| OCR Text |
Show 2.1 .4 An expression for the last term in equation (4) is found by multiplying the equation (2) by h. and by summing up, 9 P • •* Eh. - - = - Eh.div m" + Eh.p. (6) 1 9t x x x x The convection term in equation (1) becomes - * • - » . -*• - div(Zh.mV) = - EmV -Vh. - Eh.div mV (7) 1 1 ii I I - > •* = -C"•VT - Eh.div mV l l where C" is the local heat capacity flow rate/area, C"=Ec.mV, which includes the flow of moisture (liquid and vapour), volatiles and the gas initially in the pores of the particle. It is assumed that the heat conduction and radiation in the pores obey the Fourier law q = - AVT (8) By substituting the expressions (5), (6), (7) and (8) into the equation (1), we obtain pc |x - div(AVT) + Eh.p. + C"-VT = 0 (9) 9t ii The first term in this equation accounts for the storage of heat, the second term accounts for the heat transported by thermal conduction (and radiation), the third term accounts for the energy of chemical reactions and the vaporization of liquid water and the last term is due to the convective thermal transport (steam, liquid water and volatiles). For one-dimensional cases (infinite plate, infinite cylinder and sphere) the equation (9) becomes 3T 1 9 ,, T 9T, „, • •„ 3T n #„ A1 pc at " T ^ ( X r 97) + Zhipi + c 97 = ° (10) r The combined convection and radiation boundary condition is used for the particle surface h (T - T ) + aoiTt - TN = A(f^) (11) e g s r s dr s |
