Laminar Forced Convection in Viscous Shear-Thinning Liquid Flows Inside Circular Pipes: Case for a Modified Power-Law Rheology

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
J. Subedi ◽  
S. Rajendran ◽  
R. M. Manglik
Keyword(s):  
Heat Transfer ◽  
Shear Rate ◽  
Convective Heat Transfer ◽  
Power Law ◽  
Shear Thinning ◽  
Frictional Loss ◽  
Viscous Shear ◽  
Laminar Forced Convection ◽  
Rheology Model ◽  
Low Shear

Abstract Laminar forced convection in viscous, non-Newtonian polymeric liquids that exhibit pseudoplastic or shear-thinning behavior is characterized. The fluid rheology is characterized by a new asymptotic power-law (APL) model, which appropriately represents extensive data for apparent viscosity variation with shear rate—from the low-shear constant-viscosity plateau to shear thinning at high shear rates. This is contrasted with the traditional Ostwald-de-Waele or power-law (PL) model that invariably over-extends the pseudoplasticity in the very low shear-rate region. The latter's limitations are demonstrated by computationally obtaining frictional loss and convective heat transfer results for fully developed laminar flows in a circular pipe maintained at uniform heat flux. The Fanning friction factor and Nusselt number, as would be anticipated from the rheology map of pseudoplastic fluids, are functions of flow rate with the APL model unlike the Newtonian-like constant value obtained with the PL model. Comparisons of the two sets of results highlight the extent of errors inherent in the PL rheology model, which range from 23% to 68% for frictional loss and 3.8% to 13.7% for heat transfer. The new APL rheology model is thus shown to be the more precise characterization of viscous shear-thinning fluids for their thermal processing applications with convective heat transfer.

scholarly journals A semi-infinite hydraulic fracture driven by a shear-thinning fluid

2018 ◽  
Vol 838 ◽  
pp. 573-605 ◽  
Author(s):  
Fatima-Ezzahra Moukhtari ◽  
Brice Lecampion
Keyword(s):  
Shear Rate ◽  
Power Law ◽  
Hydraulic Fracture ◽  
Complex Structure ◽  
Shear Thinning ◽  
High Shear Rate ◽  
Asymptotic Region ◽  
High Shear ◽  
Confining Stress ◽  
Low Shear

We use the Carreau rheological model which properly accounts for the shear-thinning behaviour between the low and high shear rate Newtonian limits to investigate the problem of a semi-infinite hydraulic fracture propagating at a constant velocity in an impermeable linearly elastic material. We show that the solution depends on four dimensionless parameters: a dimensionless toughness (function of the fracture velocity, confining stress, material and fluid parameters), a dimensionless transition shear stress (related to both fluid and material behaviour), the fluid shear-thinning index and the ratio between the high and low shear rate viscosities. We solve the complete problem numerically combining a Gauss–Chebyshev method for the discretization of the elasticity equation, the quasi-static fracture propagation condition and a finite difference scheme for the width-averaged lubrication flow. The solution exhibits a complex structure with up to four distinct asymptotic regions as one moves away from the fracture tip: a region governed by the classical linear elastic fracture mechanics behaviour near the tip, a high shear rate viscosity asymptotic and power-law asymptotic region in the intermediate field and a low shear rate viscosity asymptotic far away from the fracture tip. The occurrence and order of magnitude of the extent of these different viscous asymptotic regions are estimated analytically. Our results also quantify how shear thinning drastically reduces the size of the fluid lag compared to a Newtonian fluid. We also investigate simpler rheological models (power law, Ellis) and establish the small domain where they can properly reproduce the response obtained with the complete rheology.

The Simulation of Aggregated Colloids Under Flow

1992 ◽  
Vol 289 ◽  
Author(s):  
John R. Melrose
Keyword(s):  
Shear Rate ◽  
Large Scale ◽  
Shear Thinning ◽  
High Shear ◽  
Shear Rates ◽  
Rouse Model ◽  
High Shear Rates ◽  
Structural Breakdown ◽  
Large Scale Simulations ◽  
Low Shear

AbstractAn overview is given of theories of aggregates under flow. These generally assume some sort of structural breakdown as the shear rate is increased. Models vary with both the rigidity of the bonding and the level of treatment of hydrodynamics. Results are presented for simulations of a Rouse model of non-rigid, (i.e. central force) weakly bonded aggregates. In large scale simulations different structures are observed at low and high shear rates. The change from one structure to another is associated with a change in the rate of shear thinning. The model captures low shear rate features of real systems absent in previous models: this feature is ascribed to agglomerate deformations. Quantitatively, the model is two orders of magnitude out from experiment but some scaling is possible.

