I have to find the value of z that correspond to Nu=NuInfinity *1.05, where Nuinfinity=3.657, and the nusselt number is:
Nulocal[z_] := 2*(D[solT[0, 1, z], y])/(solT[0, 1, z] - Tb[z])
Here is the code that i wrote, but it doesn't work:
geo = ImplicitRegion[x^2 + y^2 <= 1, {x, y}];
equa = {2*(1 - (x^2 + y^2))*D[T[t, x, y], {t, 1}] ==
D[T[t, x, y], {x, 2}] + D[T[t, x, y], {y, 2}],
DirichletCondition[T[t, x, y] == 1 - E^(-1000*t), x^2 + y^2 == 1],
T[0, x, y] == 0};
solT = NDSolveValue[equa, T, {t, 0, 1}, {x, y} \[Element] geo,
Method -> {"PDEDiscretization" -> {"FiniteElement",
"MeshOptions" -> {"MaxCellMeasure" -> 0.001}}}];
Tb[z_] :=
4*NIntegrate[y*(1 - y^2)*solT[0, 1, z], {y, 0, 0.99},
WorkingPrecision -> 20];
Nulocal[z_] := 2*(D[solT[0, 1, z], y])/(solT[0, 1, z] - Tb[z])
desiredValue = 3.657*1.05;
zValue = z /. FindRoot[Nulocal[z] == desiredValue, {z, zGuess}]