Summary
An analytical study has been made to determine the heat transfer characteristics of a stagnation point flow in which there are temperature-dependent heat sources or sinks. Results have been obtained for both strong and weak sources or sinks for a Prandtl number of 0.7. An analytical method, applicable to all Prandtl numbers, was utilized which circumvented the need for extensive numerical solutions and which, at the same time, provided a closed-form representation for the heat transfer. A few numerical solutions were carried out to verify the method.
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Abbreviations
- a i :
-
constants depending on Prandtl number
- c p :
-
specific heat at constant pressure
- f :
-
dimensionless velocity variable
- g :
-
function defined by equation (13)
- g n :
-
functions of η (n=1, 2, 3,...)
- k :
-
thermal conductivity
- Pr :
-
Prandtl number, μc p /k
- q :
-
heat transfer rate per unit area at surface
- Q :
-
heat flux parameter, q/k(u 1/ν)1/2
- S :
-
rate of heat generation or removal per unit volume (divided by ρc p )
- T :
-
static temperature; T w , wall temperature; T ∞, free-stream temperature
- u 1 :
-
proportionality constant for free-stream velocity
- U ∞ :
-
free-stream velocity
- v :
-
normal velocity component
- x :
-
coordinate measuring distance along surface from stagnation point
- y :
-
coordinate measuring distance normal to surface
- β :
-
heat generation parameter, equation (3)
- η :
-
dimensionless normal coordinate, \(y\sqrt {u_1 /v} \)
- θ :
-
dimensionless temperature
- θ n :
-
functions of η (n=1, 2, 3,...)
- μ :
-
absolute viscosity
- ν :
-
kinematic viscosity
- ρ :
-
density
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Sparrow, E.M., Cess, R.D. Temperature-dependent heat sources or sinks in a stagnation point flow. Appl. sci. Res. 10, 185 (1961). https://doi.org/10.1007/BF00411912
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DOI: https://doi.org/10.1007/BF00411912