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solving ODE..set of differential equations

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( dH)/dt=-R_H ; where R_H=A_H*H*exp⁡((-E_H)/RT)

dM/dt=2/3 R_H-R_(M ) ; where R_M=A_M*M*exp⁡((-E_M)/RT)
dW/dt=3R_M-R_(W ) ; where R_W=A_W*W*exp⁡((-E_W)/RT)
( dF)/dt=-R_(W );
dC/dt=-( 1/3 R_H+R_(M )+R_(W )) ;

ρC_P ∂T/∂t=∂/∂x(K_eff ∂T/∂x)+∑_(i=H,M,W,C)▒〖R_i 〖∆H〗_i 〗
at top
- K_eff ∂T/∂z= 0
at bottom
- K_eff ∂T/∂z= σ ε (T_a^4- T^4 )

2 Replies Last Post 15 juil. 2016, 01:39 UTC−4
Jeff Hiller COMSOL Employee

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Posted: 8 years ago 13 juil. 2016, 17:22 UTC−4
Hello Sooraj,
You may want to clarify for Discussion Forum users what questions you have.
Jeff
Hello Sooraj, You may want to clarify for Discussion Forum users what questions you have. Jeff

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Posted: 8 years ago 15 juil. 2016, 01:39 UTC−4
Hematite to magnetite: 3Fe2O3 + CO = 2Fe3O4 + CO2
Magnetite to wustite: Fe3O4 + CO = 3FeO + CO2
Wustite to iron: FeO + CO = Fe + CO2
Boudouard reaction: CO2 + C = 2CO

these reactions should be solved using chemical reaction engineering module.
First order kinetics has been assumed here. ie using Arrhenius equation. as defined in that module. values of the constant has been defined below,

A_H=10^19/s A_M=10^18/s A_W=10^14/s
E_H=580 KJ/mole E_M=580 KJ/mole E_W=390 KJ/mole
∆H (H→M)=-16 KJ/mole
∆H (M→W)=42 KJ/mole
∆H (W→Fe)=-17 KJ/mole
∆H (C-gasification)=172 KJ/mol
σ=5.667×10^(-8) watt/m^2-K
ε=0.8
T=1,500K
Density (kg/ m3):
H= 5,200; M= 5,160; W=5,500; Fe= 7,800; C= 2,267
Heat capacity Cp (J/ kg-K):
H= 100; M= 100; W=80; Fe= 65; C= 80

where H= Hematite, M=Magneite, W=Wustite, F=Iron, C =Carbon.


I have already posted the set of first order kinetics eqs earlier
Hematite to magnetite: 3Fe2O3 + CO = 2Fe3O4 + CO2 Magnetite to wustite: Fe3O4 + CO = 3FeO + CO2 Wustite to iron: FeO + CO = Fe + CO2 Boudouard reaction: CO2 + C = 2CO these reactions should be solved using chemical reaction engineering module. First order kinetics has been assumed here. ie using Arrhenius equation. as defined in that module. values of the constant has been defined below, A_H=10^19/s A_M=10^18/s A_W=10^14/s E_H=580 KJ/mole E_M=580 KJ/mole E_W=390 KJ/mole ∆H (H→M)=-16 KJ/mole ∆H (M→W)=42 KJ/mole ∆H (W→Fe)=-17 KJ/mole ∆H (C-gasification)=172 KJ/mol σ=5.667×10^(-8) watt/m^2-K ε=0.8 T=1,500K Density (kg/ m3): H= 5,200; M= 5,160; W=5,500; Fe= 7,800; C= 2,267 Heat capacity Cp (J/ kg-K): H= 100; M= 100; W=80; Fe= 65; C= 80 where H= Hematite, M=Magneite, W=Wustite, F=Iron, C =Carbon. I have already posted the set of first order kinetics eqs earlier

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