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Radiative and convective heat transfer in a plane layer of absorbent curtain

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Abstract

An examination is made of the thermal state of a plane layer of gray gas injected into a turbulent stream of high temperature gas flowing over a permeable flat plate.

Similarity-type formulations of problems are encountered both in examination of flow near a stagnation point, and also in analysis of the lifting of the boundary layer by intense injection through a porous plate [1]. The examination described relates to the following idealized formulation of the problem (Fig. la).

In a plane layer of gray absorbing medium, formed by plane-parallel diffusely radiating surfaces (1-porous plate; 2-boundary of high temperature turbulent gas stream), heat transfer is accomplished by radiation and convection of the layer normal to the surfaces and by molecular heat conduction. All the physical and optical properties of the medium and of the boundary surfaces are assumed to be constant, independent of temperature.

The temperature of the wetted surface of the specimen and also that of the fictitious surface determining the upper bound of the lift-off region, are given.

Also assumed given is the velocity of the injected medium, which is constant throughout the entire lift-off layer. This idealization appreciably facilitates our examination without in principle changing its features.

A very simplified examination of this problem was given in [2]. The special case of a medium with low optical thickness was examined in [3,4].

The problem was examined in [5] under the assumption that molecular heat conduction in the medium is negligibly small.

In the formulation considered the generalized energy equation has the form

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References

  1. 1.

    Heat and Mass Transfer and Friction in the Turbulent Boundary Layer [in Russian], SSR, SO AN In-t teplofiziki, Novosibirsk, 1964.

  2. 2.

    S. N. Shorin, “Radiative heat transfer in an absorbing medium,” Izv. AN SSSR, OTN, no. 3, 1951.

  3. 3.

    R. Goulard and M. Goulard, “One-dimensional energy transfer in radiant media,” Int. J. Heat Mass Transfer, vol. 1, no. l, 1960.

  4. 4.

    R. Goulard, “The coupling of radiation and convection in detached shock layer,” J. Quantit. Spectrosc. Radiat. Transfer, vol. 1, no. 3–4, 1961.

  5. 5.

    V. N. Adrianov, “Radiative heat transfer in a plane layer of moving medium,” collection: Heat and Mass Transfer Vol. 2, [in Russian], Nauka i Tekhnika, Minsk, 1965.

  6. 6.

    N. A. Rubtsov,” Radiative heat transfer in a plane layer of absorbing medium,” PMTF [Applied Mechanics and Technical Physics], no. 5, 1965.

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Kutateladze, S.S., Rubtsov, N.A. Radiative and convective heat transfer in a plane layer of absorbent curtain. J Appl Mech Tech Phys 9, 667–673 (1968). https://doi.org/10.1007/BF00912868

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Keywords

  • Heat Transfer
  • Boundary Layer
  • Convective Heat Transfer
  • Flat Plate
  • Stagnation Point