Summary
The heat transfer by laminar flow of visco-elastic liquids has been studied by using the constitutive equations of motion of visco-elastic liquids and the energy equation. The Couette flow and plane Poiseuille flow have been examined in detail and found to be characterized by two parameters P.E. andR c . The presence of the elasticity in the liquid is found to increase the temperature.
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Abbreviations
- x1,x2,x3:
-
space coordinates
- v′,v2,v3:
-
velocity components
- ρ:
-
density of the liquid
- μ:
-
coefficient of viscosity
- μ c :
-
coefficient of cross-viscosity
- γ:
-
relaxation time
- v :
-
kinematic coefficient of viscosity
- v c :
-
kinematic coefficient of cross-viscosity
- S ij :
-
stress-tensor
- \(\bar S_{j^i } \) :
-
rate of stress tensor
- d ij :
-
rate of strain tensor
- ξ,η,ζ:
-
dimensionless coordinates
- L :
-
characteristic length
- U 0 :
-
characteristic velocity
- f :
-
non-dimensional velocity
- T 0 :
-
temperature of the lower wall
- T 1 :
-
temperature of the upper wall
- K :
-
conductivity
References
Schlichting, H., ZAMM31 (1951) 78.
Oldroyd, J. G., Proc. Roy. Soc. A200 (1950) 523.
Jain, M. K., Proc. third Congr. Theor. Appl. Mech. India, 1957, 217.
Sharma, S. K., ZAMM39 (1959) 313.
Schlichting, H., Boundary Layer theory Pergamon Press, London, 1955.
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Jain, M.K. Heat transfer by laminar flow of visco-elastic liquids through parallel walls. Appl. sci. Res. 11, 295–303 (1963). https://doi.org/10.1007/BF03184988
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DOI: https://doi.org/10.1007/BF03184988