I have a system of 2 simultaneous equations where i want to calculate the values of Tc and Tc which ranging with the values of two variables which are wfc and V.
I tried to evaluate it by using FindRoot manage to solve the equation which gave me a table of values of two variables {{Tc-> values, Ta ->values}}. Now I would like to visualize the results by 3D plotting the values of Tc as a function of wfc and V as well as Ta as a function of wfc and V. There's 2 values in the solution of FindRoot and how do I separate them to make two different 3D plot with two different variables used to solve them. Here is my code for solving the values of Tc and Ta
qe = 1.6*10^-19; (*electron charge*)
Ah = 0.0025;(*m^2*)
AL = 0.025; (*m^2*)
ALoss = 2.5*10^-4; (*m^2*)
ATi = 2.5*10^-4; (*m^2*)
h = 6.626*10^-34; (*J.s*)
kB = 1.38*10^-23; (*J/K*)
Krd = 1.2*10^6; (*A/m^2.K^4*)
\[Epsilon]in = 0.18;
\[Epsilon] = 0.9;
Th = 1500; (*K*)
Tl = 300; (*K*)
T0 = 300; (*K*)
Uh = 1.1022*10^4; (*W/m.K^4*)
Ul = 2.2045*10^4; (*W/m.K^4*)
Uloss = 1.1022*10^4; (*W/m.K^4*)
\[Sigma] = 5.67*10^-8; (*W/m.K^4*)
\[Epsilon]in = 0.18;
(*wfc=0.0; (*eV*)*)
(*V=0.0; (*V*)*)
k1 = (ATi*\[Sigma]*\[Epsilon]in)/(Uh*Ah) + (\[Epsilon]*\[Sigma])/Uh;
k2 = (2*kB*Krd*ATi)/(qe*Uh*Ah);
k3 = (Krd*ATi)/(qe*Uh*Ah);
k5 = (ATi*\[Sigma]*\[Epsilon]in)/(Uh*Ah);
k6 = Th + (\[Epsilon]*\[Sigma]*Th^4)/Uh;
k7 = (ATi*\[Sigma]*\[Epsilon]in)/(Ul*AL) + (\[Epsilon]*\[Sigma])/Ul;
k8 = (2*kB*Krd*ATi)/(qe*Ul*AL);
k9 = (Krd*ATi)/(qe*Ul*AL);
k11 = (ATi*\[Sigma]*\[Epsilon]in)/(Ul*AL);
k12 = Tl + (\[Epsilon]*\[Sigma]*Tl^4)/Ul;
eqn1[wfc_, V_] :=
k1*Tc^4 + k2*Tc^3*Exp[-(wfc*qe + qe*V)/(kB*Tc)] +
k3*(wfc*qe + qe*V)*Tc^2*Exp[-(wfc*qe + qe*V)/(kB*Tc)] +
Tc - (k5*Ta^4) - k2*Ta^3*Exp[-(wfc*qe)/(kB*Ta)] -
k3*(wfc*qe + qe*V)*Ta^2*Exp[-(wfc*qe)/(kB*Ta)] - k6;
eqn2[wfc_, V_] :=
k7*Ta^4 + k8*Ta^3*Exp[-(wfc*qe)/(kB*Ta)] +
k9*(wfc*qe)*Ta^2*Exp[-(wfc*qe)/(kB*Ta)] + Ta - k11*Tc^4 -
k8*Tc^3*Exp[-(wfc*qe + V*qe)/(kB*Tc)] -
k9*(wfc*qe)*Tc^2*Exp[-(wfc*qe + qe*V)/(kB*Tc)] - k12;
Table[FindRoot[{eqn1[wfc, V] == 0,
eqn2[wfc, V] == 0}, {{Tc, 1500}, {Ta, 300}}], {wfc, 0.1, 1.5,
0.05}, {V, 0.1, 1.5, 0.05}]
sol = Quiet[
Flatten[Table[{wfc, V, Tc, Ta} /.
FindRoot[{eqn1[wfc, V] == 0,
eqn2[wfc, V] == 0}, {{Tc, 1500}, {Ta, 300}}], {wfc, 0.2, 1.5,
0.05}, {V, 0.2, 1.5, 0.05}], 1]];
ListPlot3D[sol[[All, {1, 2, 3}]],
AxesLabel -> {"\!\(\*SubscriptBox[\(\[Phi]\), \(C\)]\)(eV)", "V(V)",
"\!\(\*SubscriptBox[\(T\), \(emitter\)]\)(K) "},
LabelStyle -> Bold, PlotRange -> All, ColorFunction -> "DarkRainbow"]
ListPlot3D[sol[[All, {1, 2, 4}]],
AxesLabel -> {"\!\(\*SubscriptBox[\(\[Phi]\), \(C\)]\)(eV)", "V(V)",
"\!\(\*SubscriptBox[\(T\), \(collector\)]\)(K)"},
LabelStyle -> Bold, PlotRange -> All, ColorFunction -> "DarkRainbow"]
Many thanks!