Abstract
In this research the steady three-dimensional flow of a Walter’s B fluid in a vertical channel with porous wall, through which the fluid is injected uniformly into the channel through one side of the channel, is studied analytically using Homotopy Analysis Method (HAM). The channel is assumed to be infinite and uniform. The effects of the elasticity of the fluid on the flow and heat transfer on the walls of the channel are discussed.
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Abbreviations
- c p :
-
Specific heat at constant pressure
- e :
-
Rate of strain tensor
- g :
-
Gravitational acceleration vector
- I :
-
Identity tensor
- k :
-
Thermal conductivity
- k 0 :
-
Short memory coefficient
- L, B, D:
-
Dimensions of the channel
- Pe:
-
Peclet number
- P :
-
Pressure
- P x , P y :
-
Pressure variations in the x and y directions
- p :
-
Embedding parameter
- Re:
-
Cross-flow Reynolds number
- S :
-
Elastic number
- T :
-
Temperature
- T :
-
Cauchy stress tensor
- T0, T1:
-
Temperatures of the walls
- t :
-
Time
- U :
-
Uniform injection velocity
- u, v, w:
-
Components of the velocity vector
- V :
-
Velocity vector
- θ :
-
Dimensionless temperature
- τ :
-
Relaxation time
- φ 0 :
-
Arbitrary function
- ρ :
-
Density
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Joneidi, A.A., Domairry, G. & Babaelahi, M. Homotopy Analysis Method to Walter’s B fluid in a vertical channel with porous wall. Meccanica 45, 857–868 (2010). https://doi.org/10.1007/s11012-010-9295-y
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DOI: https://doi.org/10.1007/s11012-010-9295-y