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 newtonian and non-newtonian fluids in rectangular ducts

In this paper, a general class of viscoelastic model is used to investigate numerically the pattern and strength of the secondary flows in rectangular pipes as well as the influence of material parameters on them. To solve the coupled governing equation system, an implicit finite volume method based on the SIMPLEST algorithm, which is applicable for both time-dependent and steady-state flow computations, has been developed and extended for viscoelastic flow computations by applying the decoupled techniques. The main feature of the method is to split the solution process into a series of steps in which the continuity of the flow field is enforced by solving a Poisson's equation for the pressure, and at the end of the steps, both the pressure and velocity fields are made to satisfy one and the same momentum equation. For viscoelastic flow computations, artificial diffusion terms are introduced on both sides of the discretized constitutive equations to improve numerical stability. It is found that there are in total two vortices in each quadrant of the pipe at different aspect ratios (from 1 to 16), and at each ratio the pattern of secondary flows takes the same form for different material parameters, but their strength is very sensitive to the viscoelastic material parameters. Numerical results indicate that the presence of secondary flow strongly depends on the primary flow rate and the elasticity of the fluid, namely, the first and the second normal stress differences as well as their functional departure from the constant multiple viscosity.

Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method

The flow of a viscoelastic fluid in an undulating tube is of importance both for modeling the flow of polymeric fluids through porous media and for testing numerical techniques for the simulation of viscoelastic flows. This geometry represents one of the simplest pore models for the consideration of the converging-diverging nature of the flow field in applications ranging from enhanced oil recovery to manufacturing of advanced composites using resin transfer molding. For an upper convected Maxwell fluid, a mixed pseudospectral/finite difference method (PSFD) is developed, employing the coordinate system provided by the streamlines and the lines orthogonal to them. For an Oldroyd-B fluid, a modification of the PSFD method is used, implemented in a stretched cylindrical coordinate system (PCFD method). For both the Maxwell and the Oldroyd-B fluid, solutions converged with mesh refinement are obtained up to high Deborah numbers. The results obtained using the Maxwell fluid show no increase in the flow resistance with increasing flow elasticity, in reference to the purely viscous flow. The results for the Oldroyd-B fluid show a very small increase in the flow resistance. These findings are in disagreement with experimental data reported in the literature, which have been obtained with Boger fluids. For the Maxwell fluid, a perturbation analysis valid for small amplitudes of undulation shows that extremely steep boundary layers are developed with increasing elasticity in the flow. The boundary layers are developed both near the wall and the centerline of the tube and their resolution becomes a key element for any potentially successful numerical method. In addition, their presence explains, at least partially, the failure of previous attempts by other investigators to obtain converged solutions at high values of elasticity.

Calculations of steady-state viscoelastic flow in an undulating tube

The effect of second normal stress difference is analysed by observing the co-flow of two batches of the same viscoelastic fluid, each with a different pigmentation, in straight ducts. The development of secondary motions is observed by tracking the motion of the interface between both fluids. Numerical simulations are also performed on the basis of a multi-mode differential viscoelastic fluid model and are compared with the experiments. A good agreement is found between the experimental observations and their numerical counterparts. (C) 1997 Elsevier Science B.V.

On the development of secondary motions in straight channels induced by the second normal stress difference: experiments and simulations

An iteration technique has been developed to solve the equations of motion for flow of an incompressible Newtonian fluid through circular tube with a radius which varies sinusoidally in the axial direction. The iteration is essentially geometric; one proceeds from a solution for flow through a tube in which the waveleneth of diameter chance in the axial direction is

Flow through tubes with sinusoidal axial variations in diameter

Non-Newtonian flow in pipes of non-circular cross section

Consideration is given to the flow of Newtonian and non-Newtonian liquids through a “corrugated” pipe of circular cross section whose radius sinusoidally along its longitudinal axis. The flow is produced by a constant pressure gradient. The theory predicts that in the Newtonian case, the corrugated wall of the pipe causes a reduction in flow rate when compared with the value expected on the basis of a straight pipe of the same mean radius. This prediction is confirmed by experiment. In the case of elastico-viscous liquids, the theoretical analysis for a certain fluid model indicates that the reduction in flow rate may be amplified or reduced by the non-Newtonian properties of the liquid depending on the precise flow conditions. The qualitative predictions are again confirmed by experiment. The possible practical implications of the work are outlined.

On the flow of Newtonian and non-Newtonian liquids through corrugated pipes

Experiments on the flow of Newtonian and non-Newtonian liquids through corrugated pipes confirmed the theoretically derived prediction that the corrugated wall of the pipe causes a reduction in Newtonian flow rate compared with the value expected on the basis of a straight pipe of the same mean radius. In the case of elastico-viscous liquids, the theoretical analysis for a certain fluid model indicates that the reduction in flow rate may be either amplified or reduced by the non-Newtonian properties of the liquid, depending on the precise flow conditions. In the experiments, the Newtonian fluids used were water and glycerol-water mixtures and the non-Newtonian fluids were aqueous solutions of polyacrylamide. Implications of the results of this study for the effects of wax deposition in crude oil pipelines, for the effects of pipe coated internally with bitumen, and for "drag reduction" by the addition of small amounts of high-molecular-weight polymer to Newtonian solvents in turbulent pipe flow are discussed briefly.

Experiments on the flow of newtonian and non-newtonian liquids through corrugated pipes

A growing number of human pathogens are becoming resistant to most common antibiotics. Each year, antibiotic-resistant infections are responsible for 35,000 deaths in the United States and billions of dollars in health care costs. This problem is magnified by the fact that very few new antibiotic therapies have been developed and approved for human use in recent years. Historically, plants and other products found in nature have served as essential sources for the discovery of novel antibacterial agents. Piper species are aromatic plants whose secondary metabolites have been shown to have wide ranging human health effects including anti-tumor, anti-diabetic, and anti-inflammatory activity. In collaboration with Dr. Claudia Ospina at Inter American University of Puerto Rico, we generated a crude chemical extract from Piper leaves and will be assessing the antimicrobial activity of this extract against a broad range of bacterial species known to exhibit multidrug resistance. Future studies will involve isolating the active compounds (and/or fractions) from the Piper crude extract using column chromatography and/or HPLC. The pure compounds will be characterized using different spectroscopic techniques such as NMR, IR and MS.  We anticipate isolating and identifying several bioactive compounds from the crude Piper leaf extract that exhibit antimicrobial activity.

https://pwvas.org/index.php/pwvas/article/download/893/795

A. G. Dodson

Papers

Non-Newtonian flow in pipes of non-circular cross section

On the flow of Newtonian and non-Newtonian liquids through corrugated pipes

Experiments on the flow of newtonian and non-newtonian liquids through corrugated pipes

Investigating the antimicrobial activity of a crude leaf extract derived from Piper species.