Asymptotic analysis of turbulent boundary-layer flow of purely viscous non-Newtonian fluids

Loureiro, Juliana; Freire, Atila P. Silva

doi:10.1016/j.jnnfm.2013.05.003

Cited by 11 publications

(5 citation statements)

References 25 publications

(60 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence these equations have been attracted from modelling as well as solutions point of view. The advancement in the study of non-Newtonian fluids has been made even by the recent investigators (See [1] – [10] and many studies therein).…”

Section: Introductionmentioning

confidence: 99%

Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface

2014

View full text Add to dashboard Cite

This article addresses the boundary layer flow and heat transfer in third grade fluid over an unsteady permeable stretching sheet. The transverse magnetic and electric fields in the momentum equations are considered. Thermal boundary layer equation includes both viscous and Ohmic dissipations. The related nonlinear partial differential system is reduced first into ordinary differential system and then solved for the series solutions. The dependence of velocity and temperature profiles on the various parameters are shown and discussed by sketching graphs. Expressions of skin friction coefficient and local Nusselt number are calculated and analyzed. Numerical values of skin friction coefficient and Nusselt number are tabulated and examined. It is observed that both velocity and temperature increases in presence of electric field. Further the temperature is increased due to the radiation parameter. Thermal boundary layer thickness increases by increasing Eckert number.

show abstract

Section: Introductionmentioning

confidence: 99%

Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface

2014

View full text Add to dashboard Cite

show abstract

“…The shear stress component τ xy in Eq (2) for the power-law fluid model is defined as (see details in [ 29 ]) where K is the consistency coefficient and n is the power-law index. In the above constitutive equation n = 1 corresponds to Newtonian fluid behavior.…”

Section: Problem Statement and Mathematical Formulationmentioning

confidence: 99%

Heat Transfer Analysis for Stationary Boundary Layer Slip Flow of a Power-Law Fluid in a Darcy Porous Medium with Plate Suction/Injection

et al. 2015

View full text Add to dashboard Cite

In this paper, we investigate the slip effects on the boundary layer flow and heat transfer characteristics of a power-law fluid past a porous flat plate embedded in the Darcy type porous medium. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law fluid is transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system of ordinary differential equations is solved numerically using Matlab bvp4c solver. Numerical results are presented in the form of graphs and the effects of the power-law index, velocity and thermal slip parameters, permeability parameter, suction/injection parameter on the velocity and temperature profiles are examined.

show abstract

“…In Loureiro and Silva Freire [110], the asymptotic structure of the turbulent boundary layer of a non-Newtonian power-law fluid is discussed. The application of double limits to the equations of motion shows that the turbulent boundary layer exhibits a canonical two-layered structure defined by two principal equations.…”

Section: Logarithmic Solutions For Non-newtonian Purely Viscous Fluidsmentioning

confidence: 99%

“…The asymptotic structure of the turbulent boundary layer for a Carreau fluid is also analyzed in Loureiro and Silva Freire [110]. For a Carreau fluid, the viscosity and local shear rate are related according to where µ ∞ and µ 0 are the limiting viscosity levels, θ is the relaxation time and n the power-law index.…”

Section: Logarithmic Solutions For Non-newtonian Purely Viscous Fluidsmentioning

confidence: 99%

“…--Turbulent layer thickness, δ = (u 2 τ /u 2 o )L --Power-law sub-layer thickness, δ = (Ku n−2 τ /ρ) 1/n , with K = (µ 0 − µ o )θ n−1 --Newtonian sub-layer thickness, δ = [((µ 0 − µ o )/µ o )θ n−1 u n−1 τ ] 1/(n−1) . --The behavior of a Carreau fluid was illustrated in Loureiro and Silva Freire [110] through the data of Japper-Jaafar et al [114] for a Carreau-Yasuda fluid with power-law indexes ranging from 0.3 to 0.9. Figure 30 shows the mean velocity data in terms of the inner flow variables y + w = yu τ /ν w and y + o = yu τ /ν o .…”

Section: Logarithmic Solutions For Non-newtonian Purely Viscous Fluidsmentioning

confidence: 99%

See 1 more Smart Citation

The persistence of logarithmic solutions in turbulent boundary layer systems

Freire

2015

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

from the first principles of mechanics and the formalism of a continuous field characterized by density and viscosity.Thus, the complete absence of a comprehensive theory that can convincingly deal with disordered flows may come to many as a surprise. The crux of the matter, obviously, is the strong non-linear character of the advection terms in the equations of motion. Under certain conditions-in particular, high Reynolds numbers-fluid flows become unstable, growing rapidly to a complicated and confused state that is termed turbulent and has a large number of degrees of freedom.In fact, it can be argued that an exact and detailed description of the manner in which a turbulent flow evolves is physically meaningless due to the inherent difficulty in specifying its boundary and initial conditions for situations that are of interest in practical problems. A microscopic account of the flow behavior is certainly relevant for the understanding of local and instantaneous irregularities, but what is normally of real interest is the behavior of the macroscopic regularities of the flow. Therefore, it seems that the appropriate description of a turbulent flow needs to resort to statistical methods.Provided the irregular variation of the flow properties can be averaged over, say, some interval of time, the field properties can be decomposed into smoothed out (mean part) and rapidly varying quantities (fluctuating part). Once this procedure is accepted, substitution of the decomposed field variables into the Navier-Stokes equations results in a new equation for the mean variables, but with additional terms involving double correlations of the fluctuations, quantities that are formally unknown and that, hence, require modeling. The resulting second-order tensor-the Reynolds stress tensor-represents the transport of momentum due to the turbulent fluctuations and has the Abstract The present work studies the prevalence of logarithmic solutions in the near wall region of turbulent boundary layers. Local solutions for flows subject to such diverse effects as compressibility, wall transpiration, heat transfer, roughness, separation, shock waves, unsteadiness, non-Newtonian fluids or a combination of these factors are discussed. The work also analyzes eleven different propositions by several authors for the near wall description of the mean velocity profile for the incompressible zero-pressuregradient turbulent boundary layer. The asymptotic structure of the flow is discussed from the point of view of double limit processes. Cases of interest include attached and separated flows for the velocity and temperature fields.

show abstract

Asymptotic analysis of turbulent boundary-layer flow of purely viscous non-Newtonian fluids

Cited by 11 publications

References 25 publications

Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface

Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface

Heat Transfer Analysis for Stationary Boundary Layer Slip Flow of a Power-Law Fluid in a Darcy Porous Medium with Plate Suction/Injection

The persistence of logarithmic solutions in turbulent boundary layer systems

Contact Info

Product

Resources

About