Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-31T18:54:23.775Z Has data issue: false hasContentIssue false

On the sensitivity of heat transfer in the stagnation-point boundary layer to free-stream vorticity

Published online by Cambridge University Press:  28 March 2006

S. P. Sutera
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island
P. F. Maeder
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island
J. Kestin
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island

Abstract

Experiments have given evidence of strong sensitivity of the stagnation-point heat transfer on cylinders to small changes in the intensity of free-stream turbulence. A similar effect on local heat-transfer rates to flat plates has been measured, but only when a favourable pressure gradient is present. In this work it is theorized that vorticity amplification by stretching is a possible, and perhaps the dominant, underlying mechanism responsible for this sensitivity. A mathematical model is presented for a steady, basically plane stagnation flow into which is steadily transported disturbed unidirectional vorticity having the only orientation susceptible to stretching. The resulting velocity and temperature fields in the stagnation-point boundary layer are analysed assuming the fluid to be incompressible and to have constant properties. By means of iterative procedures and electronic analogue computation an approximate solution to the full Navier-Stokes equations is achieved which indicates that amplification by stretching of vorticity of sufficiently large scale can occur. Such vorticity, present in the oncoming flow with a small intensity, can appear near the boundary layer with an amplified intensity and induce substantial three-dimensional effects therein. It is found that the thermal boundary layer is much more sensitive to the induced effects than the velocity boundary layer. Computations indicate that a certain amount of distributed vorticity in the oncoming flow causes the shear stress at the wall to increase by 5%, while the heat transfer there is augmented by 26% in a fluid with a Prandtl number of 0.74. Preliminary computations reveal that the sensitivity of the thermal boundary layer increases with Prandtl number.

Type
Research Article
Copyright
© 1963 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Geidt, W. H. 1951 Effect of turbulence level of incident air stream on local heat transfer and skin friction on a cylinder. J. Aero. Sci. 18, 725.Google Scholar
Kemp, N. H. 1959 Vorticity interaction at an axisymmetric stagnation point in a viscous, incompressible fluid. J. Aero/Space Sci. 26, 543.Google Scholar
Kestin, J. & Maeder, P. F. 1957 Influence of turbulence on the transfer of heat from cylinders. N A C A TN 4018.Google Scholar
Kestin, J. Maeder, P. F. & Sogin, H. H. 1961 The influence of turbulence on the transfer of heat to cylinders near the stagnation point. Z. angew. Math. Phys, 12, 11532.Google Scholar
Kestin, J., Maeder, P. F. & Wang, H. E. 1961a Influence of turbulence on the transfer of heat from plates with and without a pressure gradient. Int. J. Heat Mass Transf, 3, 13354.Google Scholar
Kestin, J. Maeder, P. F. & Wang, H. E. 1961b On boundary layers associated with oscillating streams. Appl. Sci. Res. A, 10, 1.Google Scholar
Lighthill, M. J. 1954 The response of laminar skin friction and heat transfer to fluctuations in the stream velocity. Proc. Roy. Soc. A, 224, 1.Google Scholar
Lin, C. C. 1957 Motion of the boundary layer with a repidly oscillating external flow. Proc. 9th Int. Congr. Appl. Mech, 4, 155.Google Scholar
Moore, F. K. 1951 Unsteady laminar boundary layer flow. N A C A TN 2471.Google Scholar
Moore, F. K. & Ostrach, S. 1956 Average properties of compressible laminar boundary layer with unsteady flight velocity. NACA TN 3886.Google Scholar
Ostrach, S. 1955 Compressible laminar boundary layer and heat transfer for unsteady motions of a flat plate. NACA TN 3569.Google Scholar
Sato, K. & Sage, B.H. 1958 Thermal transfer in turbulent gas streams : Effect of turbulence on macroscopic transport from spheres. Trans. ASME, 80, 1380.Google Scholar
Schlichting, H. 1932 Berechnung ebener periodischer Grenzschichtströmungen. Phys. Z, 33, 327.Google Scholar
Schlichting, H. 1960 Boundary Layer Theory (transl. J. Kestin). New York: McGraw-Hill.
Short, W. H., Brown, R. A. S. & Sage, B. H. 1960 Thermal transfer in turbulent gas streams. Effect of turbulence on local transport from spheres. J. Appl. Mech, 27, 393.Google Scholar
Stuart, J. T. 1959 The viscous flow near a stagnation point when the external flow has uniform vorticity. J. Aero/Space Sci, 26, 124.Google Scholar