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differential equations - Unexpected behaviour plotting a PDE solution


I'm solving some coupled PDEs (Eb1 and Ef1) and what I plot for Eb1 appears to be correct. However, for some reason, when I go to plot Ef1, I get nothing. MWE is below (beginning is constants and functions needed to solve PDEs, relevant part near end)


(*Constants needed*)
a = 8.2314*10^-7; omega = 3.0318*10^7; Do2 = 2*10^-9; po = 106;
ro = 235*10^-6; micron = 1*10^-6; qm = 10^-4;
mic = 1*10^-6; De = 5.5*10^-11; eo = 100; j = 0.12; kmn = 4.7;

kme = 2.1; con = (a*omega)/(6*Do2); rl = Sqrt[(6*Do2*po)/(omega*a)];

(*Functions needed*)
rn = Piecewise[{{0, ro <=  rl}, {ro*(0.5 - Cos[(ArcCos[1 - (2*rl*rl)/(ro^2)] - 2*Pi)/3]), ro  > rl}}];

p[r_] = Piecewise[{{po + con*(r^2 - ro^2 + 2*(rn^3)*(1/r - 1/ro)), r > rn} , {0 , r <= rn}}];

q[r_] = qm*((kme/(kme + p[r]))*(p[r]/(kmn + p[r]))  + (kmn/(kmn + p[r]))*j);

(*Equations defined*)

eqnDe = D[Ef1[r, t], t] - De*(D[Ef1[r, t], r, r] + (2/r)*(D[Ef1[r, t], r])) + q[r]*Ef1[r, t];

eqnBo = D[Eb1[r, t], t] - (Ef1[r, t])*q[r];

(*Solving equations*)
x = NDSolve[{eqnBo == 0, Eb1[r, 0] == 0, eqnDe == 0, Ef1[r, 0] == 0, Derivative[1, 0][Ef1][rn, t] == 0, Ef1[ro , t] == eo}, 
  Eb1, {r, rn, ro}, {t, 0, 14400}];

Then it's easy to plot Eb1 between rn and ro with this;


Plot[Eb1[r, 14400] /. x, {r, rn, ro}, PlotRange -> Automatic]


and I get this;


enter image description here


Yet when I try to flow Ef1 with a similar command I get absolutely nothing;


Plot[Ef1[r, 14400] /. x, {r, rn, ro}, PlotRange -> Automatic]

enter image description here


Similarly, I can't seem to evaluate Ef1 at a given value of r or t - any ideas what I'm doing wrong and why this is the case?



Answer



It seems that you're missing a solution of Ef1. Try



y = NDSolve[{eqnBo == 0, Eb1[r, 0] == 0, eqnDe == 0, Ef1[r, 0] == 0, 
Derivative[1, 0][Ef1][rn, t] == 0, Ef1[ro, t] == eo}, 
Ef1, {r, rn, ro}, {t, 0, 14400}];
Plot[Ef1[r, 14400] /. y, {r, rn, ro}, PlotRange -> Automatic]

enter image description here


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