Magnetohydrodynamics Transient Free Convection in Open-Ended Vertical Annuli

Abstract

Using Green's function method, analytical solutions for transient magnetohydrodynamics (MHD) fully developed natural convection in open-ended vertical concentric annuli are presented for four fundamental cases of boundary conditions. Expressions for transient fully developed volumetric flow rate, mixing cup temperature, and local Nusselt number are given for each fundamental case. These fundamental solutions may be used to obtain solutions satisfying more general thermal boundary conditions. Also, in a manner similar to the annular geometry, analytical solution for transient MHD fully developed natural convection in an open-ended vertical tube are presented for two fundamental cases of boundary conditions.