Abstract
A similar solution has been obtained to the problem of simultaneous radiation and convection for nonsteady stagnation point flow over a three-dimensional blunt body with both boundary layer suction and injection.
The diffusion approximation is used to characterize the radiative heat flux. The three-dimensional, time-dependent equations of motion and the energy equation have been transformed into a set of ordinary differential equations by the similarity transformation and the resulting ordinary differential equations have been solved numerically. The effects of accelerating and decelerating flow, the three-dimensional geometry, injection and suction, hot and cold wall conditions, and the conduction-to-radiation parameter on the temperature distribution within the flow have been investigated.
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Abbreviations
- A :
-
constant
- C, D :
-
geometry and nonsteady parameter respectively
- c p :
-
specific heat at constant pressure
- f :
-
nondimensional stream function in x-direction
- F :
-
nondimensional pressure function
- g :
-
nondimensional stream function in y-direction
- k :
-
thermal conductivity
- N :
-
conduction-to-radiation parameter \(\left( { = \frac{{k\kappa }}{{4\sigma T_\infty ^3 }}} \right)\)
- P :
-
pressure
- Pr :
-
Prandtl number
- Pr m :
-
modified Prandtl number \(\left( { = \frac{{P\gamma }}{{1 + \tfrac{4}{{3N}}}}} \right)\)
- q :
-
total heat flux
- q r :
-
radiation heat flux
- t :
-
time
- T :
-
temperature
- u, v, w :
-
the x, y, and z-direction velocity components respectively in the boundary layer
- U, V :
-
the x and y-direction velocity components respectively at the edge of the boundary layer
- x :
-
coordinate tangent to surface in the main flow direction
- y :
-
coordinate tangent to surface in the cross flow direction
- z :
-
coordinate normal to the surface
- α :
-
acceleration parameter
- η :
-
similarity variable in z and t
- θ :
-
nondimensional temperature for nonlinear case \(\left( { = \frac{T}{{T_\infty }}} \right)\)
- \(\bar \theta\) :
-
nondimensional temperature for linearized case \(\left( { = \frac{{T - T_{\text{W}} }}{{T_\infty - T_{\text{W}} }}} \right)\)
- κ :
-
absorption coefficient
- μ :
-
viscosity
- ν :
-
kinematic viscosity
- ρ :
-
density
- σ :
-
Stefan-Boltzmann constant
- primes:
-
denote differentiation with respect to η
- w:
-
conditions at the wall
- x, y, z :
-
conditions in the x, y, and x-directions respectively
- ∞:
-
conditions in the free stream
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Cheng, E.H., Özişik, M.N. Heat transfer in a radiating, nonsteady, three-dimensional stagnation flow. Appl. Sci. Res. 28, 185–197 (1973). https://doi.org/10.1007/BF00413066
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DOI: https://doi.org/10.1007/BF00413066