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Shrinking Core: Non-Isothermal

Shrinking Core: Non-Isothermal. Quak Foo Lee Chemical and Biological Engineering The University of British Columbia. Shrinking Core: Non-Isothermal. Heat generated at reaction front , not throughout the volume In Steady State, Solve. T c. T s. r c. r. T f. R. T Conditions.

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Shrinking Core: Non-Isothermal

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  1. Shrinking Core: Non-Isothermal Quak Foo Lee Chemical and Biological Engineering The University of British Columbia

  2. Shrinking Core: Non-Isothermal • Heat generated at reaction front, not throughout the volume • In Steady State, • Solve Tc Ts rc r Tf R

  3. T Conditions

  4. Boundary Condition 1: r = rc Heat is generated = Heat conducted out through product layer Area

  5. Boundary Condition 2: r = R Heat arriving by conduction = Heat removed for from within particle convection Can be obtained from B.C. 1 Bi-1

  6. Solution • Combine equations and eliminate TS to get Tc-Tf

  7. Recall from Isothermal SC Model Substitute CA,c into (Tc –Tf) equation

  8. Tc - Tf Conduction Convection Reaction Mass Transfer Diffusion in Product Layer

  9. Can Heat Transfer Control the Rate in Endo- and Exothermal Rxn? • Consider CA,c≈CA,f; initially rapid reaction • Endothermic with poor heat transfer, heat will be consumed in reaction, and if can’t transfer heat in, TC will drop  reaction rate ↓ markedly and rate of reaction become the slow step occurring at a rate dictated by the flow of heat. • Exothermic initial rapid reaction and with poor Q, TCwill 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.

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