J.P. Hartnett

Heat Transfer to Newtonian and Non-Newtonian Fluids in Rectangular Ducts

Publisher Summary This chapter provides an overview of the analytical and experimental hydrodynamics and heat transfer studies of Newtonian and non-Newtonian fluids in laminar and turbulent flow through rectangular tubes. The chapter in particular focuses on the rectangular duct geometry, with emphasis on the friction factor and heat transfer behavior of non-Newtonian fluids. It is recognized that non-Newtonian behavior is generally more complicated than Newtonian flow. In the case of non-Newtonian fluids, the theoretical predictions yield low estimates of the heat transfer under laminar flow conditions. The fact that the available experimental heat transfer measurements lie above the predictions could reflect an inadequacy in the analytical model. For non-Newtonians in turbulent flow through rectangular channels, the situation is even more complicated. Some non-Newtonian fluids act as pseudoplastics, showing some reduction in friction and heat transfer as compared with a Newtonian fluid. Other non-Newtonian fluids experience large reductions in the friction factor and in heat transfer under turbulent flow conditions.

Heat transfer to a viscoelastic fluid in laminar flow through a rectangular channel

Abstract The measured local and mean Nusselt numbers for a viscoelastic fluid in laminar flow through a rectangular channel are found to be much higher than those of a purely viscous fluid or a Newtonian fluid. The differences cannot be explained on the basis of a superimposed free convection effect. Rather, the increase is due primarily to secondary flows which are induced in the viscoelastic fluid as a result of the normal force differences acting at the boundaries which are unique to elastic fluids. The pressure drop behavior is unaffected by the presence of secondary flows and predictions based on a purely viscous power law model give good agreement with the measured values.

Non-Newtonian viscosity measurements in the intermediate shear rate range with the falling-ball viscometer

Abstract An attempt to use the falling-ball experiment to measure the non-Newtonian viscosity in the intermediate shear rate range was successfully accomplished by combining the direct experimental observations with a simple analytical model for the average shear and shear rate at the surface of a sphere. The viscosity data of aqueous solutions of Carbopol-960, carboxymethyl cellulose, polyethylene oxide and polyacrylamide obtained from the falling-ball viscometer gave good agreement with those from other viscometers, confirming the general applicability of the analytical approach. In the experiments with the highly viscoelastic polyacrylamide solutions the terminal velocity was observed to be dependent on the time interval between the dropping of successive balls. This time-dependent phenomenon was used to determine characteristic diffusion times of the concentrated solutions of polyacrylamide. These values were, in turn, compared with characteristics relaxation times determined by the Powell-Eyring model. The experimental program revealed that the falling-ball viscometer has very limited utility for the measurement of the steady shear viscosity of aqueous polymer solutions.

Heat transfer behavior of Reiner-Rivlin fluids in rectangular ducts

Numerical studies are reported for the fully developed heat transfer behavior of elastic non-Newtonian fluids in steady laminar flow through rectangular ducts. The Reiner-Rivlin formulation with finite values of the second normal stress coefficient is used to model the flow. The limiting case of zero secondary normal stress difference corresponds to a purely viscous power-law fluid. Finite difference methods are developed to obtain the heat transfer results for the H2 thermal boundary condition for different combinations of heated and adiabatic walls. The influence of the second normal stress coefficient, the Reynolds number, the Peclet Number and the aspect ratio on the heat transfer are considered. It is found that the secondary flow, which is associated with the presence of second normal stresses, results in a significant increase in the heat transfer, especially for aspect ratios of 0.5 and 1.0. The general behavior of the Nusselt number predicted for the Reiner-Rivlin fluid is found to be in good agreement with experimental results reported for viscoelastic fluids.

Steady flow of non-Newtonian fluids through rectangular ducts

Abstract The present paper contains a numerical study for the secondary flow of a Reiner-Rivlin non-Newtonian fluid in laminar flow through ducts of square and rectangular cross section. Finite difference methods are developed to obtain the primary flow, the secondary flow, and the friction factor. The influence of the second normal stress coefficient, the Reynolds number, and the aspect ratio on the magnitude of the secondary flow are considered. In general, the effect of the secondary flow on the primary flow rate and friction factor is found to be negligible.

