The present study is related to the analytical investigation of the magnetohydrodynamic flow of Ag - MgO/ water hybrid nanoliquid with slip conditions via an extending surface. The thermal radiation ...and Joule heating effects are incorporated within the existing hybrid nanofluid model. The system of higher-order partial differential equations is converted to the nonlinear system of ordinary differential equations by interpreting the similarity transformations. With the implementation of a strong analytical method called HAM, the solution of resulting higher-order ordinary differential equations is obtained. The results of the skin friction coefficient, Nusselt number, velocity profile, and temperature profile of the hybrid nanofluid for varying different flow parameters are attained in the form of graphs and tables. Some important outcomes showed that the Nusselt number and skin friction are increased with the enhancement in Eckert number, stretching parameter, heat generation parameter and radiation parameter for both slip and no-slip conditions. The thermal profile of the hybrid nanofluid is higher for suction effect but lower for Eckert number, stretching parameter, magnetic field, heat generation and radiation parameter. For both slip and no-slip conditions, the hybrid nanofluid velocity shows an upward trend for both the stretching and mixed convection parameters.
As the coronavirus outbreak quickly surges worldwide, many countries are adopting non-therapeutic preventive measures, which include travel bans, remote office activities, country lockdown, and most ...importantly, social distancing. However, these measures face challenges in Bangladesh, a lower-middle-income economy with one of the world's densest populations. Social distancing is difficult in many areas of the country, and with the minimal resources the country has, it would be extremely challenging to implement the mitigation measures. Mobile sanitization facilities and temporary quarantine sites and healthcare facilities could help mitigate the impact of the pandemic at a local level. A prompt, supportive, and empathic collaboration between the Government, citizens, and health experts, along with international assistance, can enable the country to minimize the impact of the pandemic.
In this investigation, heat transportation together with irreversibility analysis for the flow of couple stress hybrid nanofluid past over a stretching surface is considered. The innovative ...characteristics and aims of this work are to note that the transportation heat couple stress model involves EMHD, viscous dissipation, Joule heating, and heat absorption, and omission. The hybrid nanofluid is prepared due to the suspension of the solid nanoparticles of the SWCNTs and MWCNTs in pure human blood. This mathematical model is an appropriate model for biological advantages including testing of human blood for drug deliveries to various parts of the human body. Particularly, the Prandtl number used for the blood is 21 and very large as compared to the other base fluids. Necessary modifications are used to translate the defining partial differential equations and boundary conditions into a layout that can be computed. To obtain mathematical approximations for the resulting scheme of nonlinear differential equations, the innovative homotopy analysis method (HAM) is used. The explanation for velocity, energy, and entropy are exposed and the flow against various influential factors (Formula: see text) is discussed graphically. The numerical values are calculated and summarized for dimensionless Formula: see text In addition, the current study is compared for various values of Formula: see text to that published literature and an impressive agreement in terms of finding is reported. It has also been noticed that the Formula: see text and Formula: see text factors retard the hybrid nanofluid flow, while the temperature of fluid becomes upsurges by the rise in these factors. 11.95% enhancement in the heat transfer rate has been attained using the hybrid nanofluids.
We reformulate a stochastic epidemic model consisting of four human classes. We show that there exists a unique positive solution to the proposed model. The stochastic basic reproduction number R0s ...is established. A stationary distribution (SD) under several conditions is obtained by incorporating stochastic Lyapunov function. The extinction for the proposed disease model is obtained by using the local martingale theorem. The first order stochastic Runge-Kutta method is taken into account to depict the numerical simulations.
•A stochastic SIVR epidemic model is reformulated.•Existence and uniqueness of the proposed model are established.•Stationary distribution and extinction of the disease are derived under several conditions.•Stochastic first order Runge-Kutta method is taken into account for model simulation.
Abstract
The current study focuses on the laminar flow of copper and copper oxide (
$${\text{Cu/blood}}$$
Cu/blood
and
$${\text{Cu}} + {\text{CuO/blood}}$$
Cu
+
CuO/blood
) hybrid nanoliquid, ...considering blood as a carrier fluid in a rectangular domain between two permeable channels. This study may manipulate for the purpose such as the drug delivery process, flow dynamic mechanism of the micro-circulatory system. In the proposed model, MHD and heat source/sink on the flow pattern have been studied. Furthermore, the sides of each channel are permeable, allowing the nanoliquid to escape, filter, squeezing and dilating with a fixed velocity. Appropriate transformations are incorporated to convert the governing partial differential equations and the boundary conditions suitable for computation. The elegant homotopy analysis method (HAM) is used to obtain analytic approximations for the resulting system of nonlinear differential equations. The features of flow characteristics such as velocity, and temperature profiles in response to the variations of the emerging parameters are simulated and examined with a physical explanation. The magnetic field plays a vital role in the blood flow and therefore the existing literature has been extending with the addition of magnetic field. Among the many outputs of the study, it is found that the pressure distribution decline with the accumulated values of the magnetic parameter at the center of the flow regime. The augmentation in the temperature distribution estimates the pH values and electric conductivity. Therefore, the
$${\text{Cu}}\,\,{\text{and}}\,\,{\text{CuO}}$$
Cu
and
CuO
hybrid nanofluids are used in this study for medication purposes. The magnetic field has an important role in the blood flow and therefore the extending study has been extending using the magnetic field. The heat emission/absorption term is added to the energy equation to maintain the homogeneous temperature for the blood flow. We expect that this work will provide efficient outputs for medical purposes such as drug delivery.
