Anomalous features in the model of “second order fluids”

Fosdick, Roger; Rajagopal, Κ. R.

doi:10.1007/bf00250351

Cited by 311 publications

(159 citation statements)

References 5 publications

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“…Considering some rheological complex fluids such as polymer solutions, blood, ice creams and synovia fluid, Abbas et al (2006) argued that the second-grade fluid model adopted in the work of Fosdick and Rajagopal (1979) does not give reasonable results for flows of highly elastic fluids (polymer melts) that occur at high Deborah number. For such situations the upper-convected Maxwell (UCM) model is quite appropriate.…”

Section: Introductionmentioning

confidence: 99%

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Omowaye

Animasaun

2016

JAFM

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An upper-convected Maxwell (UCM) fluid flow over a melting surface situated in hot environment is studied. The influence of melting heat transfer and thermal stratification are properly accounted for by modifying the classical boundary condition of temperature to account for both. It is assumed that the ratio of inertia forces to viscous forces is high enough for boundary layer approximation to be valid. The corresponding influence of exponentially space dependent internal heat generation on viscosity and thermal conductivity of UCM is properly considered. The dynamic viscosity and thermal conductivity of UCM are temperature dependent. Classical temperature dependent viscosity and thermal conductivity models are modified to suit the case of both melting heat transfer and thermal stratification. The governing non-linear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformations and completed the solution numerically using the Runge-Kutta method along with shooting technique (RK4SM). The numerical procedure is validated by comparing the solutions of RK4SM with that of MATLAB based bvp4c. The results reveal that increase in stratification parameter corresponds to decrease in the heat energy entering into the fluid domain from freestream and this significantly reduces the overall temperature and temperature gradient of UCM fluid as it flows over a melting surface. The transverse velocity, longitudinal velocity and temperature of UCM are increasing function of temperature dependent viscous and thermal conductivity parameters. At a constant value of melting parameter, the local skin-friction coefficient and heat transfer rate increases with an increase in Deborah number.

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Section: Introductionmentioning

confidence: 99%

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Omowaye

Animasaun

2016

JAFM

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“…Numerous papers have applied this idea in developing constitutive relations. See, for example, [2,8,[24][25][26][27]. Equation (8) is appropriate for obtaining restrictions on the constitutive parameters.…”

Section: The Governing Equationsmentioning

confidence: 99%

Entropy Analysis for a Nonlinear Fluid with a Nonlinear Heat Flux Vector

Yang

Massoudi

Kirwan

2017

Entropy

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Flowing media in both industrial and natural processes are often characterized as assemblages of densely packed granular materials. Typically, the constitutive relations for the stress tensor and heat flux vector are fundamentally nonlinear. Moreover, these equations are coupled through the Clausius-Duhem inequality. However, the consequences of this coupling are rarely studied. Here we address this issue by obtaining constraints imposed by the Clausius-Duhem inequality on the constitutive relations for both the stress tensor and the heat flux vector in which the volume fraction gradient plays an important role. A crucial result of the analysis is the restriction on the dependency of phenomenological coefficients appearing in the constitutive equations on the model objective functions.

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“…Having said this, it should be mentioned that, like the second-order fluid model, this particular rheological model has been the subject of much controversy in relation to the sign of the material constant k 0 . That is, in order for the model to comply with certain thermodynamics constraints, it has been argued by Fosdick and Rajagopal 23,24) that k 0 should be negative. Interestingly, for polymeric liquids experimental data are in favor of the positive sign adopted originally by Walters and Baines for k 0 .…”

Section: Mathematical Formulationmentioning

confidence: 99%

Hydromagnetic Instability of Viscoelastic Fluids in Blasius Flow

Khabazi

Sadeghy

2009

J. Soc. Rheol., Jpn

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The effect of a fluid's elasticity is investigated on the instability of Blasius flow at the presence of a transverse magnetic field. To determine the critical Reynolds number as a function of the elasticity and magnetic numbers, a twodimensional linear temporal stability analysis is used assuming that the viscoelastic fluid of interest obeys Walters' B model as its constitutive equation. Neglecting terms nonlinear in the perturbation quantities, an eigenvalue problem is obtained which is solved numerically using the Chebychev collocation method. Based on the results obtained in this work, fluid's elasticity is predicted to have a destabilizing effect on Blasius flow. In contrast, the effect of the magnetic field is predicted to be always stabilizing in Blasius flow, at least in the range of parameters used in this work.

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Anomalous features in the model of “second order fluids”

Cited by 311 publications

References 5 publications

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Entropy Analysis for a Nonlinear Fluid with a Nonlinear Heat Flux Vector

Hydromagnetic Instability of Viscoelastic Fluids in Blasius Flow

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