# Question:PDE problems with newton iteration - Drying of moist particles

## Question:PDE problems with newton iteration - Drying of moist particles

Maple

Dear all,

A few months ago I posed a question on drying of moist particles. Since then my study continued but has never finished.

In short:

I need to make a model for drying milk particles in a fluidized bed. This model is made in by using numerical analysis. The core of the model exists of coupled PDEs for heat and mass transfer.

Maple is used to check whether the output is correct. Yet it appears that the maple output if less reliable than the output.

My model:

The model I use is based on a simple coupled 2 order diffusion equation (for heat and mass).

The main issue is that nothing in this equation is constant.

-          diffusion is dependent on  heat and mass

-          boundary conditions are changing over time

-          density is changing due to change in moisture

For the sake of stability I had tried to use gid refinement in the time and space dimension. This refinement did not work out properly since pdsolve could not solve the pde when using refinement.

Yet for this current question I only have the diffusion coefficient as dependent coefficient. The problem now is that Maple continuously pops up errors.

-          raphson is not converging,

-

For the mass balance in C(oncentration):

PD_Mass:=diff(C(r,t),t)=1/(r*r)*diff(r*r*Diffusion_watersolid(CToXdry(C(r,t)))*diff(C(r,t),r),r);

Initial conditions:

IC1 := C(r, 0) = XwetToC(X_pinlet);

boundary conditions

BC1:=D(C)(0, t)=0;

BC2:=C(R_p,w) = XwetToC(RH_Bed/100);

With

Diffusion_watersolid :=(X_d)-> (8.723*(10^(-9)))*(X_d^3)-(7.515*(10^(-10)))*(X_d^2)+2.785*(10^(-11))*(X_d)+3.646*(10^(-12));

OR

Diffusion_watersolid :=(X_d)-> 1.55e-14*exp(55.087*X_d);

OR

Diffusion_watersolid :=(X_d)-> X_d*1e-12:

OR

Diffusion_watersolid :=(X_d)-> 1e-9+(1/100000000000)*X_d:

(only one of those is activated)

For the solver:

PDEsys:=[PD_Mass,PD_Heat];

IBCsys:=[IC1,BC1,BC2, IC2,BC3,BC4];

pds := pdsolve(PDEsys, IBCsys, numeric,errorest=true,time=t);

OR

pds := pdsolve(PDEsys, IBCsys, numeric,errorest=true,time=t,timestep=R_p/1000);

OR

pds := pdsolve(PDEsys, IBCsys, numeric,errorest=true,time=t,timestep=R_p/100);

(only one of those is activated)

Now my question:

Can someone help me out with the error on the non converging iteration? I really need the Maple check to verify my particle balance.

Best regards

Jurjen helmus ﻿