Boundary Condition 1: r = r c Heat is generated = Heat conducted out through product layer Area
Boundary Condition 2: r = R Heat arriving by conduction = Heat removed for from within particle convection Bi -1 Can be obtained from B.C. 1
Solution Combine equations and eliminate T S to get T c -T f
Recall from Isothermal SC Model Substitute C A,c into (T c –T f ) equation
T c - T f ConductionConvection Diffusion in Product Layer Reaction Mass Transfer
Can Heat Transfer Control the Rate in Endo- and Exothermal Rxn? Consider C A,c ≈ C A,f ; initially rapid reaction a) Endothermic with poor heat transfer, heat will be consumed in reaction, and if can’t transfer heat in, T C will drop reaction rate ↓ markedly and rate of reaction become the slow step occurring at a rate dictated by the flow of heat. b) Exothermic initial rapid reaction and with poor Q, T C will increased, then rate of reaction ↑ and eventually reach point where gaseous reactant can’t be transferred fast enough (external mass transfer or diffusion). Hence rate is limited.