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Laminar boundary-layer flow past a two-dimensional slot

Published online by Cambridge University Press:  12 April 2006

Ian J. Sobey
Ian J. Sobey
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Present address: Department of Engineering Science, University of Oxford, Parks Road.
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Abstract

Observations by Cornhill ' Roach (1976) of sudanophilic lesions in the vicinity of intercostal arteries in rabbit aortas have shown that lesions develop on the downstream side of the associated ostia. There is considerable conjecture as to the role which varying levels of wall shear stress play in the development of such lesions; Cornhill ' Roach implicate high wall shear stress levels. We develop a consistent model of steady boundary-layer flow past a side slot assuming that there is Stokes flow in the side slot and that the main body of the boundary layer remains undisturbed. Our results show that increased levels of wall shear stress occur both upstream and downstream of the slot. If the withdrawal of fluid through the side slot is sufficiently great there may be a stagnation point on the downstream side of the slot. The wall shear stress level near the slot depends on both normal and transverse motions at the mouth of the slot. Indeed, very near the slot, on a length scale comparable with the slot width, the wall shear stress level depends only on the transverse motions at the mouth of the slot.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 1 , 1 November 1977 , pp. 33 - 47
Copyright
© 1977 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. 1965 Handbook of Mathematical Functions. Dover.
Brighton, P. W. M. & Jackson, P. S. 1978 Submitted to Quart. J. Mech. Appl. Math.
Cornhill, J. F. & Roach, M. 1976 Atherosclerosis 23, 489.
Davids, N. & Kandarpa, K. 1974 In Fluid Dynamic Aspects of Arterial Disease (ed. R. M. Nerem), p. 16. Ohio State University, Columbus.
Dean, W. R. & Montagnon, P. 1949 Proc. Camb. Phil. Soc. 45, 389.
Fry, D. L. 1973 Ciba Found. Symp. no. 12. Atherogenesis: Initiating Factors, p. 93.
Hunt, J. C. R. 1971 J. Fluid Mech. 49, 159.
Lighthill, M. J. 1958 Fourier Analysis and Generalised Functions. Cambridge University Press.
Lutz, R. J., Cannon, J. N. & Munroe, R. E. 1974 In Fluid Dynamic Aspects of Arterial Disease (ed. R. M. Nerem), p. 5. Ohio State University, Columbus.
Moffatt, H. K. 1964 J. Fluid Mech. 18, 1.
Smith, F. T. 1973 J. Fluid Mech. 57, 803.
Smith, F. T. 1976 Mathematika 23, 62.
Sneddon, I. N. 1951 Fourier Transforms. McGraw-Hill.
Stewartson, K. 1968 Proc. Roy. Soc. A 306, 275.
Stewartson, K. & Williams, P. G. 1969 Proc. Roy. Soc. A 312, 187.
Weinbaum, S. 1968 J. Fluid Mech. 33, 39.