Newton Boundary Research Articles

Thermal radiation influence on non-Newtonian nanofluid flow along a stretchable surface with Newton boundary condition

This article focuses on the heat transfer on a mixed convection flow of nanoparticles suspended non-Newtonian nanofluid past a stretching surface under Newtonian boundary conditions. The leading boundary layer equations are changed to a non-linear boundary value problem by using suitable similarity variables. BVP4c with MATLAB is used to elucidate the resultant system. The controlled parameters involved in the flow field problem and its impact on the flow components as well as the interested engineering quantities are examined via graphs and tables. Our study results are in good agreement with the existing literature. It is noticed that the presence of radiation increases the heat inside the fluid, which leads to an increase in the thickness of the energy boundary layer and an increase in the temperature of the fluid. The temperature of the fluid decreases for higher values of the Brownian motion parameter and increases for variations in thermophoresis.

Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition

Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition

Irreversibility analysis of tangent hyperbolic fluid flow in a microchannel: a hybrid nanoparticles aspects

The tangent hyperbolic fluid model is an interesting model in all the non-Newtonian fluid models, which is developed for particular applications in chemical engineering systems such as polymer solution, ceramic processing, fluid beds, and oil recovery. Hence the intent of the present study is to explore the flow and thermal behavior of tangent hyperbolic fluid flowing through an upright microchannel. In the analysis, water and ethylene glycol are the base fluid with titanium and copper nanoparticles considered. The combined impact of nonlinear thermal radiation, no slip, buoyancy force, and Newton boundary condition on the thermal performance are studied, and further, the skin friction and Nusselt number are examined. The thermal dependent heat source effect was also taken into account. The governing equations were solved numerically by employing Runge–Kutta Fehlberg’s fourth-fifth order. The impact of the pertinent constraint on the Nusselt number, thermal field, flow field, skin friction, Bejan number, and entropy generation are depicted graphically and examined. Entropy generation rises by 15% when ethylene glycol is a base fluid and 12% when the water is a base fluid, with an enhancement of the Brinkman number by 200%. The outturn entrenched that the heat transfer rate in water-based hybrid nanofluid is more remarkable when compared with the heat transfer rate of EG-based hybrid nanofluid. It is noted that the significant increment in the Nusselt number has been attained through a rise in the Weissenberg number and power law index.

ON THE MILNOR FIBRATION OF CERTAIN NEWTON DEGENERATE FUNCTIONS

AbstractIt is well known that the diffeomorphism type of the Milnor fibration of a (Newton) nondegenerate polynomial function f is uniquely determined by the Newton boundary of f. In the present paper, we generalize this result to certain degenerate functions, namely we show that the diffeomorphism type of the Milnor fibration of a (possibly degenerate) polynomial function of the form $f=f^1\cdots f^{k_0}$ is uniquely determined by the Newton boundaries of $f^1,\ldots , f^{k_0}$ if $\{f^{k_1}=\cdots =f^{k_m}=0\}$ is a nondegenerate complete intersection variety for any $k_1,\ldots ,k_m\in \{1,\ldots , k_0\}$ .

Hodge ideals and spectrum of isolated hypersurface singularities

We introduce Hodge ideal spectrum for isolated hypersurface singularities to see the difference between the Hodge ideals and the microlocal V-filtration modulo the Jacobian ideal. Via the Tjurina subspectrum, we can compare the Hodge ideal spectrum with the Steenbrink spectrum which can be defined by the microlocal V-filtration. As a consequence of a formula of Mustață and Popa, these two spectra coincide in the weighted homogeneous case. We prove sufficient conditions for their coincidence and non-coincidence in some non-weighted-homogeneous cases where the defining function is semi-weighted-homogeneous or with non-degenerate Newton boundary in most cases. We also show that the convenience condition can be avoided in a formula of M. Zhang for the non-degenerate case, and present an example where the Hodge ideals are not weakly decreasing even modulo the Jacobian ideal.

Regularity results and numerical solution by the discontinuous Galerkin method to semilinear parabolic initial boundary value problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder

Abstract In this note we consider a parabolic evolution equation in a polygonal space-time cylinder. We show, that the elliptic part is given by a m-accretive mapping from L q (Ω) → L q (Ω). Therefore we can apply the theory of nonlinear semigroups in Banach spaces in order to get regularity results in time and space. The second part of the paper deals with the numerical solution of the problem. It is dedicated to the application of the space-time discontinuous Galerkin method (STDGM). It means that both in space as well as in time discontinuous piecewise polynomial approximations of the solution are used. We concentrate to the theoretical analysis of the error estimation.

