Abstract
An analysis is made for the steady mixed convection boundary layer flow near the two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in its own plane. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation-point. Two equal and opposite forces are impulsively applied along the x-axis so that the wall is stretched, keeping the origin fixed in a viscous fluid of constant ambient temperature. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a very efficient numerical scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed in detail. Both cases of assisting and opposing flows are considered. It is observed that, for assisting flow, both the skin friction coefficient and the local Nusselt number increase as the buoyancy parameter increases, while only the local Nusselt number increases but the skin friction coefficient decreases as the Prandtl number increases. For opposing flow, both the skin friction coefficient and the local Nusselt number decrease as the buoyancy parameter increases, but both increase as Pr increases. Comparison with known results is excellent.
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Abbreviations
- a, b,c :
-
constants
- C f :
-
skin friction coefficient
- f :
-
dimensionless stream function
- g :
-
acceleration due to gravity (ms−2)
- Gr x :
-
local Grashof number
- k :
-
thermal conductivity (Wm−1K)
- Nu x :
-
local Nusselt number
- Pr:
-
Prandtl number
- q w :
-
heat transfer from the stretching surface (Wm−2)
- Re x :
-
local Reynolds number
- T :
-
fluid temperature (K)
- T w (x):
-
temperature of the stretching surface (K)
- T ∞ :
-
ambient temperature (K)
- u, v :
-
velocity components along x and y directions, respectively (m s−1)
- x, y :
-
Cartesian coordinates along the surface and normal to it, respectively (m)
- Greek letters :
-
- α:
-
thermal diffusivity (m2s−1)
- β:
-
thermal expansion coefficient (K−1)
- η:
-
pseudo-similarity variable
- θ:
-
dimensionless temperature
- λ:
-
buoyancy parameter
- μ:
-
dynamic viscosity (kgm−1s−1)
- ν:
-
kinematic viscosity (m2s−1)
- ρ:
-
fluid density (kgm−3)
- τ w :
-
skin friction from the surface of the sheet (Pa)
- ψ:
-
stream function (m2s−1)
- Superscript :
-
- ′:
-
differentiation with respect to η
- Subscripts :
-
- w :
-
condition at the stretching sheet
- ∞:
-
condition at infinity
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Ishak, A., Nazar, R. & Pop, I. Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet. Meccanica 41, 509–518 (2006). https://doi.org/10.1007/s11012-006-0009-4
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DOI: https://doi.org/10.1007/s11012-006-0009-4