Newtonian Condition Research Articles

Impact of thermal diffusion and diffusion-thermal effects on MHD Maxwell fluid subject to Newtonian heat and mass conditions over a stretching cylinder

Current research's main focus is to incorporate the novel idea of Newtonian flux condition in MHD stretching flow of Maxwell liquid with Stefan blowing. An analysis is done to explore the heat and mass transfer characteristics of MHD Maxwell fluid towards a stretching cylinder, including thermal diffusion and diffusion-thermal energy implications in the presence of activation energy. Polar coordinates (z, r) in the shape of a cylinder are used to model the issue. To convert controlling PDEs into ODEs, similarity the variables are used. The governing equations of motion that result are tackled via the notorious R-K 4th order approach. Through graphical portrayal, the impacts of various factors, including curvature, magnetics, Stefan blowing, reaction, and activation energy parameters, are studied. Furthermore, the validation of numerical findings is prepared by benchmarking with previously determined limiting conditions, and we launch a wonderful communication with these results.

Bioconvective unsteady fluid flow across concentric stretching cylinders with thermal-diffusion and diffusion-thermo effects

The current study emphasizes bioconvective viscous fluid flow between two horizontal deformable cylinders. At the cylindrical walls, the Newtonian heat and mass condition with velocity slip is examined. The thermal and solutal transfer is optimized by amalgamating Soret–Dufour effects with variable heat source/sink. The equations that regulate the flow are simplified via appropriate transformations. The bvp4c algorithm is employed to obtain the numerical solution. The ramifications of the emerging parameters are portrayed graphically. Numerical values for drag force coefficient, heat flux, mass flux, and local motile density numbers are enumerated in tabulated form. Axial velocity accelerates on varying the unsteadiness parameter. The thermal field elevates by augmenting the Dufour number and thermal conjugate parameter. The drag force coefficient exhibits a decreasing behavior on enhancing the unsteadiness and velocity slip parameters. An opposite behavior is exhibited by heat and mass flux on amplifying the Soret and Dufour number. Motile density deteriorates on elevating the Lewis number and unsteadiness parameter. A substantial correlation has been noticed by graphically comparing the results of this study with the previous literature.

ENHANCEMENT OF DUPUIT-DARCY THERMAL CONVECTION OF SWCNT-WATER NON-NEWTONIAN NANOFLUID SATURATED POROUS MEDIUM

The focus of this manuscript is to investigate numerically the free convection of a single-wall carbon nanotube-water non-Newtonian nanofluid saturating an inclined square porous medium, where the Dupuit-Darcy model is used for modeling the fluid flow inside the cavity along with the Carreau-Yasuda model for describing the apparent viscosity of the nanofluid. The top and bottom walls of the enclosure are kept adiabatic, whereas the others are differentially heated. The governing parameters for the problem are the Rayleigh number, nanotubes volume fraction, inertial effect parameter, the Carreau-Yasuda non-Newtonian parameters as well as the inclination angle of the cavity. The finite difference method is used to resolve the governing partial differential equations of the problem. The obtained results are presented through graphs, streamlines, isotherms, and apparent viscosity contours. In addition, a scale analysis is presented to show the maximum heat transfer enhancement recorded. As a matter of fact, the obtained momentum equation enables the analysis of the Newtonian and non-Newtonian behavior of the nanofluid along with the Darcy and the departure from Darcy situation. The findings show that the increase of the single-wall carbone nanotube (SWCNT) percentage significantly enhances the heat transfer even with the increase of the fluid viscosity. Furthermore, the increase of inertial effect parameter inhibits the flow inside the cavity and causes a decrease in the convection rate. In actual fact the power-law index parameter of the Carreau-Yasuda model has a significant effect on the fluid flow strength as well as the convection rate inside the enclosure, i.e., the more the shear thinning the fluid, the better is the rate of convection. The inclination angle of -30° presents better angle for maximum convection rate. An enhancement of 8% in convection rate is recorded for the case of the Newtonian behavior, while for the shear-thinning situation the enhancement reaches eight times of that recorded of Newtonian condition.

The axisymmetric flow of an MHD Powell–Eyring fluid with viscous dissipation and Newtonian heating condition: Keller‐box method

AbstractA special investigation on the heat transfer by applying viscous dissipation and considering the Newtonian heating condition in magnetohydrodynamic Powell–Eyring fluid has been attempted. It is regarded as the flow in an axisymmetrical direction over a radially stretching surface. The converted governing system of equations is solved to obtain a closed‐form solution using the Keller‐box technique. The skin‐friction coefficient's influence fully developed local Nusselt number is then presented graphically, and temperature profiles are sorted out for the pertinent parameters. The fluid overshoot towards the plate surface with rising magnetic field strength, hence, both the fluid velocity and the hydrodynamic border line layer thickness will fall, though, the skin‐friction coefficient will increase. Various relevant results of the energy indulgence have been discussed from heating and in view of viscous dissipation phenomena. The decision with minimal cases from previous studies in the literature received confirmation of the findings.

