Analytical investigation of Carreau fluid flow through a non-circular conduit with wavy wall.

Peristaltic flow through an elliptic channel has vital significance in different scientific and engineering applications. The peristaltic flow of Carreau fluid through a duct with an elliptical cross-section is investigated in this work . The proposed problem is defined mathematically in Cartesian coordinates by incorporating no-slip boundary conditions. The mathematical equations are solved in their dimensionless form under the approximation of long wavelength. The solution of the momentum equation is obtained by applying perturbation technique ([Formula: see text] as perturbation parameter) along with a polynomial solution. We introduce a new polynomial of twenty degrees to solve the energy equation. The solutions of mathematical equations are investigated deeply through graphical analysis. It is noted that non-Newtonian effects are dominant along the minor axis. It is found that flow velocity is higher in the channels having a high elliptical cross-section. It is observed from the streamlines that the flow is smooth in the mid-region, but they transform into contours towards the peristaltic moving wall of the elliptic duct.

Insight into the heat transfer of third-grade micropolar fluid over an exponentially stretched surface.

Due to their unique microstructures, micropolar fluids have attracted enormous attention for their industrial applications, including convective heat and mass transfer polymer production and rigid and random cooling particles of metallic sheets. The thermodynamical demonstration is an integral asset for anticipating the ideal softening of heat transfer. This is because there is a decent connection between mathematical and scientific heat transfers through thermodynamic anticipated outcomes. A model is developed under the micropolar stream of a non-Newtonian (3rd grade) liquid in light of specific presumptions. Such a model is dealt with by summoning likeness answers for administering conditions. The acquired arrangement of nonlinear conditions is mathematically settled using the fourth-fifth order Runge-Kutta-Fehlberg strategy. The outcomes of recognized boundaries on liquid streams are investigated in subtleties through the sketched realistic images. Actual amounts like Nusselt number, Sherwood number, and skin-part coefficient are explored mathematically by tables. It is observed that the velocity distribution boosts for larger values of any of [Formula: see text], [Formula: see text], and declines for larger [Formula: see text] and Hartmann numbers. Furthermore, the temperature distribution [Formula: see text] shows direct behavior with the radiation parameter and Eckert number, while, opposite behavior with Pr, and K. Moreover, the concentration distribution shows diminishing behavior as we put the higher value of the Brownian motion number.

Dynamics of Rotating Micropolar Fluid over a Stretch Surface: The Case of Linear and Quadratic Convection Significance in Thermal Management.

This article analyzes the significance of linear and quadratic convection on the dynamics of micropolar fluid due to a stretching surface in the presence of magnetic force and a rotational frame. Modern technological implementations have attracted researchers to inquire about non-Newtonian fluids, so the effect of linear and nonlinear convection conditions is accounted for in the dynamics of non-Newtonian fluid. The highly nonlinear governing equations are converted into a system of dimensionless ODEs by using suitable similarity transformations. The bvp4c technique is applied in MATLAB software to obtain a numerical solution. This investigation examines the behavior of various parameters with and without quadratic convection on the micro-rotation, velocity, and temperature profiles via graphical consequences. The velocity profile decreases with a higher input by magnetic and rotating parameters, and fluid velocity is more elevated in the nonlinear convection case. However, the temperature profile shows increasing behavior for these parameters and quadratic convection increases the velocity profile but has an opposite tendency for the temperature distribution. The micro-rotation distribution is augmented for higher magnetic inputs in linear convection but reduces against thermal buoyancy.

Insight into the Role of Nanoparticles Shape Factors and Diameter on the Dynamics of Rotating Water-Based Fluid.

This article addresses the dynamic of three-dimensional rotating flow of Maxwell nanofluid across a linearly stretched sheet subject to a water-based fluid containing copper nanoparticles. Nanoparticles are used due to their fascinating features, such as exceptional thermal conductivity, which is crucial in modern nanotechnology and electronics. The primary goal of this comprehensive study is to examine the nanoparticles size and shape factors effect on the base fluid temperature. The mathematical model contains the governing equations in three dimensional partial differential equations form, and these equations transformed into dimensionless ordinary dimensional equations via suitable similarity transformation. The bvp4c technique is harnessed and coded in Matlab script to obtain a numerical solution of the coupled non-linear ordinary differential problem. It is observed that the greater input of rotating, Deborah number, and magnetic parameters caused a decline in the fluid primary and secondary velocities, but the nanoparticles concentration enhanced the fluid temperature. Further, a substantial increment in the nanofluid temperature is achieved for the higher nanoparticle's diameter and shape factors.

