Non-isothermal viscoelastic flow

The theoretical description of a non-isothermal viscoelastic flow presents a conceptual difficulty. To give a brief explanation of this problem we note that in a non-isothennal flow field the evolution of stresses will be affected by the 

FINITE ELEMENT MODELLING OF POLYMERIC FLOW PROCESSES 

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

Derivation of the working equations of upwinded schemes for heat transport in a polymeric flow is similar to the previously described weighted residual Petrov-Galerkm finite element method. In this section a basic outline of this derivation is given using a steady-state heat balance equation as an example. 

Assuming constant physical coefficients for simplicity, the steady-state energy equation is expressed as 

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A FINITE ELEMENT MODEL OF NON-ISOTHERMAL VISCOELASTIC FLOW... 

Huilgol RR, You Z (2006) On the importance of the pressure dependence of viscosity in steady non-isothermal shearing flows of compressible and incompressible fluids and in the isothermal fountain flow. J Non-Newtonian Fluid Mech 136 106-117 Hulsen MA, Van Heel APG, Van den Brule BHAA (1997) Simulation of viscoelastic flows using Brownian configuration fields. J Non-Newtonian Fluid Mech 70 79-101 Ingber MS, Mondy LA (1994) A numerical study of three-dimensional Jeffery orbits in shear flow. J Rheol 38 1829-1843... 

Although all polymer processes involve complex phenomena that are non-isothermal, non-Newtonian and often viscoelastic, most of them can be simplified sufficiently to allow the construction of analytical models. These analytical models involve one or more of the simple flows derived in the previous chapter. These back of the envelope models allow us to predict pressures, velocity fields, temperature fields, melting and solidification times, cycle times, etc. The models that are derived will aid the student or engineer to better understand the process under consideration, allowing for optimization of processing conditions, and even geometries and part performance. 

Khan, 2006) studied the case of the boundary layer problem on heat transfer in a viscoelastic boundary layer fluid flow over a non-isothermal porous sheet, taking into account the effect a continuous suction/blowing of the fluid, through the porous boundary. The effects of a transverse magnetic field and electric field on momentum and heat transfer characteristics in viscoelastic fluid over a stretching sheet taking into accoimt viscous dissipation and ohmic dissipation is presented by (Abel et al., 2008). (Hsiao, 2007) studied... 

Prasad, K.V. Abel, M. S. Khan, S.K. Datti, P. S. (2002). Non-Darcy forced convective heat transfer in a viscoelastic fluid flow over a non-Isothermal stretching sheet, /. Porous Media, 5, pp. 41-47, ISSN 1091-028X. 

Prasad, KV. Abel, M. S. Khan, S. K. (2000). Momentum and heat transfer in viscoelastic fluid flow in a porous medium over a non-isothermal stretching sheet, Int. ]. Numer. Method Heat flow, 10, pp. 786-801, ISSN 0961-5539. 

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