Bulirsch-Stoer computations for bioconvective magnetized nanomaterial flow subjected to convective thermal heating and Stefan blowing: a revised Buongiorno model for theranostic applications

Theranostics is a novel procedure that integrates therapy and diagnosis in a single platform. For its application in theranostic and photothermal therapy for melanoma skin cancer, the hydromagnetic bioconvective flow of a nanomaterial over a lengthening surface is investigated. Realistic nanomaterial modeling is achieved by incorporating passive control of the nanoparticles at the boundary. The impact of the Newtonian heating and Stefan blowing constraints are also accounted. Apposite transformations are employed and then transmuted nonlinear ODEs are resolved using the Bulirsch-Stoer and Newton-Raphson methods. The influence of Stefan blowing parameter , the magnetic field parameter , and the Biot number on the heat transfer rate has been scrutinized and optimized utilizing the response surface methodology (RSM). The sensitivity of heat transport rate is computed. It is found that the Newtonian thermal condition intensifies the nanomaterial temperature that serves as a crucial role in the termination of cancerous cells or tumors. The maximum drag coefficient is experienced for the insignificant intensity of the magnetic field and Stefan blowing. Further, the heat transfer rate is maximum when the Stefan blowing and Biot numbers are at a high level and the Hartmann number is at a low level.

Thermally Radiative Casson Fluid Flow over a Cylinder with Newtonian Heating and Heat generation/absorption

This communication explains the impact of thermally radiative flow of a Casson fluid over a cylinder with velocity slip, suction/injection, and Newtonian heating condition. The governing PDE expressions are remodeled into an ODE expressing by applying suitable variables. The homotopy analysis (HAM) technique was implemented for solving our models. The impact of velocity field, temperature distribution, skin friction coefficient, Nusselt number in terms of diverse physical parameters like Casson parameter, suction/injection parameter, Newtonian heating parameter, radiation parameters, heat generation/absorption, Hartmann number and velocity slip parameter. The Hartmann number leads to slow down the fluid velocity, skin friction coefficient and local Nusselt number. The slip parameter decreases the fluid velocity and enhance the fluid heat transfer gradient.

The Effects of Newtonian heating and velocity ratio on entropy generationc in thermally dissipating flow above a thin needle

In this article, we investigated entropy generation analysis for viscous fluid over a thin needle. Two types of viscous fluids namely air and water are considered as counter examples. The energy dissipating term is included in the axial direction. The Newtonian heating condition is considered on the needle boundary. The governing equations for the flow under consideration are modeled in terms of partial differential equations (PDEs) which are then transformed into ordinary differential equations (ODEs) by using appropriate similarity variables. The transformed ODE's are then solved numerically using a numerical technique known as the Quasi-linearization method. The effects of embedded flow parameters on velocity, skin-friction, temperature, Nusselt number, Bejan number, and the irreversibility distribution ratio are determined graphically in several plots for both air and water. It is noticed that the total entropy generation Nst rate decreases with the increasing size of the thin needle. It is also found that the velocity ratio parameter ε reduced the skin friction. It is worth noting that the needle size a and the Newtonian heating parameter γ reduced the irreversibility distribution ratio Φ.

Numerical Analysis for Effect of Newtonian Heating Condition on MHD Flow of Cu-water Nanofluid Past a Flat Plat

Present analysis involves behavior of MHD flow of Cu- water nanofluid in the presence of Newtonian heating impact towards a flat surface. Convenient transformations are used to alter the leading partial differential equations into a set of ordinary differential equations. An effective numerical approach as Runge-Kutta fourth order method is applied to solve the governing equations alongside shooting technique. Fluid flow and fluid temperature studied in graphical form for impacts of solid volume fraction, magnetic parameter and local Biot number. Additionally, local skin friction and local Nusselt number are derived via table for effects of pertinent parameters.

Soret and Dufour effects in stretching flow of Jeffrey fluid subject to Newtonian heat and mass conditions

Main emphasis of present research is to introduce the novel concept of Newtonian flux condition in MHD stretching flow of Jeffrey liquid. Flow is generated due to stretching of a permeable cylinder. Phenomena of heat and mass transfer is based through involvement of thermal-diffusion and diffusion-thermo aspects. Suitable variables are employed for conversion of partial differential frameworks into a sets of ordinary differential expressions. Analytic solutions are constructed through homotopic procedure. Salient impacts of distinct variables are reported graphically. Temperature and concentration are improved within frame of thermal/solutal conjugate variables.

