Numerical Approach toward Ternary Hybrid Nanofluid Flow Using Variable Diffusion and Non-Fourier's Concept.

In the current study, the pseudoplastic model is used to analyze the mass and energy transmission through trihybrid nanofluid flow across a stretched permeable surface. The Darcy-Forchheimer relation is employed in the momentum equation to examine the influence of porosity. Energy and mass diffusion expressions are obtained by employing the double diffusion theories, which were proposed by Cattaneo and Christov and is broadly used by several researchers. The thermal efficiency of the trihybrid nanocrystals is evaluated by integrating them with a pseudoplastic substrate. The study of titanium dioxide (TiO2), cobalt ferrite (CoFe2O4), and magnesium oxide (MgO) nanocomposite base hybrid nanofluids across a stretchable sheet is receiving considerable interest in innovation and research due to their extensive spectrum of applicability. For this reason, the phenomena are modeled in the form of a system of PDEs with the effects of a heat source, magnetic field, natural convection, and chemical reaction. Through resemblance substitutions, these are reduced to an ODE system. The resultant first-order differential equations are further processed using the computational approach PCM. For authenticity and reliability, the values are reviewed against the existing literature. The findings are displayed through figures. When compared to the simple nanofluid, the hybrid and trihybrid nanofluid have a greater tendency for fluid energy and velocity propagation rate. The velocity and heat transition rate enhance 11.73% by varying nanoparticles' values from 0.01 to 0.04, while the thermal conductivity of base fluid boosts with the addition of hybrid and trihybrid nanocomposites, up to 32% and 61%, respectively.

Numerical simulation of 3D Darcy-Forchheimer fluid flow with the energy and mass transfer over an irregular permeable surface.

The Jeffrey fluid model is capable of accurately characterizing the stress relaxation behavior of non-Newtonian fluids, which a normal viscous fluid model is unable to perform. The primary objective of this paper is to provide a comprehensive investigation into the effects of MHD and thermal radiation on the 3D Jeffery fluid flow over a permeable irregular stretching surface. The consequences of the Darcy effect, variable thickness and chemical reaction are also considered. The phenomena have been modeled as a nonlinear system of PDEs. Using similarity substitution, the modeled equations are reduced to a dimensionless system of ODEs. The parametric continuation method (PCM) is used to determine the numerical solution to the obtained sets of nonlinear differential equations. The impact of physical parameters on temperature, velocity and mass profiles are presented through Figures and Tables. It has been noticed that the energy profile magnifies with the increment of porosity term, thermal radiation and heat source term, while diminishing with the flourishing upshot of power index and Deborah number. Furthermore, the porosity term and wall thickness parameter enhance the skin friction.

Application of piecewise fractional differential equation to COVID-19 infection dynamics.

We proposed a new mathematical model to study the COVID-19 infection in piecewise fractional differential equations. The model was initially designed using the classical differential equations and later we extend it to the fractional case. We consider the infected cases generated at health care and formulate the model first in integer order. We extend the model into Caputo fractional differential equation and study its background mathematical results. We show that the fractional model is locally asymptotically stable when R 0 < 1 at the disease-free case. For R 0 ≤ 1 , we show the global asymptotical stability of the model. We consider the infected cases in Saudi Arabia and determine the parameters of the model. We show that for the real cases, the basic reproduction is R 0 ≈ 1 . 7372 . We further extend the Caputo model into piecewise stochastic fractional differential equations and discuss the procedure for its numerical simulation. Numerical simulations for the Caputo case and piecewise models are shown in detail.

Transportation of thermal and velocity slip factors on three-dimensional dual phase nanomaterials liquid flow towards an exponentially stretchable surface.

The fundamental purpose of this research is to elaborate on slip boundary conditions and the flow of three-dimensional, stable, incompressible, rotating movements of nanoparticles lying across a stretchable sheet. The mathematical model for fluid flow is created using the assumptions stated above. The partial differentials are produced after utilizing boundary layer estimates. The partial differential governing equations are reduced into three coupled ordinary differential equations by using similarity transformations. After, applying transformations the system is solved numerically. Numerical results are approved with the help of the MATLAB bvp4c algorithm. The analysis shows that velocity and temperature are strongly dependent on essential parameters like stretching ratio, velocity slip, rotation, thermal slip parameter, and Prandtl number. Numerical values of distinct parameters on heat flux and skin friction factors are shown in a tabulated form. Partial velocity and thermal slip are applied to the temperature surface. The comparison among the nano-sized particles copper oxide and silver with water base nanofluid affecting velocity and temperature fields are used for analysis. Moreover, the Graphical depiction designates that the velocity and temperature spreading of the thermal slip parameter is increasing. It is observed that Ag-water is the best heat carrier as compared to CuO-water nanofluid.

Numerical Investigation of Darcy-Forchheimer Hybrid Nanofluid Flow with Energy Transfer over a Spinning Fluctuating Disk under the Influence of Chemical Reaction and Heat Source.

The present computational model is built to analyze the energy and mass transition rate through a copper and cobalt ferrite water-based hybrid nanofluid (hnf) flow caused by the fluctuating wavy spinning disk. Cobalt ferrite (CoFe2O4) and copper (Cu) nanoparticles (nps) are incredibly renowned in engineering and technological research due to their vast potential applications in nano/microscale structures, devices, materials, and systems related to micro- and nanotechnology. The flow mechanism has been formulated in the form of a nonlinear set of PDEs. That set of PDEs has been further reduced to the system of ODEs through resemblance replacements and computationally solved through the parametric continuation method. The outcomes are verified with the Matlab program bvp4c, for accuracy purposes. The statistical outputs and graphical evaluation of physical factors versus velocity, energy, and mass outlines are given through tables and figures. The configuration of a circulating disk affects the energy transformation and velocity distribution desirably. In comparison to a uniform interface, the uneven spinning surface augments energy communication by up to 15%. The addition of nanostructured materials (cobalt ferrite and copper) dramatically improves the solvent physiochemical characteristics. Furthermore, the upward and downward oscillation of the rotating disc also enhances the velocity and energy distribution.