Thermal conductivity measurements of non-Newtonian fluids

Abstract Thermal conductivity measurements of five non-Newtonian aqueous solutions (Polyethylene Oxide, Polyacrylamide, Carboxymethyl Cellulose, Carbopol-960 and Attagel-40) are in good agreement with the corresponding values for water up to concentrations of 10,000 wppm.

Non-Newtonian fluid laminar flow and forced convection heat transfer in rectangular ducts

Abstract Numerical solutions for fully developed laminar flow forced convection heat transfer of a power law non-Newtonian fluid in rectangular ducts are presented. Finite difference methods are developed for the governing equations to obtain the velocity and temperature distributions. Friction factor results are given for flow through rectangular ducts of aspect ratios of 0.2, 0.5 and 1.0 with power law index n values of 0.5 to 1.0. For the same flow conditions the Nusselt values, maximum wall temperatures, and minimum wall temperatures for the H2 thermal boundary condition for different combinations of heated and adiabatic walls are obtained. Also the Nusselt values for slug flow ( n =0 ) are presented for the H2 boundary condition.

Turbulent friction factor correlations for power law fluids in circular and non-circular channels

Abstract A number of correlations for predicting the turbulent friction factor of purely viscous non—Newtonian fluids flowing in circular and non-circular geometries are presented. These correlations are in reasonable agreement with available data and with each other for values of the power law index close to unity for both circular and rectangular geometries. A critical test of these correlations is carried out by comparing the predicted friction factor with experimental pipe flow data at low values of the power law index. It is shown that the Dodge—Metzner correlations gives the best agreement with experiment over the entire range of available power law values, while the simple Yoo correlation and the Irvine correlation are within ± 10% of the experimental data for n ⩾ 0.3. The Tam—Tiu correlation is found to underpredict experimental pipe flow data for n values between 0.2 and 0.5.

Influence of variable viscosity of mineral oil on laminar heat transfer in a 2:1 rectangular duct

Abstract An experimental study of laminar flow heat transfer in a 2:1 rectangular duct to mineral oil is carried out. The Hl thermal boundary condition corresponding to axially constant heat flux and peripherally constant temperature is adopted for three different heating configurations : (1) top wall heated, other walls adiabatic ; (2) bottom wall heated, other walls adiabatic ; (3) top and bottom walls heated, side walls adiabatic. Corresponding experiments are carried out using water as the test fluid. The experimental results for water show that when the upper wall is heated the influence of buoyancy force is minimal. However, in the case of oil the temperature-sensitive viscosity results in enhanced heat transfer as compared to water due to the distortion of the oil velocity profile. When the lower wall is heated, the influence of both buoyancy force and the stress differences of the mineral oil caused by the variable viscosity results in a substantial increase in the heat transfer as compared to the values found for water. When both top and bottom walls are heated, the local heat transfer enhancement for the mineral oil is smaller as compared with that when each wall is heated alone since the velocity profile and the stress distribution associated with the variable viscosity are more symmetric. Thus the secondary flows are limited to those associated with natural convection and the oil results are in good agreement with the values found in water.

Pipe friction factors for concentrated aqueous solutions of polyacrylamide

Abstract Experimental friction factor results are presented for aqueous solutions of polyacrylamide (Separan AP-273) for concentrations of 1500 ppm, 2000 ppm and 2500 ppm in laminar and turbulent flow through tubes of 2.21 cm and 1.30 cm inside diameter. The solutions studied show a highly non-Newtonian behavior with values of the flow behavior index varying from 0.45 to 0.90. The measured friction factors are slightly lower than the maximum drag reduction asymptote proposed by Virk. For the concentrated viscoelastic solutions the generalized Reynolds number provides a better presentation of the data than the Reynolds number based on the apparent viscosity. In such a presentation there is no influence of pipe diameter or solution concentration on the friction factor. A power law approximation for the friction factor in terms of the generalized Reynolds number was determined using present experimental data. This expression may be used to represent the maximum drag reduction asymptote.