Unsteady free convection flow of a micropolar fluid with Newtonian heating: Closed form solution

This article investigates the unsteady free convection flow of a micropolar fluid over a vertical plate oscillating in its own plane with Newtonian heating condition. The problem is modelled in terms of partial differential equations with some physical conditions. Closed form solutions in terms of exponential and complementary error functions of Gauss are obtained by using the Laplace transform technique. They satisfy the governing equations and impose boundary and initial conditions. The present solution in the absence of microrotation reduces to well-known solutions of Newtonian fluid. Graphs are plotted to study the effects of various physical parameters on velocity and microrotation. Numerical results for skin friction and wall couple stress is computed in tables. Apart from the engineering point of view, the present article has strong advantage over the published literature as the exact solutions obtained here can be used as a benchmark for comparison with numerical/ approximate solutions and experimental data.

Nonchaotic evolution of triangular configuration due to gravitational radiation reaction in the three-body problem

Continuing work initiated in an earlier publication [H. Asada, Phys. Rev. D {\bf 80}, 064021 (2009)], the gravitational radiation reaction to Lagrange's equilateral triangular solution of the three-body problem is investigated in an analytic method. The previous work is based on the energy balance argument, which is sufficient for a two-body system because the number of degrees of freedom (the semimajor axis and the eccentricity in quasi-Keplerian cases, for instance) equals that of the constants of motion such as the total energy and the orbital angular momentum. In a system with three (or more) bodies, however, the number of degrees of freedom is more than that of the constants of motion. Therefore, the present paper discusses the evolution of the triangular system by directly treating the gravitational radiation reaction force to each body. The perturbed equations of motion are solved by using the Laplace transform technique. It is found that the triangular configuration is adiabatically shrinking and is kept in equilibrium by increasing the orbital frequency due to the radiation reaction if the mass ratios satisfy the Newtonian stability condition. Long-term stability involving the first post-Newtonian corrections is also discussed.

A lattice Boltzmann study of the asymmetry effect on the hemodynamics in stented fusiform aneurysms

In this paper, the effect of asymmetric bulges on the hemodynamics in stented fusiform aneurysms under pulsatile Newtonian flow condition has been studied numerically by the lattice Boltzmann method. In order to guarantee the efficiency and accuracy of the method, a domain decomposition technique is also considered. Numerical results show that the flow structures are significantly affected by the asymmetric bulges. For non-stented fusiform aneurysms, the maximum wall shear stress (WSS) and maximum wall pressure are found to occur near the distal end of the aneurysms at peak systole, and the magnitude of peak WSS and wall pressure usually increase along with the increase of the maximum height of the dilated region. In addition, the implantation of a stent can reduce the magnitude of the maximum wall pressure and WSS at the distal end, and a low-porosity stent gives better performance than a high-porosity stent in terms of the reduction. In particular, for stented fusiform aneurysms, the effect of asymmetry on wall pressure is found insignificant. Further, a comparison between pulsatile solution and steady-state solution at peak systole is also presented, and the results show that the difference of WSS near the proximal neck for two conditions is not apparent, while the location of the maximum wall pressure obtained from steady-state condition moves toward downstream in contrast to pulsatile condition, and the maximum WSS at the distal end is underestimated by the condition of steady-state.

Musielak-Orlicz-Sobolev spaces on metric measure spaces

Our aim in this paper is to study Musielak-Orlicz-Sobolev spaces on metric measure spaces. We consider a Hajlasz-type condition and a Newtonian condition. We prove that Lipschitz continuous functions are dense, as well as other basic properties. We study the relationship between these spaces, and discuss the Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness of the Hardy-Littlewood maximal operator, we establish a generalization of Sobolev’s inequality for Sobolev functions in Musielak-Orlicz-Hajlasz-Sobolev spaces.

Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating

In this article, the unsteady boundary layer magnetohydrodynamic (MHD) free convection flow past an oscillating vertical plate embedded in a porous medium with constant mass diffusion and Newtonian heating condition is analysed. By considering the effects of thermal radiation in the energy equation, the problem is first modeled and then written in dimensionless form, which is then solved by using the Laplace transform technique. The expressions for velocity, temperature and concentration fields are obtained and plotted graphically to see the influence of embedded parameters. The results for skin friction, Nusselt number and Sherwood number are also shown in tables. Further a table is included for the comparison of our results with those present in the literature.

WSS Investigation in Microfluidic FFS Channel at Re 500

Wall shear stress (WSS) is one of the important variables in microfluidic devices. In this paper WSS distribution for a microfluidic device in Forward Facing Step (FFS) configuration has been investigated using Reynolds number 500 and step height 1μm. Numerical simulation was performed usingAnsys-CFX software with the assumption of Newtonian fluid and laminar condition. The simulation result showed that wall shear stress distribution increased after the fluid passing through the step.