Bio-Convection Effects on Prandtl Hybrid Nanofluid Flow with Chemical Reaction and Motile Microorganism over a Stretching Sheet.

This study aims to determine the heat transfer properties of a magnetohydrodynamic Prandtl hybrid nanofluid over a stretched surface in the presence of bioconvection and chemical reaction effects. This article investigates the bio-convection, inclined magnetohydrodynamic, thermal linear radiations, and chemical reaction of hybrid nanofluid across stretching sheets. Also, the results are compared with the nanofluid flow. Moreover, the non-Newtonian fluid named Prandtl fluid is considered. Microfluidics, industry, transportation, the military, and medicine are just a few of the real-world applications of hybrid nanofluids. Due to the nonlinear and convoluted nature of the governing equations for the problem, similarity transformations are used to develop a simplified mathematical model with all differential equations being ordinary and asymmetric. The reduced mathematical model is computationally analyzed using the MATLAB software package's boundary value problem solver, Runge-Kutta-fourth-fifth Fehlberg's order method. When compared to previously published studies, it is observed that the acquired results exhibited a high degree of symmetry and accuracy. The velocity profiles of basic nanofluid and hybrid nanofluid are increased by increasing the Prandtl parameters' values, which is consistent with prior observations. Additionally, the concentration and temperature of simple and hybrid nanofluids increase with the magnetic parameter values.

Analytical solutions of PDEs by unique polynomials for peristaltic flow of heated Rabinowitsch fluid through an elliptic duct.

In this research, we have considered the convective heat transfer analysis on peristaltic flow of Rabinowitsch fluid through an elliptical cross section duct. The Pseudoplastic and Dilatant characteristics of non-Newtonian fluid flow are analyzed in detail. The Rabinowitsch fluid model shows Pseudoplastic fluid nature for [Formula: see text] and Dilatant fluid behaviour for [Formula: see text] The governing equations are transformed to dimensionless form after substituting pertinent parameters and by applying the long wavelength approximation. The non-dimensional momentum and energy equations are solved analytically to obtain the exact velocity and exact temperature solutions of the flow. A novel polynomial of order six having ten constants is introduced first time in this study to solve the energy equation exactly for Rabinowitsch fluid flow through an elliptic domain. The analytically acquired solutions are studied graphically for the effective analysis of the flow. The flow is found to diminish quickly in the surrounding conduit boundary for Dilatant fluid as compared to the Pseudoplastic fluid. The temperature depicted the opposite nature for Pseudoplastic and Dilatant fluids. The flow is examined to plot the streamlines for both Pseudoplastic and Dilatant fluids by rising the flow rate.

Entropy and stability analysis on blood flow with nanoparticles through a stenosed artery having permeable walls.

In this research, the electro-osmotic effects are highlighted for a blood-based hybrid nanofluid flow across an artery infected with multiple stenosis. The artery has permeable walls together with slip boundary effects. The slip and permeable boundary conditions model the more realistic blood flow problems. The governing equations of the problem are converted into non-dimensional form by introducing adequate dimensionless variables and acquired the exact solutions. The detailed study of heat transfer is given by Joule heating and viscous dissipation effects. The disorder of fluid flow is investigated by the mathematical study of entropy generation. Analytically attained solutions are examined graphically for both symmetric and non-symmetric shapes of stenosis. Streamlines are analyzed for varying values of flow rate Q and electro-osmotic parameter m. The flow velocity has smallest values on the axis of channel and gets higher value near the boundary walls. The temperature profile delineates opposite behavior to the velocity, and it is parabolic in nature. The velocity reduces towards the non-uniform stenosis except for electroosmotic parameter m. The temperature has larger magnitude in the case of anti-symmetric stenosis. Moreover, the stability of velocity solution is also analyzed.

