固体延焼の基礎的研究 その1. 薄板の無炎燃え下がり延焼
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The combustion of solid materials which contain no oxydant in themselves takes place only on their surface supported by the air supply from outside. For the first step of the study of the propagation of combustion of this kind, the downward propagation of smouldering (combustion without flame) along a vertical sheet of cardboard was investigated, because this proved to be the simplest case both experimentally and theoretically.The fire front proceeds downwards with a velocity V (cm/s) making an angle θ with the vertical. The propagation velocity υ perpendicular to the fire front was observed in a vessel of temperature Ta with rectangular pieces of cardboard of various breadth and thickness, and the results for υ2 were summarized as follows:υ2=0.55 × 10-2{1/b+1/d+0.53/bd}(1/(Ti-Ta)-1.55 × 10-3)where Ti is the vessel temperature which makes the cardboard ignite instantaneously and was found, in an electric furnace, to be 460°C.In the theoretical part, the authors considered the heat balance in a part of length dX in the strip just in front of the fire front with the following assumptions.(1) When a solid material in the open air ignites, combustion gases envelop it and prevent fresh air from getting to the burning surface. Combustion takes place when fresh air reaches the surface by natural convection. The heat dQ1 produced in the part dX in the time dt is considered to be proportional to the velocity of the ascending convection current which was assumed to vary as the temperature difference (T-Ta) between dX and the ambient air.(2) dQ1 is also proportional to the velocity of the combustion reaction which depends upon the ambient temperature. Since υ should be infinite when Ta→Ti , dQ1 was assumed to be proportional to 1/(Ti-Ta).(3) dQ1 is proportional, too, to the surface area dS of the part dX. When burning, however, the surface of the solid material is covered with a stagnant boundary layer of combustion gases and the fresh air is supplied by diffusion through this layer from outside. Therefore, the surface area of dX was assumed to be 2(b+d+ε)dX instead of (b+d)dX, where ε is about four times the thickness of this layer.(4) Heat is dissipated through this stagnant layer of temperature T into the ambient field of temperature Ta. Thus the heat dissipated dQ2 from dX in dt was assumed to be 2h(b+d+ε)dX(T-Ta)dt, where h is the heat transmission coefficient.From these considerations, Fourier's equation was derived as follows :cρ (∂T/∂t)=k(∂2T/∂X2)cosec2θ+2(1/b+1/d+ε/bd)(q/(Ti-Ta)-h)(T-Ta),where q is a constant depending upon the chemical properties of the cardboard.
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