Łojasiewicz exponents of certain analytic functions

We consider the exponent of Łojasiewicz inequality ‖∂f(z)‖≥c|f(z|θ for two classes of analytic functions and we will give an explicit estimation for θ. First we consider certain non-degenerate functions which is not convenient. In §3.4, we give an example of a polynomial for which θ0(f) is not constant on the moduli space and in §3.5, we show that the behaviors of the Łojasiewicz exponents are not similar as the Milnor numbers by an example.In the last section (§4), we give also an estimation for product functions f(z)=f1(z)⋯fk(z) associated to a family of a certain convenient non-degenerate complete intersection varieties. In either class, the singularity is not isolated. We will give explicit estimations of the Łojasiewicz exponent θ0(f) using combinatorial data of the Newton boundary of f. We generalize this estimation for non-reduced function g=f1m1⋯fkmk.

THE EFFECT OF 3D TECHNOLOGIES IN STEREOMETRY TRAINING

The software proposed in the report can be used as a technological tool in the teaching and learning of the discipline of stereometry. The aim is to improve the learning process by supporting the development of students’ creativity and spatial imagination, qualities needed in the study of spatial geometric bodies. A new boundary method is used in the generation of geometric objects. This new method uses elements of the Cavalieri Indivisible method and Isaac Newton's boundary method, thus achieving higher accuracy with respect to generated objects compared to 3D systems that use the rules of trigonometry in the construction of geometric bodies. This article performs a comparative analysis between a traditional and a new method for generating 3D geometric objects according to certain parameters and criteria. The new method involved in the analysis was proposed by the author of the report. While the traditional one is based on trigonometry. Two parameters were studied, one for accuracy in generating objects, and the second determining speed. In order to generate cylindrical bodies, are used the quadratic Bézier curve and the 3D modeling technique known as an extrusion, which transforms two-dimensional objects into three-dimensional ones.. One way to generate a prism and pyramid is by extruding polygons. This report presents a new way of constructing edged bodies. The considered technique for 3D modeling participates in the analysis of the studied methods.

Spectral quasi-linearization and irreversibility analysis of magnetized cross fluid flow through a microchannel with two different heat sources and Newton boundary conditions

Spectral quasi-linearization and irreversibility analysis of magnetized cross fluid flow through a microchannel with two different heat sources and Newton boundary conditions

Repercussion of Hall current, no-slip, and Newton boundary condition on the thermal energy of the Carreau fluid in a microchannel

ABSTRACT This research article addresses the physical characteristics of the Carreau fluid flow through a horizontal microchannel subjected to Newton boundary conditions, Hall current, and heat generation. The momentum and energy balance equations have been solved numerically by using the fourth-fifth ordered Runge–Kutta-Fehlberg method. The numerical results of velocity and energy mathematical models have been used to conclude the entropy generation, skin friction, and Nusselt number. The Hall parameter develops the axial velocity, transverse velocity, and temperature profile. The axial and transverse velocity shows distinct behaviour for Weissenberg number (by enhancing and diminishing) depending on the power law index. The optimum values of the Weissenberg number, Brinkman number and Hall current parameter escalate the temperature profile. Irreversibility rate falls with magnetic parameter and Weissenberg number. On the other hand, irreversibility ratio enhances by the augmentation of magnetic parameter and diminishes by the escalation of Brinkman number. The Hall current parameter and Weissenberg number enhance the skin friction in both axial and transverse velocities. The Brinkman number and Biot number upturn the heat transfer by convection process at the upper wall area of the channel.

Significance of nonlinear Boussinesq approximation and non-uniform heat source/sink on nanoliquid flow with convective heat condition: sensitivity analysis

The quadratic convective flow of nanoliquid over an elongating plate subjected to non-uniform heat source/sink, partial slip, and Newton boundary conditions is studied by using the modified Buongiorno model. The correlation for effective thermal conductivity and viscosity of nanoliquid are taken from the experimental work of Corcione. The dimensionless velocity, temperature, rate of heat transport, and mass transport distributions are simulated by solving the nonlinear boundary value problem using the finite difference method. The additional novelty of the present study is an application of response surface methodology to scrutinize the interactive impact of key parameters on the rate of heat transfer. Further, the influence of key parameters is deliberated on various flow fields using the surface and streamline plots. The higher velocities are noticed for the case of nonlinear Boussinesq approximation as compared with the usual Boussinesq approximation. The temperature enhances with a non-uniform heat source/sink aspect. The sensitivity of the heat transfer to the nanoparticle volume fraction remains positive.