Heat Transfer of Hybrid Nanomaterials Base Maxwell Micropolar Fluid Flow over an Exponentially Stretching Surface.

A numerical investigation of three-dimensional hybrid nanomaterial micropolar fluid flow across an exponentially stretched sheet is performed. Recognized similarity transformations are adopted to convert governing equations from PDEs into the set ODEs. The dimensionless system is settled by the operating numerical approach bvp4c. The impacts of the nanoparticle volume fraction, dimensionless viscosity ratio, stretching ratio parameter, and dimensionless constant on fluid velocity, micropolar angular velocity, fluid temperature, and skin friction coefficient in both x-direction and y-direction are inspected. Graphical outcomes are shown to predict the features of the concerned parameters into the current problem. These results are vital in the future in the branches of technology and industry. The micropolar function Rη increases for higher values of the micropolar parameter and nanoparticle concentration. Micropolar function Rη declines for higher values of the micropolar parameter and nanoparticle concentration. Temperature function is enhanced for higher values of solid nanoparticle concentration. Temperature function declines for higher values of the micropolar parameter. The range of the physical parameters are presented as: 0.005<ϕ2<0.09, Pr=6.2, 0

Role of pine wilt disease based on optimal control strategy at multiple scales: A case study of Korea.

Pine wilt disease is one of the most serious conifer diseases: this is because pine trees contribute greatly to the economy and domestic wealth in Korea. Our model of this disease is based on the parametrisation of infectious pine trees in Korea for the period of 2010-2019. The model captures the growth in case onsets and the estimated results are almost compatible with the reported data. To control the spread of this disease to the whole pine tree community, we found a threshold parameter called 'basic reproduction number' using the nextgeneration matrix method. During the analysis of the model, equilibrium points were first computed: there are two points -one has no disease class and other has all the disease classes. For the global behaviour of the mathematical model of these two points, Lypunove functional theory was used for disease-free and endemic equilibrium. Sensitivity analysis was performed to observe the relative importance of these parameters to the transmission and prevalence of pine wilt disease. To control the dissemination of the disease, we formulated an optimal control problem. Strategies used to control this disease were based on the consequences of the significant effects of the estimated parameters on the basic reproduction number. We re-examined the mathematical system to determine the agreement between numerically and analytically calculated outcomes. After analysing the problem numerically, we can discern that the numerical findings support the results calculated analytically.

A Mathematical and Statistical Estimation of Potential Transmission and Severity of COVID-19: A Combined Study of Romania and Pakistan.

During the outbreak of an epidemic, it is of immense interest to monitor the effects of containment measures and forecast of outbreak including epidemic peak. To confront the epidemic, a simple SIR model is used to simulate the number of affected patients of coronavirus disease in Romania and Pakistan. The model captures the growth in case onsets, and the estimated results are almost compatible with the actual reported cases. Through the calibration of parameters, forecast for the appearance of new cases in Romania and Pakistan is reported till the end of this year by analysing the current situation. The constant level of number of patients and time to reach this level is also reported through the simulations. The drastic condition is also discussed which may occur if all the preventive restraints are removed.

Bio-inspired Analytical Heuristics to Study Pine Wilt Disease Model.

This paper portrays the dynamics of pine wilt disease. The specific formula for reproduction number is accomplished. Global behavior is completely demonstrated on the basis of the basic reproduction number [Formula: see text]. The disease-free equilibrium is globally asymptotically stable for [Formula: see text] and in such a case, the endemic equilibrium does not exist. If [Formula: see text] exceeds one, the disease persists and the unique endemic equilibrium is globally asymptotically stable. Global stability of disease-free equilibrium is proved using a Lyapunov function. A graph-theoretic approach is applied to show the global stability of the unique endemic equilibrium. Sensitivity analysis has been established and control strategies have been designed on the basis of sensitivity analysis.

Stability analysis of pine wilt disease model by periodic use of insecticides.

This work is related to qualitative behaviour of an epidemic model of pine wilt disease. More precisely, we proved that the reproductive number has sharp threshold properties. It has been shown that how vector population can be reduced by the periodic use of insecticides. Numerical simulations show that epidemic level of infected vectors becomes independent of saturation level by including the transmission through mating.