Up to the authors knowledge, 14 constitutes one of the rst works in analysing a nite element discretization for the non isothermal oldroyd stokes equations. A dual mixed formulation for nonisothermal oldroydstokes. Isothermal and nonisothermal flow of ptt fluid in liddriven. This is a consequence of joules second law which states that the internal energy of a fixed amount of. Our analysis coupled with numerical solution of the problem with both temperaturedependent viscosities distinguishes this work from earlier efforts. Axisymmetric simulation of viscoelastic filament thinning. Mckinley department of mechanical engineering, massachusetts institute of technology, cambridge, massachusetts 029 received 29. B nanofluid with thermal radiation and activation energy effects.
For the total extrastress tensor t, we select the oldroyd b constitutive model 27. Dynamics of coupled reacted flow of oldroydb material. Non isothermal flow of a thin film of fluid with temperaturedependent viscosity on a stationary horizontal cylinder phys. Non isothermal modification of purely elastic flow instabilities in torsional flows.
This new finite element has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass. Mixed convection heat transfer in stagnation flows is also of some interest in. Anwar beg 2 and ali kadir 2 1 department of mathematics, faculty of natural sciences, hitec university, taxila cantt, pakistan. Citeseerx computing and information finite element. Isothermal and nonisothermal viscoelastic flow of ptt fluid. On flows of viscoelastic fluids of oldroyd type with wall. The model is described by a system of equations where the stokes and. On the derivation of macroscopic models for compressible. Isothermal and nonisothermal flow of ptt fluid in lid. Aug 11, 2008 the present paper is concerned with non isothermal spherical couette flow of oldroyd b fluid in the annular region between two concentric spheres. The state and adjoint equations are solved using the finite element method. Streamlines for newtonian flow at re60 a isothermal case. Effect of magnetic field on mixed convection flow of.
Efficient numerical modelling of nonisothermal viscoelastic. Isothermal processes are of special interest for ideal gases. Mckinley department of mechanical engineering, massachusetts institute of technology, cambridge, massachusetts 029 received 29 february 2000. Fem simulation of nonisothermal viscoelastic fluids core. Numerical study of activation energy and thermal radiation.
Here we relate the values for ai and bi to physical quantities and establish conditions to assure that 0 oldroyd b jet. Isothermal steady spinning of an oldroyd fluid b, aiche. The viscoelasticity of the fluid is assumed to dominate the inertia such that the latter can be neglected in the momentum and energy equations. Oct 01, 2009 the latter three equations are a non isothermal version of the threefield stokes oldroyd model, formulated to have the same dependent variable set as the equations governing viscoelastic flow. Viscoelastic flow around a cylinder with oldroyd b for we 2. Pdf nonisothermal spherical couette flow of oldroydb fluid. However, a pdf version of this paper is also available. This investigation deals with analytical solutions of thin film flow for withdrawal and drainage of an incompressible generalized oldroyd b fluid on a vertical cylinder under the influence of non isothermal. This investigation deals with analytical solutions of thin film flow for withdrawal and drainage of an incompressible generalized oldroyd b fluid on a vertical cylinder under the influence of non isothermal effects. Flow and heat transfer of hydromagnetic oldroydb fluid in a. Feb 01, 2021 the exothermic reaction expression through first order non isothermal reaction merikin et al. Isothermal steady spinning of an oldroyd fluid b isothermal steady spinning of an oldroyd fluid b chung, tai. The inner sphere rotates with a constant angular velocity while the outer sphere is kept at rest. Effect of magnetic field on mixed convection flow of oldroyd.
Compressible isothermal and non isothermal forms of the oldroyd b model derived using the generalized bracket formulation are. Pdf temperature effect on spherical couette flow of. This is a consequence of joules second law which states that the internal energy of a fixed amount of an ideal gas depends only on its temperature. Analysis of an augmented fullymixed formulation for the non. Viscoelastic flows occur in a variety of applications, including polymer. The oldroyd b non newtonian model is employed which allows relaxation and retardation effects to be included. Isothermal processes are often used and a starting point in analyzing more complex, non isothermal processes. The present paper is concerned with non isothermal spherical couette flow of oldroyd b fluid in the annular region between two concentric spheres. Some existence and stability results for nonisothermal flows. Optimal control of nonisothermal viscous fluid flow. International audiencewe propose a mixed formulation for nonisothermal oldroyd stokes problem where the both extra stress and the heat fluxs vector are considered.
Numerical simulation of nonisothermal viscoelastic flows at high. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The maximum and minimum stream function values are also given with peak locations. We consider the stokes oldroyd equations, defined here as the stokes equations with the newtonian constitutive equation explicitly included. S0 and adiabatic q0 distance a use teb to construct a table of t as a function of xa b use k aeert to obtain k as a function of xa c use stoichiometry to obtain ra as a function of xa d calculate. Some existence and stability results for nonisothermal. Pdf and epub downloads, according to the available data and abstracts views on vision4press platform. See 6 for analysis of the solution of equations 1215. Dec 30, 2015 this investigation deals with analytical solutions of thin film flow for withdrawal and drainage of an incompressible generalized oldroyd b fluid on a vertical cylinder under the influence of non isothermal effects. International journal of c 2007 institute for scientific numerical analysis and modeling computing and information volume 4, number 34, pages 425440 finite element approximation of the non isothermal stokes oldroyd equations christopher cox, hyesuk lee, and david szurley dedicated to max gunzburger on the occasion of his 60th birthday.
