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Show - 5 - - k. ~. = hi(T. - Ti) + €.o(T: - T!) at y = 0 BT, av 1&Y = 0, 7iY = 0, u = 0, (6) (7) (S) In this paper at the tube wall there is no slip and the wall is maintained at a constant temperature Tw such that u=v=o, Ts=T,=Tw. (S) A recent discussion of radiative transfer in dispersed media is available (Menguc and Viskanta, 19S9), and both continuous and discrete models are being used. Radiative transfer in the porous bed is modeled using a differential (continuous) approximation (Liou and Ou, 1979; Harshvardhan et ai., 19S1). The solid bed is considered to absorb, emit and scatter thermal radiation, but the combustion products (C02 , H20, etc.) are assumed to be radiatively nonparticipating, because the product of the partial pressure and the characteristic distance between the particles, I, is very small [(pco2 + PH20) I « 1 atm-em). The bed and the surfaces of the particles are assumed to be gray. The conservation of radiant energy equation is -+ V·~ = -,B(1-w)(~ - 4Eb ) and the irradiance ~ is governed by V2~ = rl(~ - 4Eb) (10) where the parameter T/ is defined as 1]2 = 3,& (l-w)(l-gw) (11) At the boundary on the radiative flux components can be related to the irradiance. The details are well known and are available in the literature (Liou and Ou, 1979; Harshwardhan, 19S1; Menguc and Viskanta, 19S5). For example, the boundary condition on the radiative flux component in the y-direction is given by Fj = fsaT: + PsFy at Y = ° (12) F + = _1_ (~ _ ~ U9) at y = 0 y 41r a,B &y (13) where a = (3/2)(1-gw). Similar expressions can be written at y = H and at the pipe |
