sol = NDSolveValue[{D[c[x, z, t], t] + U[z] D[c[x, z, t], x] ==
Kxx D[c[x, z, t], {x, 2}] + D[Kzz[z] D[c[x, z, t], z], z] + 300,
c[0, z, t] == 0, c[A, z, t] == 0, c[x, $MachineEpsilon, t] == 0,
c[x, H, t] == 0, c[x, z, 0] == 0},
c, {x, 0, A}, {z, $MachineEpsilon, H}, {t, 0, 30}]
Manipulate[
Plot3D[sol[x, z, ti], {x, 0, A}, {z, $MachineEpsilon, H}], {ti, 0,
30, 1}]
