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Question: Help on drying of moist particles (diffusion and convection with heat and mass transfer)

Question:Help on drying of moist particles (diffusion and convection with heat and mass transfer)

JRHelmus 24 Maple
differential-equation pde pdsolve
March 28 2008
0

Dear All,

I’m quite new into maple and this website as well. Nevertheless I hope you want to help me out.
 
After weeks of struggling with Maple, I finally decided to call for help from your side.
 
I’m performing a research on drying of moist particles for my graduation project. In Maple I want to model the drying process of one single moist particle in an air flow. Most of the elements in the system, like diffusion, are made variable to keep the situation in the model as realistic as possible.
 
The main problem now is that Maple does not accept my PDE system as such. It continuously provides me with errors, which do not make any sense.
 
Can someone please take a look at my maple model, for I’m getting fed up with Maple?
 
Thanks a lot in advance!
 
JR Helmus
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The maple model is too large to put here thus. I will focus mainly at the equations. Please note all the constants in the eq that are actually functions:
 
The model is built up from several parts
-          Particle properties
o       constant
o       dependent
-          air properties
o       constant
o       dependent
o       environment properties
-          Dimensionless numbers
-          PDE for heat and mass
-          Initial conditions
-          Boundary conditions
-          Solver
-          plotter
 


PDE’s
PD_Mass:=diff(X(r,t),t)=1/(r*r)*diff(r^2*Diffusion_watersolid(X(r,t))*diff(X(r,t),r),r);
PD_Heat:=Density_P*Cp_p*diff(T(r,t),t)=1/(r^2)*diff(r^2*lambda_p*diff(T(r,t),r),r);
 
IBC
IC1:=X(r,0)=0.06;
IC2:=T(r,0)=60;
BC1:=D[1](X)(0, t)=0;
BC2:=Density_P*D[1](X)(R_p,t) = K_c*(P0(T(R_p,t))*(wateractivity(X(R_p,t))-RH_air/100));
BC3:=D[1](T)(0, t)=0;
BC4:=lambda_p*(D[1](T)(R_p, t))=h_particle(X(R_p,t),T(R_p,t))*(T_b-T(R_p,t))-K_c*(P0(T(R_p,t))*(wateractivity(X(R_p,t))-RH_air/100))*Delta_H_vaporation;
 
Solver:
PDEsys:=(PD_Heat,PD_Mass):
IBCsys:=(IC1, IC2,BC1,BC2,BC3,BC4):
ans:= pdsolve(PDEsys, IBCsys):
 
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