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Show 2.1 .3 MODEL DESCRIPTION The equation for the conservation of energy can be found from the enthalpy balance for a differential element inside the particle. In vector notation 3Zp.h. •> -* - = -div(q + £h.m7) = - div q - div(Zh.mV) (1) i n ii 9t L 1 1 1 where p. is the local volumetric mass of substance i. The substance denoted by the index i can be water, steam, solid or gas. For the solid substance mV = 0. 3 I The equation for the conservation of mass for the substance i is _ 9p.; -+ - - = - div mV + p. (2) at where p. is the source or sink of the substance i. By summing up all the substances we obtain for the whole mixture |£ = - div m" (3) since the sum of the sources and the sinks is zero, Zp.=0. l p is the local density of the particle including the solid, liquid and gas phases. By denoting 9h Ci = (9T1)p and PC = EpiCi (4) where c. is the specific heat of the substance i and Pc is the volumetric heat capacity of the whole mixture, we obtain for the time derivate in the equation (1) 3Zp.h. dh. 9p. i i I I 9t 3t 3t = PC TTT: + ^h 9 t x 3t It is assumed that all the substances (solid, liquid, vapour, volatiles) are locally at the same temperature in the latter form of the equation (5). |