Heat Transfer Enhancement in Annular Shear-Thinning Flows Over a Sudden Pipe Expansion

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Power Law ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Transfer Enhancement ◽  
Heat Transfer Augmentation ◽  
Prandtl Numbers ◽  
Power Law Index ◽  
The Impact

Heat transfer enhancement in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5, 0.7}; n = {1, 0.8, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers, Nu, higher than the fully developed value, in the downstream pipe, is observed only for Pr = 10 and 100. Higher Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane. Heat transfer augmentation for Pr = 10 and 100, is more dramatic for suddenly expanding annular flows, in comparison with suddenly expanding pipe flow. For a given annular diameter ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr = 100, always results in higher peak Nu values, for both Newtonian and shear-thinning non-Newtonian flows.

Convective heat transfer for power law fluids in packed and fluidised beds of spheres

2004 ◽  
Vol 59 (3) ◽  
pp. 645-659 ◽  
Author(s):  
Rupali Shukla ◽  
S.D. Dhole ◽  
R.P. Chhabra ◽  
V. Eswaran
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Power Law ◽  
Power Law Fluids ◽  
Fluidised Beds

Rheology of Polyaniline-Dinonylnaphthalene Disulfonic Acid (DNNDSA) Montmorillonite Clay Nanocomposites in the Sol State: Shear Thinning versus Pseudo-Solid Behavior

2008 ◽  
Vol 8 (4) ◽  
pp. 1842-1851 ◽  
Author(s):  
Ashesh Garai ◽  
Arun K. Nandi
Keyword(s):  
Shear Rate ◽  
Storage Modulus ◽  
Power Law ◽  
Network Formation ◽  
Loss Modulus ◽  
Shear Thinning ◽  
Disulfonic Acid ◽  
Clay Nanocomposites ◽  
Crossover Point ◽  
Clay Concentration

The melt rheology of polyaniline (PANI)-dinonylnaphthalenedisulfonic acid (DNNDSA) gel nanocomposites (GNCs) with organically modified (modified with cetyl trimethylammonium bromide)-montmorillonite (om-MMT) clay has been studied for three different clay concentrations at the temperature range 120–160 °C. Field emission scanning electron microscopy (FE-SEM), wide angle X-ray scattering (WAXS), differential scanning calorimetry (DSC) and dc-conductivity data (∼10–3 S/cm) indicate that the PANI-DNNDSA melt is in sol state and it is not de-doped at that condition. The WAXS data indicate that in GNC-1 sol clay tactoids are in exfoliated state but in the other sols they are in intercalated state. The zero shear viscosity (η0), storage modulus (G′) and loss modulus (G″) increase than that of pure gel in the GNCs. The pure sol and the sols of gel nanocomposites (GNCs) exhibit Newtonian behavior for low shear rate (<6 × 10–3 s–1) and power law variation for the higher shear rate region. The characteristic time (λ) increase with increasing clay concentration and the power law index (n) decreases with increase in clay concentration in the GNCs indicating increased shear thinning for the clay addition. Thus the sols of om-clay nanocomposites of PANI-DNNDSA system are easily processible. The storage modulus (G′) of GNC sols are higher than that of pure PANI-DNNDSA sol, GNC1 sol shows a maximum of 733% increase in storage modulus and the percent increase decreases with increase in temperature. Exfoliated nature of clay tactoids has been attributed for the above dramatic increase of G′. The PANI-DNNDSA sol nanocomposites behave as a pseudo-solid at higher frequency where G′ and loss modulus (G′′) show a crossover point in the frequency sweep experiment at a fixed temperature. The crossover frequency decreases with increase in clay concentration and it increases with increase in temperature for GNC sols. The pseudo-solid behavior has been explained from jamming or network formation of clay tactoids under shear. A probable explanation of the two apparently contradictory phenomena of shear thinning versus pseudo-solid behavior of the nanocomposite sols is discussed.

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