Double‐diffusive natural convective stream due to moving vertical plate with nonlinear thermal radiation and Newton's boundary constraint

AbstractThis article investigates the heat and mass transmission of the double‐diffusive convective stream over a moving vertical plate with nonlinear thermal radiation and newton boundary conditions. The governing partial differential equations of the stream, heat, and concentration profiles were transformed into a system of nonlinear ordinary differential equation by utilizing resemblance transformation. This system was then resolved numerically by applying the fourth order Runge‐Kutta method with most efficient shooting technique. The effect of convection, buoyancy ratio, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number are graphically scrutinized. The numerical results are obtained for velocity, temperature, and concentration profiles. It is found that when the velocity profile increases, heat and mass transfer rate decreases with an increase in the parametric value of buoyancy ratio parameter. It is found that the effect of nonlinear thermal radiation stabilizes the thermal boundary layer growth. The skin friction coefficient decreases with an increase in Prandtl number. However, the Nusselt number increases with an increase in the local convective heat transfer rate. The present results are very much promising, and further, there is a very good agreement of results when compared with earlier published results for some limiting conditions.

Heat transfer and irreversibility rate in MHD flow of a hybrid nanofluid with Newton boundary condition, slip flow, and nonlinear thermal radiation

AbstractThe magnetohydrodynamic flow of a water‐based hybrid nanoliquid through a vertical microchannel has been investigated in the presence of collective effects, such as volume fraction of nanoparticle, suction/injection, magnetic field, temperature‐dependent heat source, hydrodynamic slip, and convective boundary conditions. The current mathematical formulations have been worked out numerically by using the fourth‐ and fifth‐order Runge–Kutta–Fehlberg scheme. The physical aspects of variation in velocity, temperature, entropy generation, and Bejan number with considered governing parameters have been discussed via corresponding graphs. The obtained numerical results demonstrated that radiation parameter and nanoparticle volume fraction reduce the thermal energy of the hybrid nanofluid. Moreover, entropy generation diminishes with the Hartmann number and permeability parameter, whereas it enhances with the Grashof number and Biot number.

Exploration of irreversibility and thermal motion of a nanoliquid with the Newton boundary condition by using the Darcy–Forchheimer rule

AbstractThis study has been conducted to focus on magnetohydrodynamic flow of a nanoliquid through a microchannel in the presence of a magnetic field. In this article, carbon nanotubes suspended in an aqueous medium were our considered fluid, and we focused on both singlewall and multiwall carbon nanotubes. The numerical calculations have been made via the fourth‐ and fifth‐order Runge–Kutta–Fehlberg method. The flow of the nanoliquid in a microchannel with porosity has been scrutinized with the existence of mutual effects, like, the nanoparticle volume fraction, suction or injection, thermal‐dependent heat source, convective boundary conditions, Darcy friction factor, and thermal motion of the nanoparticles. The influence of every major parameter on the profile of momentum, temperature, and entropy generation has been displayed graphically, and we discuss their physical aspects. The numerical outcomes demonstrated that the momentum profile augmented with the buoyancy force, angle of inclination, and Darcy number. Thermal energy was enriched with the heat source parameter, Darcy number, and Hartmann number. The irreversibility rate declined with the volume fraction of nanoparticle and radiation parameter, while it increases with the buoyancy force, Eckert parameter, and Darcy friction factor.

Transient solution of temperature field of conjugate laminar forced convection heat transfer in functionally graded hollow cylinder

AbstractIn this study, the numerical analysis of conjugate heat transfer of laminar flow in a functionally graded hollow cylinder (FGHC) made of metal/ceramic for a two‐dimensional fluid and wall conduction subject to Newton boundary condition is considered. The fluid and FGHC energy equations are coupled through the continuity of temperature and heat flux at the inner wall‐fluid interface while the outer surface is subject to convective heat transfer. The continuity, momentum, and energy equations of the fluid are discretized using the finite volume approach. The effects of fluid and functionally graded material parameters, such as volume fraction index, volume composition, time history, wall‐to‐fluid thermal diffusivity ratio, wall‐to‐fluid thermal conductivity ratio, Biot number, Peclet number, and Prandtl number are investigated on the temperature field in the FGHC. The result shows that on account of the inhomogeneity of the material property, the volume fraction index has a significant effect on the other parameters and the temperature variation along the thickness. The lower the volume fraction index, the higher the inner wall (metal side) temperature, and the temperature gradient along the thickness. However, except for the variation in the wall‐to‐fluid thermal conductivity ratio, the lower the volumetric fraction, the lower the outer wall (ceramic side) temperature distribution.

