Effects of Fluid Viscoelasticity in Non-Isothermal Flows

Abstract

The study of non-Newtonian fluids is of fundamental importance in practically all branches of science and engineering that deal with incompressible fluid flow. Blood rheology, food processing, petroleum engineering, polymer blending and pharmaceutical product development are only but a few areas in which non-Newtonian fluids play a major role. Inelastic fluids with shear rate dependent viscosities are an example of non-Newtonian fluids, such fluids are called Generalized Newtonian fluids. Fluids that exhibit elastic effects are another example of non-Newtonian fluids, these fluids are called Viscoelastic fluids. We focus attention on viscoelastic fluids whose viscosities are either independent of applied shear-rates (Boger fluids) or whose viscosities are shear-rate dependent (e.g. the Generalized Oldryd-B fluids). In either case the fluid viscosity will be considered temperature dependent and our investigations will focus on the fluids’ heat transfer characteristics in simple flows. As in Chinyoka (2008; 2009a;b; 2010; 2011) the viscoelastic fluid behavior is compared to that for corresponding inelastic (Newtonian and/or Generalized Newtonian) fluids and it is demonstrated that depending on the physical application, viscoelasticity may or may not be favorable. For a comprehensive overview of non-Newtonian flows in general and viscoelastic fluid phenomena in particular, we refer to the excellent treatises of Bird et al. (1987); Ferry (1981). Investigations of heat transfer in fluid flow have mostly been conducted for inelastic fluids. Temperature dependent flows of viscoelastic fluids have been largely limited by the slow development of the relevant universally accepted non-isothermal constitutive models. The mathematical discussion of the constitutive modeling of non-isothermal effects in the flow of viscoelastic fluids is still underway and the references Dressler et al. (1999); Hutter et al. (2009); Peters & Baaijens (1997); Sugend et al. (1987); Wapperom & Hulsen (1998) provide a clear picture as to the current developments. What is now beyond doubt, among these representative cited works, is that temperature changes in such flowing polymeric systems should at the very minimum capture the effects of the three processes; conductive heat transfer effects, entropic effects due to stress work and energetic effects due to the changes in the polymer orientations. Secondary effects, say due radiation and chemical reactions can be included or neglected depending on the exact nature of the physical situation. The major difference between the most recent work Hutter et al. (2009) and previous works is the realization in Hutter et al. (2009) that the usual modeling of energetic effects using the conformational tensor may fail to capture those energetic effects that may arise from fast deformation/relaxation processes due to microscopic changes, say, resulting from continual 20