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Show 2.1.13 By using the temperature distributions (25) between the moving cores the boundary conditions (21) for the moving cores become dx, ( ek+r9k) Fk( F o'xk' = ck(ek-ek-i)Fk-i<FO'V - Hk zf (28> dFo k=K...N, F^ - (Fo,X, )=0. For the moving core N closest to the particle surface,the particle surface temperature 6 is used as ek+r eN+rV The derivatives (with respect to x) of F, (Fo,x) are k fk(Fo) F'(Fo,X, ) = - ^ , f (Fo)^0 Xk 1-exP{-fk(Fo)gk(Xk+1)} fk-1(Fo) exp{-fk_1(Fo)gk_1(XR)} Xk 1-exp{-fk_1(Fo)gk_1(Xk)} FjJ^lFo,^) = -±-j ^ =-! * , fk-1(Fo)fO Fk(Fo,XR) = Ijr , fk(Fo)=0 and Xk * k<W Fk_l(Fo,Xk) = -j - , fw(Po)-0 Xk gk-1(V The set of boundary conditions (28) forms N^Kfl simultaneous nonlinear differential equations for the moving isotherms. These equations are integrated numerically. By choosing the time step AFo small enough the functions F~ and F'_ can be approximated to be constants during the time step, and their values are calculated by using the initial values of X, at the K. beginning of the time step (or values at the end of the previous time step). We obtain (2cn xk(Fo+AFo) = xk(Fo) • (VVWk-i - <ek+1-ek)Fk} *£ When X„(Fo+^Fo)<0, where K denotes the isotherm closest to the center, the isotherm X disappears in the center plane, line or point (and the index K is increased by one). |