1990 Max Jakob Memorial Award Lecture: Viscoelastic Fluids: A New Challenge in Heat Transfer

Abstract

A review of the current knowledge on the fluid mechanics and heat transfer behavior of viscoelastic aqueous polymer solutions in channel flow is presented. Both turbulent and laminar flow conditions are considered. Although the major emphasis is on fully established circular pipe flow, some results are also reported for flow in a 2:1 rectangular channel. For fully established turbulent channel flow, it was found that the friction factor, f, and the dimensionless heat transfer factor, jH, were functions of the Reynolds number and a dimensionless elasticity value, the Weissenberg number. For Weissenberg values greater than approximately 10 (the critical value) the friction factor was found to be a function only of the Reynolds number; for values less than 10 the friction factor was a function of both Re and Ws. For the dimensionless heat transfer coefficient jH the corresponding critical Weissenberg value was found to be about 100. The heat transfer reduction is always greater than the friction factor reduction; consequently, the heat transfer per unit pumping power decreases with increasing elasticity. For fully established laminar pipe flow of aqueous polymer solutions, the measured values of the friction factor and dimensionless heat transfer coefficient were in excellent agreement with the values predicted for a power law fluid. For laminar flow in a 2:1 rectangular channel the fully developed friction factor measurements were also in agreement with the power law prediction. In contrast, the measured local heat transfer coefficients for aqueous polymer solutions in laminar flow through the 2:1 rectangular duct were two to three times the values predicted for a purely viscous power law fluid. It is hypothesized that these high heat transfer coefficients are due to secondary motions, which come about as a result of the unequal normal stresses occurring in viscoelastic fluids. The anomalous behavior of one particular aqueous polymer solution—namely, polyacrylic acid (Carbopol)—is described in some detail, raising some interesting questions as to how viscoelastic fluids should be classified. In closing, a number of challenging research opportunities in the study of viscoelastic fluids are presented.