Global weak solutions to degenerate coupled transport processes in partially saturated deformable elastic-inelastic porous media

In this work we prove the existence of global weak solutions to a degenerate and strongly coupled parabolic system arising from the transport processes through partially saturated deformable porous materials. The hygro-thermal model is coupled with quasi-static evolution equations modeling elastic and inelastic mechanical deformations. Physically relevant Newton boundary conditions are considered for water pressure and temperature of the porous system. The traction boundary condition is imposed on the deformable solid skeleton of the porous material. Degeneration occurs in both elliptic and parabolic part of the balance equation for mass of water. The coupling between water pressure, temperature, stress tensor and internal variables occurs in transport coefficients, constitutive functions and the decomposition of the total strain tensor into elastic and plastic parts due to mechanical effect and strain tensor due to thermal expansion.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/63/abstr.html

English

This paper is concerned with the analysis of the finite element method for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. The weak solution loses regularity in a neighbourhood of boundary singularities, which may be at corners or at roots of the weak solution on edges. The main attention is paid to the study of error estimates. It turns out that the order of convergence is not dampened by the nonlinearity if the weak solution is nonzero on a large part of the boundary. If the weak solution is zero on the whole boundary, the nonlinearity only slows down the convergence of the function values but not the convergence of the gradient. The same analysis is carried out for approximate solutions obtained by numerical integration. The theoretical results are verified by numerical experiments.

Термомеханічна задача про коливання в'язкопружного гумоподібного стержня при динамічному навантаженні

The problem on vibration of a viscoelastic rod under dynamic load at one of its ends is considered. The external loading has a signfficant influence on the dynamic characteristics of the material. By using the complex moduli, the problem on vibration of the viscoelastic rod was solved. The complex shear and Young's moduli of a rubberlike material should exhibit the same dependence on frequency. The properties of a rubberlike material was applied. The temperature influence is associated both with the Newton boundary conditions and dissipative heating. The dissipative function is expressed in terms of deformations. The frequencies of high-damping materials occur at or near frequencies that are normally of interest in vibration problems at room temperature. For solving the problem a finite element model was applied. Using this model, qualitative analysis of the influence of dynamic load and dissipative heating on the resonant vibrations of viscoelastic rod is performed. According to the theory of viscoelasticity an analysis of the results was done. The reliability of the values of frequencies for the first resonances was checked. The numerical results qf the problem on vibration of a viscoelastic cylindrical rod under dynamic load at one of its end by the general thermomechanical laws on vibration in damped mechanical systems were obtained and investigated. Distribution of the temperature of dissipative heating along the rod axis is analyzed.

Deforming spaces of m-jets of hypersurfaces singularities

Let K be an algebraically closed field of characteristic zero, and V a hypersurface defined by an irreducible polynomial f with coefficients in K.In this article we prove that an Embedded Deformation of V which admits a Simultaneous Embedded Resolution induces, under certain conditions, a deformation of the space of m-jets Vm, m≥0. An example of an Embedded Deformation of V which admits a Simultaneous Embedded Resolution is a Γ(f)-deformation of V, where V has at most one isolated singularity, and f is non-degenerate with respect to the Newton Boundary Γ(f).

Domain decomposition algorithms for problems of thermomechanical contact between several elastic bodies

We consider a thermoelastic multibody contact problem for finite bodies with unilateral mechanical and imperfect thermal contact conditions. Using a penalty method, we obtain a weak formulation of this problem in the form of a system of linear and nonlinear variational equations in Hilbert space. To solve this variational system, we propose a class of iterative Robin type domain decomposition algorithms. In each iterative step of these algorithms one have to solve two linear variational equations for each of the bodies, which correspond to heat conduction problem with Newton boundary conditions on the possible contact areas and linear elasticity problem with additional volume forces and Robin boundary conditions respectively. The program implementation of proposed algorithms is made for plane thermoelastic contact problems with the use of linear and quadratic finite element approximations on triangles. The numerical analysis is performed for one-body and two-body thermoelastic contact problems.