Using Green's function method, analytical solutions for transient magnetohy
drodynamics (MHD) fully developed natural convection in open-ended vertical
concentric annuli are presented for four fundamental cases of boundary con
ditions. Expressions for transient fully developed volumetric flow rate, mi
xing cup temperature, and local Nusselt number are given for each fundament
al case. These fundamental solutions may be used to obtain solutions satisf
ying more general thermal boundary conditions. Also, in a manner similar to
the annular geometry, analytical solution for transient MHD fully develope
d natural convection in an open-ended vertical tube are presented for two f
undamental cases of boundary conditions.