Finite element approximation of the nonisothermal stokesoldroyd. The derived solutions are presented under series form for velocity profile, temperature distribution, volume flux, average film velocity and shear stress in both cases. Jan 04, 2009 nonisothermal melt spinning processes 183 has an upper bound for the. Ye ilata 2002 formulated the problem for the non isothermal flow of an oldroyd b fluid between two rotating parallel plates and investigated how. Streamlines for newtonian flow at re60 a isothermal. The central vortex is observed to shift in the positive. Stable computations over a wide range of weissenberg numbers are assured by using the root conformation approach in a finite volume framework on general unstructured meshes. Withdrawal and drainage of thin film flow of a generalized oldroyd b fluid on non isothermal cylindrical surfaces by saif ullah, arshad ullah and mohsan iqbal cite. Isothermal and nonisothermal viscoelastic flow of ptt. Nonisothermal and viscoelastic effects in the squeeze flow. Gaticaz ricardo oyarz ua x abstract in this work we present an augmented mixed nite element method for the oldroyd stokes problem describing the motion of a non isothermal incompressible uid subject to a heat source. Recall that the modified non isothermal stokes oldroyd equations were designed with two viscosity functions. Pdf temperature effect on spherical couette flow of oldroyd.
Based on special cfd techniques including adaptivitylocal grid alignment in spacetime and fast hierarchical fem techniques. Pdf on thermodynamics of viscoelastic rate type fluids with. Pdf stability of thermal convection of an oldroydb fluid. In that work, the authors provide a complete analysis of a mixedprimal formulation for the coupled problem, in which the main unknowns. Heat transfer in a nonnewtonian jeffreys fluid over a non. Heat transfer in a nonnewtonian jeffreys fluid over a nonisothermal wedge. To my father and son, damanik, my mother and wife, julia and shinta. Nonisothermal modification of purely elastic flow instabilities in torsional flows. Pdf stability of thermal convection of an oldroydb. Fem simulation of nonisothermal viscoelastic fluids.
Here we relate the values for ai and bi to physical quantities and establish conditions to assure that 0 dec 30, 2015. Viscoelastic flow around a cylinder with oldroydb for we 2. Non isothermal flows of newtonian slender glass fibers 155 and the temperature boundary conditions are tl at zo, d2t 0 at zl dz2 14 here, w and t are the mean axial velocity and the bulk temperature respectively, given by 2 r wc r2 s o rwdr, s r rwtdr. We propose a mixed formulation for nonisothermal oldroydstokes problem where the both extra stress and the heat fluxs vector are considered. Thus a polymerlike stress tensor is included so that the dependent variable structure of a viscoelastic model is in place.
We propose a mixed formulation for the non isothermal stokes oldroyd problem where both the extra stress tensor and the heat fluxs vector are considered. Pdf optimal control of nonisothermal viscous fluid flow. Pdf withdrawal and drainage of thin film flow of a. The above relations are known as arrhenius kinetics where r 1 is the constant of universal gas, b is product species, e is activation energy, k 0 reflects the rate constant, a is concentration of. We prove that under some restrictions on the material constants and the data, there exists a strong solution which is locally unique. Heat transfer in a nonnewtonian jeffreys fluid over a non isothermal wedge. A numerical solution for nonisothermal mhd flow of an oldroydb fluid through a channel with. Numerical simulation of non isothermal viscoelastic flows at high. Nonisothermal and viscoelastic effects in the squeeze. Dec 24, 20 we consider the boundaryvalue problem for the steady isothermal flow of an incompressible viscoelastic liquid of oldroyd type in a bounded domain with a navier type slip boundary condition. Based on such a formulation, a dual mixed finite element is constructed and analyzed. Jan 01, 2017 in this study, we have constructed a mathematical model to investigate the heat sourcesink effects in mixed convection axisymmetric flow of an incompressible, electrically conducting oldroyd b fluid between two infinite isothermal stretching disks.
A numerical solution for non isothermal mhd flow of an oldroyd b fluid through a channel with stretching walls is presented. The geometrical singularity at the reentrant corner is a. In this numerical study, an original approach to simulate non isothermal viscoelastic fluid flow at high weissenberg numbers is presented. Some exact solutions for the rotational flow of oldroydb fluid. Abstract this paper investigates a theoretical model of a mixed convective oldroyd. Non isothermal behavior is simulated by allowing the model constants viscosities and relaxation time to vary with temperature. Pdf the present paper is concerned with non isothermal spherical couette flow of oldroyd b fluid in the annular region between two concentric spheres find, read and cite all the research. Withdrawal and drainage of thin film flow of a generalized. Analysis of an augmented fullymixed formulation for the. A dual mixed formulation for nonisothermal stokesoldroyd. Pdf we propose a mixed formulation for nonisothermal oldroyd stokes problem where the both extra stress and the heat fluxs vector are considered find, read and cite all the research you. Sorry, we are unable to provide the full text but you may find it at the following locations. Pdf finite element approximation of the nonisothermal.
The equations were designed in this manner with the ultimate goal of implementing a viscoelastic constitutive model in mind. Further, the upper bound value depends on the characteristic relaxation time of the polymer. The effects of viscous dissipation and joule heating are also considered in the heat equation. Pdf a dual mixed formulation for nonisothermal oldroyd. The present paper is concerned with nonisothermal spherical couette flow of oldroyd b fluid in the annular region between two concentric spheres. Me 510 non newtonian fluids oldroyd model lecture notes drew wollman restrictions on oldroyd model 1. Acknowledgements i would like to thank my main supervisor, prof. Nonisothermal modification of purely elastic flow instabilities in.
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