This work addresses the ability to manage the distribution of heat transmission for fluid flow occurs upon a paraboloid thin shaped hot needle by using hybrid nanoparticles containing Copper Oxide ...(CuO) and Silver (Ag) with water as pure fluid. The needle is placed horizontally in nanofluid with an application of Hall current and viscous dissipation. The popular Buongiorno model has employed in the current investigation in order to explore the impact of Brownian and thermophoretic forces exerted by the fluid. The modeled equations with boundary conditions are transformed to non-dimensional form by incorporating a suitable group of similarity variables. This set of ordinary differential equations is then solved by employing homotopy analysis method (HAM). After detail study of the current work, it has established that the flow of fluid reduces with growth in magnetic effects and volume fractions of nanoparticles. Thermal characteristics increase with augmentation of Eckert number, magnetic field, volume fractions of nanoparticles, Brownian motion parameter and decline with increase in Prandtl number. Moreover, concentration of nanoparticles reduces with corresponding growth in Lewis number and thermophoresis, chemical reaction parameters while increases with growth in Brownian motion parameter.
Fractional calculus characterizes a function at those points, where classical calculus failed. In the current study, we explored the fractional behavior of the stagnation point flow of hybrid nano ...liquid consisting of TiO
and Ag nanoparticles across a stretching sheet. Silver Ag and Titanium dioxide TiO
nanocomposites are one of the most significant and fascinating nanocomposites perform an important role in nanobiotechnology, especially in nanomedicine and for cancer cell therapy since these metal nanoparticles are thought to improve photocatalytic operation. The fluid movement over a stretching layer is subjected to electric and magnetic fields. The problem has been formulated in the form of the system of PDEs, which are reduced to the system of fractional-order ODEs by implementing the fractional similarity framework. The obtained fractional order differential equations are further solved via fractional code FDE-12 based on Caputo derivative. It has been perceived that the drifting velocity generated by the electric field E significantly improves the velocity and heat transition rate of blood. The fractional model is more generalized and applicable than the classical one.
In this work, the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out. The chemical reaction and viscous dissipation has also considered ...for flow system in the presence of microorganism. The hybrid nanoparticles comprising of Copper Formula: see text and Alumina Formula: see text are considered for current flow problem. Mathematically the flow problem is formulated by employing the famous Buongiorno's model that will also investigate the consequences of thermophoretic forces and Brownian motion upon flow system. Group of similar variables is used to transform the model equations into dimensionless form and have then solved analytically by homotopy analysis method (HAM). It has established in this work that, flow of fluid declines due to increase in bioconvection Rayleigh number, buoyancy ratio and volume fractions of nanoparticles. Thermal flow grows due to rise in Eckert number, Brownian, thermophoresis parameters and volume fraction of nanoparticles. Concentration profiles increase due to growth in Brownian motion parameter and reduces due to increase in thermophoresis parameter and Lewis number. Motile microorganism profile declines due to augmentation in Peclet and bioconvection Lewis numbers. Moreover, the percentage enhancement in the drag force and rate of heat transfer using conventional nanofluid and hybrid nanofluid are observed and discussed. The hybrid nanofluid increases the skin friction and heat transfer rate more rapidly and efficiently as compared to other traditional fluids. A comparison of the present study with the existing literature is also conducted with a closed agreement between both results for variations in thickness of the needle.
This research work aims to scrutinize the mathematical model for the hybrid nanofluid flow in a converging and diverging channel. Titanium dioxide and silver TiO2 and Ag are considered as solid ...nanoparticles while blood is considered a base solvent. The couple-stress fluid model is essentially use to describe the blood flow. Therefore, the couple-stress term was used in the recent study with the existence of a magnetic field and a Darcy-Forchheiner porous medium. The heat absorption/omission and radiation terms were also included in the energy equation for the sustainability of drug delivery. An endeavor was made to link the recent study with the applications of drug delivery. It has already been revealed by the available literature that the combination of TiO2 with any other metal can destroy cancer cells more effectively than TiO2 separately. Both the walls are stretchable/shrinkable, whereas flow is caused by a source or sink with α as a converging/diverging parameter. Governing equations were altered into the system of non-linear coupled equations by using the similarity variables. The homotopy analysis method (HAM) was applied to obtain the preferred solution. The influences of the modeled parameters have been calculated and displayed. The confrontation of wall shear stress and hybrid nanofluid flow increased as the couple stress parameter rose, which indicates an improvement in the stability of the base fluid (blood). The percentage (%) increase in the heat transfer rate with the variation of nanoparticle volume fraction was also calculated numerically and discussed theoretically.
The energy transmission through micropolar fluid have a broad range implementation in the field of electronics, textiles, spacecraft, power generation and nuclear power plants. Thermal radiation's ...influence on an incompressible thermo-convective flow of micropolar fluid across a permeable extensible sheet with energy and mass transition is reported in the present study. The governing equations consist of Navier-Stokes equation, micro rotation, temperature and concentration equations have been modeled in the form of the system of Partial Differential Equations. The system of basic equations is reduced into a nonlinear system of coupled ODE's by using a similarity framework. The numerical solution of the problem has been obtained via PCM (Parametric Continuation Method). The findings are compared to a MATLAB built-in package called bvp4c to ensure that the scheme is valid. It has been perceived that both the results are in best agreement with each other. The effects of associated parameters on the dimensionless velocity, micro-rotation, energy and mass profiles are discussed and depicted graphically. It has been detected that the permeability parameter gives rise in micro-rotation profile.
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