Sommario
Si descrive un metodo approssimato per il calcolo del flusso di calore in strato limite laminare senza gradiente di pressione. L'equazione dell'energia viene scritta in una forma approssimata che, tramite un cambio di variabili, diventa identica all'equazione della quantità di moto. Il metodo descritto in un lavoro precedente viene poi applicato al calcolo del flusso di calore per condizioni iniziali arbitrarie. II metodo viene poi esteso al caso di flusso con gradiente di pressione e i risultati relativi ai flussi con profili simili sono in buon accorda con le soluzioni esatte.
Summary
An approximate method of computing the heat transfer in laminar boundary-layer without pressure gradient is described. The energy equation is written in an approximate form which, through a change of variables, becomes identical to the momentum equation. The method described in a preceding paper is then applied to determine the heat transfer for arbitrary initial conditions. The procedure is then extended to the flow with pressure gradient and the results compare well with the exact similar solutions.
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Abbreviations
- L :
-
Reference length
- p' :
-
pressure gradient
- P r :
-
Prandtl number
- q :
-
heat flux at the wall
- T :
-
temperature
- T e :
-
external temperature
- T w :
-
wall temperature
- n :
-
streamwise velocity component
- U :
-
external flow velocity
- x :
-
streamwise co-ordinate
- y :
-
normal co-ordinate
- ξ:
-
auxiliary co-ordinate
- λ :
-
heat conduction coefficient
- ψ :
-
stream function
- Μ :
-
viscosity coefficient
- ϱ :
-
density
- θ :
-
defined in Eq. (11)
- Τ :
-
shear stress at the wall
References
H.Schlichting,Boundary-layer theory, Mc Graw Hill, 1960.
M. J. Lighthill,Contributions to the theory of heat transfer through a laminar boundary-layer, Proc. Roy. Soc. London, A 202, pp. 359–377, 1950.
A.Reggiori,A method of computing skin friction and adiabatic wall temperature in a laminar boundary-layer without pressure gradient, Meccanica no. 1, Vol. VII, 1972.
N. Curle andH. J. Davies,Modern fluid dynamics, Vol. 2, Van Nostrand Reinhold Co., London 1971.
D. R.Chapman and M. W.Rubesin,Temperature and velocity profiles in the compressible laminar boundary-layer with arbitrary distribution of surface temperature, J. Aero. Sci., pp. 547–565, 1949.
G. M.Low,The compressible laminar boundary-layer with fluid injection, NACA TN 3404, 1955.
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Reggiori, A. An approximate method of computing the heat transfer in laminar boundary-layer. Meccanica 9, 75–79 (1974). https://doi.org/10.1007/BF02209509
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DOI: https://doi.org/10.1007/BF02209509