses in many fields. Exponentially stretching sheets with variable thermal conductivity and diffusivity is another topic of importance in fluid mechanics. Moreover, rotating MHD fluids have various applications in the industry. So, in particular, we would study rotating MHD Williamson nanofluid having variable diffusivity and thermal conductivity flowing above an exponentially stretching sheet. In this work, we proposed modified wavelets method to find the solutions of the developed mathematical model of the considered problem. The effectiveness of the developed scheme is certified by the help of tables and graphs. It is worthy to point out that the skin friction coefficient in x and y direction increases gradually against the selection of magnetic field effects and Williamson parameter. Tabular study presented to show that the suggested algorithm is convergent, and it can be extended to more physical models on non-Newtonian type.

Maximizing electrical output and reducing heat-related losses in photovoltaic thermal systems with a thorough examination of flow channel integration and nanofluid cooling.

In recent years, global energy demand has surged, emphasizing the need for nations to enhance energy resources. The photovoltaic thermal (PV/T) system, capable of generating electrical energy from sunlight, is a promising renewable energy solution. However, it faces the challenge of overheating, which reduces efficiency. To address this, we introduce a flow channel within the PV/T system, allowing coolant circulation to improve electrical efficiency. Within this study, we explore into the workings of a PV/T system configuration, featuring a polycrystalline silicon panel atop a copper absorber panel. This innovative setup incorporates a rectangular flow channel, enhanced with a centrally positioned rotating circular cylinder, designed to augment flow velocity. This arrangement presents a forced convection scenario, where heat transfer primarily occurs through conduction in the uppermost two layers, while the flow channel beneath experiences forced convection. To capture this complex phenomenon, we accurately address the two-dimensional Navier-Stokes and energy equations, employing simulations conducted via COMSOL 6.0 software, renowned for its utilization of the finite element method. To optimize heat dissipation and efficiency, we introduce a hybrid nanofluid comprised of titanium oxide and silver nanoparticles dispersed in water, circulating through the flow channel. Various critical parameters come under scrutiny, including the Reynolds number, explored across the range of 100-1000, the volume fractions of both nanoparticle types, systematically tested within the range of 0.001-0.05, and the controlled speed of the circular cylinder, maintained within the range of 0.1-0.25 m/s. It was found that incorporating silver nanoparticles as a suspended component is more effective in enhancing PV/T efficiency than the addition of titanium oxide. Additionally, maintaining the volume fraction of titanium oxide between 4 and 5% yields improved efficiency, provided that the cylinder rotates at a higher speed. It was observed that cell efficiency can be regulated by adjusting four parameters, such as the Reynolds number, cylinder rotation speed, and the volume fraction of both nanoparticles.

Mathematical Modeling and backward bifurcation in monkeypox disease under real observed data.

We propose a mathematical model to analyze the monkeypox disease in the context of the known cases of the USA epidemic. We formulate the model and obtain their essential properties. The equilibrium points are found and their stability is demonstrated. We prove that the model is locally asymptotical stable (LAS) at disease free equilibrium (DFE) under R0<1. The presence of an endemic equilibrium is demonstrated, and the phenomena of backward bifurcation is discovered in the monkeypox disease model. In the monkeypox infectious disease model, the parameters that lead to backward bifurcation are θr, τ1, and ξr. When R0>1, we determine the model's global asymptotical stability (GAS). To parameterize the model using real data, we obtain the real value of the model parameters and compute R1=0.5905. Additionally, we do a sensitivity analysis on the parameters in R0. We conclude by presenting specific numerical findings.

Three dimensional study for entropy optimization in nanofluid flow through a compliant curved duct: A drug delivery and therapy application.

This research explores the three-dimensional characteristics of nanofluid dynamics within curved ducts, in contrast to earlier studies that mainly focus on two-dimensional flow. By using this ground-breaking method, we can capture a more accurate depiction of fluid behavior that complies with the intricate duct design. In this study, we investigate the three dimensional flow and entropic analysis of peristaltic nanofluid flows in a flexible curved duct, comparing the effects of silver and copper nanoparticles. To obtain accurate results, we assume physical constraints such as long wavelength and low Reynolds number and used a perturbation technique through NDSolve commands for finding exact solutions of the obtained differential equations. A comprehensive error analysis is provided through residual error table and figures to estimate a suitable range of the physical factors. Our findings indicate that the velocity of the nanofluid is directly proportional to the elasticity of the walls, while the mass per unit volume inversely affects velocity. We show that reducing the aspect ratio of the duct rectangular section can decrease entropy generation by raising magnitudes of damping force exerted by to the flexible walls of the enclosure. Additionally, using a larger height of the channel than the breadth can reduce stream boluses. The practical implications of this study extend beyond turbines and endoscopy to biomedical processes such as drug delivery and microfluidic systems.

Numerical study of fractional order COVID-19 pandemic transmission model in context of ABO blood group.

The worldwide association of health (WHO) has stated that COVID-19 (the novel coronavirus disease-2019) as a pandemic. Here, the common SEIR model is generalized in order to show the dynamics of COVID-19 transmission taking into account the ABO blood group of the infected people. Fractional order Caputo derivative are used in the proposed model. Our study is guided by the results that have been obtained by Chen J, Fan H, Zhang L, et al. from three unique medical clinics in Wuhan and Shenzhen, China. In this study, the feasibility region of the proposed model are calculated plus the points of equilibrium. Also, the equilibrium points stability is examined. A unique solution existence for the proposed paradigm is proved via utilizing the fixed point theory with regards to Caputo fractional derivative. Numerical experiments of the proposed paradigm is done and we show its sensitivity to the fractional order.

Theoretical and numerical analysis of novel COVID-19 via fractional order mathematical model.

In the work, author's presents a very significant and important issues related to the health of mankind's. Which is extremely important to realize the complex dynamic of inflected disease. With the help of Caputo fractional derivative, We capture the epidemiological system for the transmission of Novel Coronavirus-19 Infectious Disease (nCOVID-19). We constructed the model in four compartments susceptible, exposed, infected and recovered. We obtained the conditions for existence and Ulam's type stability for proposed system by using the tools of non-linear analysis. The author's thoroughly discussed the local and global asymptotical stabilities of underling model upon the disease free, endemic equilibrium and reproductive number. We used the techniques of Laplace Adomian decomposition method for the approximate solution of consider system. Furthermore, author's interpret the dynamics of proposed system graphically via Mathematica, from which we observed that disease can be either controlled to a large extent or eliminate, if transmission rate is reduced and increase the rate of treatment.