A. Introduction

(by R. C. Armstrong and H. H. Winter)

Section 179 describes ways in which heat transfer in non-Newtonian fluids is different from that in Newtonian fluids. As polymers constitute the largest class of non-Newtonian fluids, we shall focus our attention on them. Moreover, we shall focus on differences in heat transfer characteristics between Newtonian and polymeric fluids that can be attributed to differences in viscous behavior between these two classes of fluids. These distinctions involve both the shear rate dependence that is commonly observed in non-Newtonian fluids and also the different magnitude of the viscosity in polymers as opposed to low-molecular-weight fluids. In addition to these viscous effects, it is clearly possible that many interesting changes in heat transfer problems could result from the "elastic" character of polymeric fluids. For example, in duct flows involving noncircular cross sections, certain non-Newtonian fluids show qualitatively different secondary velocity patterns than Newtonian fluids. These clearly have some effect on heat transfer. Very little can yet be said quantitatively about these "elastic" effects, however.*

In addition to these differences in heat transfer between Newtonian and non-Newtonian fluids, there are differences in the kinds of information that we are generally interested in for nonisothermal flows of these two classes of fluids. Let us break the possible calculations into two categories: global and local. For Newtonian fluids it is the global result, the evaluation of a heat transfer coefficient to relate bulk temperature differences to heat fluxes, that is of most interest. This heat transfer coefficient, which is used for sizing heat exchanger equipment and estimating bulk temperature changes, is not as useful for non-Newtonian fluids for two reasons: first, in problems with significant viscous heating, which are common for molten polymers, the heat transfer coefficient cannot be defined meaningfully; and second, because of the peculiar physical properties of polymers, heat transfer between a flowing polymer and its surroundings is generally ignored. There are, of course, exceptions to this last statement, such as cooling extruders for low-temperature extrusion of foamed polymers and cooling of polymerization reactors.

For polymeric fluids, evaluation of the local temperature field is usually of primary interest. Because of the sensitivity of the physical properties to temperature, the temperature field can have a pronounced effect on the flow field and therefore on the process itself. In addition, many polymers are temperature sensitive and will degrade at high temperatures, say, at T_degrad. It is important to be sure that the local temperature never exceeds T_degrad. Finally, relaxation phenomena in polymers are strongly temperature sensitive, and the amount and location of residual stress or strain in a polymeric product will depend on the local temperature history of the polymer.