Summary
The interaction of free convection with thermal radiation in boundary layer flow from an inclined isothermal plate is studied numerically. Introducing appropriate transformations the equations governing the flow are expressed in the form of local nonsimilarity equations valid near the leading edge as well as in the downstream region. A group of transformations is also introduced such that the flow near the leading edge and far downstream can be described. Heated upward facing plates with positive and negative inclination angles are investigated. When the inclination is negative the boundary layer separates from the surface and the numerical solutions can be extended downstream past the point of separation. From the present investigation it may be concluded that the position of the separation point moves away from the leading edge with the increase of either of the thermal radiation parameter or the surface temperature parameter of the heated surface.
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Ostrach, S.: An analysis of laminar free convection flow and heat transfer about a flat plate parallel to the direction of the generating body force. NACA TN 2635 (1952).
Pera, L., Gebhart, B.: Natural convection boundary layer over horizontal and slightly inclined surfaces. Int. J. Heat Mass Transfer16, 1131–1146 (1973).
Hasan, M. M., Eichorn, R.: Local nonsimilarity solution of free convection flow and heat transfer from an inclined isothermal plate. J. Heat Transfer ASME Ser. C101, 642–647 (1979).
Chen, T. S. and Tzuoo, K. L.: Vortex instability of free convection flow over horizontal and inclined surfaces. J. Heat Transfer, ASME Ser. C103, 637–643 (1982).
Chess, R. D.: Interaction of thermal radiation with free convection heat transfer. J. Heat Transfer ASME Ser. C104, 637–647 (1982).
Arpaci, V. S.: Effect of thermal radiation on the laminar free convection from a heated vertical plate. Int. J. Heat Mass Transfer11, 871–881 (1968).
Cheng, E. H., Ozisik, M. N.: Radiation with free convection in an absorbing, emitting and scattering medium. Int. J. Heat Mass. Transfer15, 1243–1252 (1972).
Hasegawa, S., Echigo, R., Fakuda, K.: Analytic and experimental studies on simultaneous radiative and free convective heat transfer along a vertical plate. Proc. Jpn. Soc. Mech. Eng.38, 2873–2883 (1972) and39, 250–257 (1973).
Bankston, J. D., Lloyed, J. R., Novonty, J. L.: Radiation convection interaction in an absorbing-emitting liquid in natural convection boundary layer flow. J. Heat Transfer ASME Ser. C99, 125–127 (1977).
Sparrow, E. M., Cess, R. D.: Radiation heat transfer — augmented edition. Washington D. C.: Hemisphere Chap. 7 and 10, 1978.
Viskanta, R., Grosh, R. J.: Boundary layer in thermal radiation absorbing and emitting media. Int. J. Heat Mass Transfer5, 179–806 (1962).
Cess, R. D.: The interaction of thermal radiation in boundary layer heat transfer. Proc. Third Int. Heat Transfer Conf.5, 154–163 (1966).
Ali, M. M., Chen, T. S., Armaly, B. F.: Natural convection-radiation interaction in boundary layer flow over horizontal surface. AIAA J.22, 1797–1803 (1984).
Hossain, M. A., Takhar, H. S.: Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Heat Mass Transfer31, 243–248 (1996).
Hossain, M. A., Pop, I., Ahmed, M.: MHD free convection from an isothermal plate inclined at a small angle to the horizontal. Int. J. Theor. Appl. Fluid Mech. (to appear).
Jones, D. R.: Free convection from a semi-infinite flat plate inclined at a small angle to the horizontal. Q. J. Mech. Appl. Math.28, 77–98 (1973).
Lanczos, C.: Applied analysis. London: Pitman, 1957.
Hunt, R., Wilks, G.: Continuous transformation of boundary layer equations between similarity regimes. J. Comp. Phys.40, 478–490 (1981).
Keller, H. B.: Numerical methods in boundary layer theory. Annu. Rev. Fluid Mech.10, 417–433 (1978).
Stewartson, K.: On the free convection from a horizontal plate. J. Appl. Math. Phys.9, 274–281 (1958).
Bejan, A.: Convective heat transfer. New York: Wiley 1995.
Cebeci, T., Bradshaw, P.: Physical and computational aspects of convective heat transfer. New York: Springer 1984.
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Hossain, M.A., Rees, D.A.S. & Pop, I. Free convection-radiation interaction from an isothermal plate inclined at a small angle to the horizontal. Acta Mechanica 127, 63–73 (1998). https://doi.org/10.1007/BF01170363
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DOI: https://doi.org/10.1007/BF01170363