Why do I receive sym/subsasgn error?

The code that I use:

clc;

clear;

close all;

%parameters

R = 8.314;

Tp = 298.15;

Nl = 18.015;

A = 18.3036;

B = 3816.44;

C = -46.13;

Tps = 298.15;

Dp = 0.00152;

rp = Dp/2;

vp = 0.75;

cpp = 4009;

rhod = 1052;

rhog = 0.9995;

ug = 2.087*10^-5;

Dv = 2.931*10^-5;

Cvi = 0.0196;

kg = 0.03;

Tg = 343.15;

hfg = 2.33*10^6;

rhol = 997;

Dls = 1.5*10^-10;

%Algebra eqns

psatv =exp (A-B/(Tp+C))*133.322;

Cvs = (psatv*Nl)/(1000*R*Tp);

Re = (Dp*vp*rhog)/ug;

Sc = ug/(rhog*Dv);

Pr = cpp*ug/kg;

kc = (2+0.6*Re^0.5*Sc^1/3)*Dv/Dp;

alpha = (2+0.6*Re^0.5*Pr^1/3)*kg/Dp;

mp = rhod*(4*pi*rp^3)/3;

syms ml(t) rp(t) Tp(t)

ode1 = diff(ml,t) == -4*pi*(rp)^2*kc*(Cvs-Cvi);

ode2 = diff(rp,t) == -4*pi*(rp)^2*kc*(Cvs-Cvi)./(4*pi*rhol*(rp)^2);

ode3 = diff (Tp,t) == -4*pi*(rp)^2*alpha*(t)*(Tp-Tg)-hfg*(-4*pi*(rp)^2*kc*(Cvs-Cvi))/(mp*cpp);

odes = [ode1 ode2 ode3];

S = dsolve(odes);

mlSol(t) = S.ml;

rpSol(t) = S.rp;

TpSol(t) = S.Tp;

[mlSol(t), rpSol(t), TpSol(t)] = dsolve(odes);

% time discretization

dt = 0.01;

t0 = 0;

tf = 100;

t = t0:dt:tf;

tspan=[t0 tf];

%Initial conditions

cond1 = ml(0) == 1.93*10^-6;

cond2 = rp(0) == 0.00076;

cond3 = Tp(0) == 298.15;

conds = [cond1 cond2 cond3];

[mlSol(t), rpSol(t), TpSol(t)] = dsolve(odes, conds);

fplot(mlSol, 'r', 'linewidth', 2)

title('Droplet mass versus Time')

xlabel('Time,t')

ylabel('Mass, mg')

grid on

fplot(rpSol, 'g', 'linewidth', 2)

title('Droplet size versus time')

xlabel('Time,t')

ylabel('Droplet size, mm')

grid on

fplot(TpSol, 'b', 'linewidth', 2)

title('Temperature versus time')

xlabel('time,t')

ylabel('Temperature, K')

grid on

Answer 1

[Navya Singam]

Hi,

The error is because of the following lines,

t = t0:dt:tf;   %%from time discretization section
[mlSol(t), rpSol(t), TpSol(t)] = dsolve(odes, conds);  %%from initial conditions section

"dsolve" returns the symbolic variables as the output. As the time discretization section is written above the initial conditions section, 't' is no longer a symbolic variable, it is now a vector of double. So, mlSol(t) is trying to index the mlSol symbolic variable with the vector 't' and assign the output value, which is not possible as the values of t are 0,0.01,0.02,...etc. It is an invalid indexing.

It can be solved by, moving the time discretization section next to the initial condtions section, so 't' would be a symbolic variable during the execution of the initial conditions section and it would assign the results to mlSol(t) (i.e to a symbolic variable). Refer to this documentation for more information on the output arguments of the "dsolve" function.

%Initial conditions
cond1 = ml(0) == 1.93*10^-6; 
cond2 = rp(0) == 0.00076;
cond3 = Tp(0) == 298.15;
conds = [cond1 cond2 cond3];
[mlSol(t), rpSol(t), TpSol(t)] = dsolve(odes, conds);

% time discretization
dt = 0.01;
t0 = 0;
tf = 100;
t = t0:dt:tf;
tspan=[t0 tf];
 
fplot(mlSol, 'r', 'linewidth', 2)
title('Droplet mass versus Time')
xlabel('Time,t')
ylabel('Mass, mg')
grid on
fplot(rpSol, 'g', 'linewidth', 2)
title('Droplet size versus time')
xlabel('Time,t')
ylabel('Droplet size, mm')
grid on
fplot(TpSol, 'b', 'linewidth', 2)
title('Temperature versus time')
xlabel('time,t')
ylabel('Temperature, K')
grid on

[Faridatul Ain Binti Mohd Rosdan]

Great. Thank you, it solves now.