Fluids of differential type: Critical review and thermodynamic analysis

Dunn, James E.; Rajagopal, Κ. R.

doi:10.1016/0020-7225(94)00078-x

Cited by 546 publications

(262 citation statements)

References 41 publications

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“…Boundary layer equations which best describe upper convected Maxwell fluid flow can be derived starting from Cauchy equations of motion. Following (Dunn and Rajagopal (1995) and…”

Section: Mathematical Formulationmentioning

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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“…Boundary layer equations which best describe upper convected Maxwell fluid flow can be derived starting from Cauchy equations of motion. Following (Dunn and Rajagopal (1995) and…”

Section: Mathematical Formulationmentioning

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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“…For detailed analysis about the signs of these normal stress moduli one may see [30]. The equations governing the magnetohydrodynamic flow with Hall effects are:…”

Section: Mathematical Formulation Of the Problem And Analytic Solutionmentioning

confidence: 99%

Effects of Hall Current on Flow of Unsteady MHD Axisymmetric Second-Grade Fluid with Suction and Blowing over an Exponentially Stretching Sheet

Zaman¹,

Sohail²,

Ali³

et al. 2014

OJMSi

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This paper investigates effects of Hall current on flow of unsteady magnetohydrodynamic (MHD) axisymmetric second-grade fluid with suction and blowing over a sheet stretching exponentially with radius. The governing non-linear partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformations. The complex analytical solution is found by using the homotopy analysis method (HAM). The existing literature on the topic shows that it is the first study regarding the effects of Hall current on flow over an exponentially stretching sheet in cylindrical coordinates. The convergence of the obtained complex series solutions is carefully analyzed. The effects of dimensionless parameters on the radial and axial components of the velocity are illustrated through plots. Also the effects of the pertinent parameters on the shear stress at the wall are presented numerically in tabular form.

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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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Fluids of differential type: Critical review and thermodynamic analysis

Cited by 546 publications

References 41 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

Effects of Hall Current on Flow of Unsteady MHD Axisymmetric Second-Grade Fluid with Suction and Blowing over an Exponentially Stretching Sheet

Hydromagnetic Instability of Viscoelastic Fluids in Blasius Flow

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