Acta Mechanica

, Volume 99, Issue 1–4, pp 21–33 | Cite as

Flow of a generalized second grade fluid between heated plates

  • G. Gupta
  • M. Massoudi
Contributed Papers
Received:
Revised:

Summary

We examine the fully developed flow of a generalized fluid of second grade between heated parallel plates, due to a pressure gradient along the plate. The constant coefficient of shear viscosity of a fluid of second grade is replaced by a shear dependent viscosity with an exponentm. If the normal stress coefficients are set equal to zero, this model reduces to the standard power-law model. We obtain the solution for the case when the temperature changes only in the direction normal to the plates for the two most commonly used viscosity models, i.e. (i) when the viscosity does not depend on temperature, and (ii) when the viscosity is an exponentially decaying function of temperature.

Keywords

Viscosity Fluid Dynamics Pressure Gradient Normal Stress Shear Viscosity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Alphanumeric

A1,A2

Kinematical tensor

b

Body force

C

Dimensionless parameter related to the pressure gradient

h

Separation between the plates

L

Velocity gradient

m

Power-law index

M

Constant appearing in the Reynolds viscosity model

p

Pressure field

\(\hat p,\hat \bar p\)

Modified pressure field

q

Heat flux vector

r

Radiant heating

T

Cauchy's stress tensor

l

Unit tensor

v

Velocity vector

V

Characteristic velocity

x

Axis along the plate

y

Axis perpendicular to the plate

Greek

α1, α2

Normal stress coefficient

ε

Specific internal energy

Γ

Dimensionless parameter related to the viscous dissipation

ϕ

Conservative body force field

η

Specific entropy

κ

Thermal conductivity

μ

Coefficient of viscosity

μ0

Reference viscosity

Π

Second invariant of the stretching tensor

θ

Temperature

θ1

Temperature of the lower plate

θ2

Temperature of the upper plate

ϱ

Density

ψ

Specific Helmholtz free energy

Operators

div

Divergence

grad

Gradient

tr

Trace

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • G. Gupta
    • 1
  • M. Massoudi
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of PittsburghPittsburghUSA
  2. 2.U.S. Department of EnergyPittsburgh Energy Technology CenterPittsburghUSA

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