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Radiative interactions in boundary layers

Published online by Cambridge University Press:  19 April 2006

S. P. Venkateshan  and
K. Krishna Prasad
S. P. Venkateshan
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012
K. Krishna Prasad
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012
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Abstract

A detailed description of radiative interactions in laminar compressible boundary layers for moderate Mach numbers is presented by way of asymptotic analysis and supporting solutions. The radiation field is described by the differential approximation. While the asymptotic analysis is valid for large N (the ratio of photon mean free path to molecular mean free path) and arbitrary Boltzmann number, Bo (the ratio of convective heat flux to radiation heat flux), the solutions are obtained for Bo [Lt ] 1, the case of strong radiative interactions.

The asymptotic analysis shows the existence of an optically thin boundary layer for large N and all Bo. For Bo [Lt ] 1, two outer regions are observed — one optically thin (at short distances from the leading edge) and the other optically thick (at large distances from the leading edge). An interesting feature not pointed out in the previous literature is the existence of a wall layer at large distances from the leading edge where convective heat flux can be ignored to the leading order of approximation. The radiation field in all cases can be very well approximated by a one-dimensional description.

The solutions have been constructed using the ideas of matched asymptotic expansions by approximate analytical procedures and numerical methods. It is shown that, to the leading order of approximation, the radiation slip method yields exactly the same result as the more complicated matching procedure. Both the cases of linear and nonlinear radiation have been considered, the former being of interest in developing approximate methods which are subsequently generalized to handle the nonlinear problem. Detailed results are presented for both cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 1 , 16 January 1979 , pp. 33 - 66
Copyright
© 1979 Cambridge University Press

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References

Cess, R. D. 1964 The interaction of thermal radiation with conduction and convection heat transfer. Advances in Heat Transfer, vol. 1. Academic Press.
Cess, R. D. 1966 Thermal radiation in boundary layer heat transfer. Proc. Third Int. Heat Transfer Conf. vol. V. New York: A.I.Ch.E.
Cheng, P. 1964 Radiating gas flow by a moment method. A.I.A.A. J. 2, 1662.Google Scholar
Curle, N. 1962 The Laminar Boundary Layer Equations. Oxford University Press.
Emanuel, G. 1968 Radiative transport in an optically thick planar medium. Int. J. Heat Mass Transfer 11, 1413.Google Scholar
Emanuel, G. 1970 Application of matched asymptotic expansions to radiative transfer in an optically thick gas. Proc. 1970 Heat Transfer and Fluid Mech. Inst. Stanford University Press.
Howarth, L. 1951 Some aspects of Rayleigh's problem for a compressible fluid. Quart. J. Mech. Appl. Math. 4 (2), 157.Google Scholar
Kaplun, S. 1954 Role of coordinates in boundary layer theory. Z. angew. Math. Phys. 2, 111.Google Scholar
Koch, W. 1972 Application of Olfe's modified differential approximation to the radiation layer problem on a flat plate. Int. J. Heat Mass Transfer 15, 2663.Google Scholar
Kruskal, M. D. 1963 Mathematical Models in Physical Sciences (ed. S. Drobot). Prentice Hall.
Lick, W. 1963 Energy transfer by radiation and conduction. Proc. 1963 Heat Transfer and Fluid Mech. Inst. Stanford University Press.
Moore, F. K. 1961 On local flat plate similarity in the hypersonic boundary layer. J. Aero. Sci. 28, 753.Google Scholar
Nagendra, H. R. 1971 Studies on free convection. Ph.D. thesis, Dept. Mech. Engng, Indian Inst. of Science.
Olfe, D. B. 1967 A modification of the differential approximation for radiative transfer. A.I.A.A. J. 5, 638.Google Scholar
Ozisik, M. N. 1973 Radiative Transfer and Interactions with Conduction and Convection. Wiley.
Pai, S. I. & Tsao, C. K. 1966 A uniform flow of a radiating gas over a flat plate. Proc. Third Int. Heat Transfer Conf. vol. v. New York: A.I.Ch.E.
Ralston, A. 1965 A First Course in Numerical Analysis. McGraw-Hill.
Ralston, A. & Wilf, H. S. 1960 Mathematical Methods for Digital Computers. Wiley.
Raizer, Iu. P. 1957 On the structure of the front of strong shock waves in gases. Sov. Phys. J. Exp. Theor. Phys. 5, 1242.Google Scholar
Roberts, S. M. & Shipman, J. S. 1972 Two Point Boundary Value Problems: Shooting Methods. Elsevier.
Schlichting, H. 1960 Bundary Layer Theory. McGraw-Hill.
Sibulkin, M. & Dennar, E. A. 1972 Radiating boundary layers at planetary entry velocities. Int. J. Heat Mass Transfer 15, 619.Google Scholar
Smith, C. 1957 A Treatise on Algebra. Macmillan.
Solan, A. & Cohen, I. M. 1967a Rayleigh problem in a radiating compressible gas. I. Plate Mach number finite. Phys. Fluids 10, 108.Google Scholar
Solan, A. & Cohen, I. M. 1967b Rayleigh problem in a radiating compressible gas. II. Plate Mach number finite. large. Phys. Fluids 10, 257.Google Scholar
Sparrow, E. M. & Cess, R. D. 1966 Radiation Heat Transfer. Brooks/Cole Publishing Co.
Taitel, Y. 1969 Exact solution for the ‘radiation layer’ over a flat plate. J. Heat Transfer, Trans. A.S.M.E. C 91, 188.Google Scholar
Usiskin, C. M. & Sparrow, E. M. 1960 Thermal radiation between parallel plates separated by an absorbing emitting non-isothermal gas. Int. J. Heat Mass Transfer 1, 28.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.
Venkateshan, S. P. 1977 Radiative interaction in boundary layers. Ph.D. thesis, Dept. Mech. Engng, Indian Inst. of Science.
Venkateshan, S. P. & Krishna Prasad, K. 1973 Asymptotic forms of radiating boundary layers. Paper no. A-16, Second Natl. Heat and Mass Transfer Conf. Ind. Inst. of Tech., Kanpur.
Venkateshan, S. P. & Krishna Prasad, K. 1975 Optically thin radiation model in boundary layer flow. HMT-33-75, Third Natl. Heat and Mass Transfer Conf. Ind. Inst. of Tech., Bombay.
Venkateshan, S. P. & Krishna Prasad, K. 1978 Radiating laminar boundary layer flow over a flat plate at a large free stream Mach number. Paper presented at Sixth Int. Heat Transfer Conf. 7–11 Aug. Toronto.
Vincenti, W. G. & Kruger, C. H. 1965 Introduction to Physical Gas Dynamics. Wiley.
Viskanta, R. 1966 Radiation transfer and interaction of convection with radiation. Advances in Heat Transfer, vol. 3. Academic Press.