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Fundamental Concepts
Published in Nicholas P. Cheremisinoff, Polymer Mixing and Extrusion Technology, 2017
The apparent viscosity of a power law fluid is a function of all the velocity gradients in nonsimple shearing flows. However, from the standpoint of practicality most laboratory viscometric techniques measure viscosity in only one velocity gradient. This is a general fluid dynamic problem treated in a later chapter. An important point to realize is that the power law equation is an empirical model and should therefore not be used for extrapolation of viscosity data. It does not level off to a Newtonian plateau, but instead keeps on increasing. Table 2 provides values of the power law coefficients K and n for different materials.
Pipe Flow
Published in Ron Darby, Raj P. Chhabra, Chemical Engineering Fluid Mechanics, 2016
A coal slurry that is characterized as a power law fluid has a flow index of 0.4 and an apparent viscosity of 200 cP at a shear rate of 1 s−1. If the coal has a specific gravity of 2.5 and the slurry is 50% coal by weight in water, what pump horsepower will be required to transport 25 million tons of coal per year through a 36 in. ID, 1000 miles long pipeline? Assume that the entrance and exit of the pipeline are at the same pressure and elevation and that the pumps are 60% efficient.
Introduction to Rheology
Published in Nicholas P. Cheremisinoff, An Introduction to Polymer Rheology and Processing, 1993
The slope η and intercept K are given the names “flow behavior index” (or “pseudoplasticity index”) and “consistency index”, respectively. The power law exponent ranges from unity to zero with increasing plasticity (i.e., at n = 1, the equation reduces to the constitutive equation of a Newtonian fluid). The value of the consistency index is obtained from the intercept on the τxy axis and hence represents the viscosity at unit shear rate. As shown later for a variety of polymers, K is very sensitive to temperature, whereas n is much less sensitive. By analogy to Newton’s law, the apparent viscosity of a power law fluid is
Wall jet nanofluid flow with thermal energy and radiation in the presence of power-law
Published in Numerical Heat Transfer, Part A: Applications, 2023
Waqar Khan Usafzai, Abdulkafi. M. Saeed, Emad H. Aly, V. Puneeth, I. Pop
Power-law nanofluids moving through various mediums have drawn significant research in a wide range of industries during the past decades. Newtonian fluids are those that follow Newton’s law of viscosity and show a direct proportion between shear stress and strain rate in laminar flow. Whereas, non-Newtonian fluids do not obey Newtonian viscosity law. Some colloids, milk, gelatin, blood, and heavy oil are examples of common nonlinear power-law fluids. The plug-like aspect of the velocity profile increases with decreasing power-law index, resulting in a blunt or plug-like flow for the power-law fluid. Numerous authors studied natural convection in power-law nanofluids. Ellahi et al. [15] studied the heat transfer properties, including the amount of heat conducted by the power-law nanofluid. Khan et al. [16] dealt with the Blasius flow model for power-law nanofluid flowing over a stretching sheet that is being convectively heated. Wang et al. [17] performed theoretical analysis to understand the heat transfer properties of power-law nanofluid in rectangular cavities. The significant findings of Ojeda and Mendez [18] showed rapid decrement in the Nusselt number for shear-thinning base fluids, whereas it increases asymptotically for shear-thickening fluid. Selimefendigil and Öztop [19] investigated the thermal performance of a coupled conjugate thermo-fluid system with various cooling configurations. Alkhatani et al. [20] considered the geometry of a vertical stretching sheet to analyze the flow of power-law nanofluid. For further details, the reader is advised to see the references [21–25].
Asymptotic analysis of boundary layer flow of a fluid with temperature-dependent viscosity
Published in Numerical Heat Transfer, Part A: Applications, 2023
Tarik Amtout, Adil Cheikhi, Mustapha Er-Riani, Aadil Lahrouz, Mustapha El Jarroudi, Adil Settati
A variety of constitutive equations have been suggested to describe the flow and heat transfer characteristics of non-Newtonian fluids, among which the empirical Ostwald-de Waele (the power-law) model has been widely used. Its apparent simplicity has made it a very attractive model for analytical and numerical research on these types of flows. For a non-Newtonian power-law fluid, the shear stress is given by the relation and the viscosity is expressed as where is the shear rate, and K is the consistency index of the fluid assumed to be dependent on the temperature, with n being the power-law index. Recall that, in the case of a constant consistency index, the classical Newtonian model is a particular case corresponding to K being the Newtonian viscosity. For positive values of n less than unity, the model describes a shear-thinning flow, whereas corresponds to a shear-thickening fluid.
Natural Convection in Power-Law Fluids in a Square Enclosure from Two Differentially Heated Horizontal Cylinders
Published in Heat Transfer Engineering, 2018
Lubhani Mishra, Raj P. Chhabra
Before leaving this section, the preceding discussion makes use of the Grashof and Prandtl numbers similar to that in the case of Newtonian fluids. While this approach affords the possibility of reconciling the results for Newtonian and power-law fluids, the two situations also differ in a rather significant manner. For a Newtonian fluid, the viscosity is constant and thus the Prandtl number is a unique property group. In contrast, for power-law fluids, the fluid viscosity depends upon the shear rate (determined by the fluid velocity and cylinder diameter) and the value of power-law index. The rate of increase or decrease of viscosity with the shear rate itself is strongly influenced by the value of the power-law index. Second, along the surface of both cylinders, the fluid viscosity is constant for a Newtonian fluid and therefore, the variation of the Nusselt number is solely due to the varying temperature gradient. In the case of power-law fluids, the variation of the fluid viscosity along the surface of the cylinder influences the local velocity (and hence temperature) field thereby influencing the local temperature gradient. This accentuated entwined nature of the velocity and temperature fields is responsible for the nonmonotonous trends seen in the distribution of local Nusselt number under varying conditions seen in Figures 14–18. Suffice it to say here that the formation of various peaks of the local Nusselt number along the surfaces of cylinders and enclosure are in complete agreement with the results of Yoon et al. [34], at least for Newtonian fluids. The increment in Prandtl number causes thinning of thermal boundary layer and accordingly, an increase in the Nusselt number. The relatively high viscosity of shear-thickening fluids for a given Grashof number and Prandtl number has a “suppression” effect on heat transfer and hence, the maximum heat transfer is obtained generally for n = 0.2.