Magnetohydrodynamics transient free convection in open-ended vertical annuli

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.