| OCR Text |
Show 2.1.11 If Ir'^ If' + wVPgkVPk-1ck-1<VTk-1,}6(r-Rk»^i r k=K 3 at - C"(r) |? = 0 (20) o r This equation can be separated into boundary conditions for the moving cores and into equations that are valid between the moving cores. The boundary conditions, expressed in dimension-less form, are dX < H W =Ck(H»x=X, - \ZZ- (21) k k dFo when x=X, , k=K...N. The dimensionless time Fo=a0t/R2, the dimensionless distance from the center x=r/R, the dimension-less location of the core k is X, =R, /R and the dimensionless temperature 6=T/T0. The dimensionless constants C, and H, are calculated by using the material properties and the measured curve e(T) (Fig.2) after the isotherms to be followed are chosen, Ck=Xk_.,/Xk and Hk={ P ^ V k - ^ k - l (Tk"Tk-1 » >a«>*k T°' The dependence of the material properties (for example the heat conductivity) on the temperature and on the density can be taken into account, since the temperature and the density between two successive cores are known in advance. However, between the two successive moving cores, the material propertie are assumed to be constants, since the temperature and the density variations are small,The dependence of the heat of pyrolysis 1, on the temperature can be taken into account by using different values for 1, on different cores T, . However, there is much lack of knowledge about the heat of pyrolysis and about the material properties of partially charred biomass fuels. Between the moving isotherms we have the equation r drK 9r' A, 9r u [ZZ) r k The heat capacity flow rate/area between the successive movinq isotherms k and k+1 is found by summing up the heat capacity |
