Conduction heat-transfer phenomena are found virtually throughout the physical world and the industrial domain. The analytical description of this heat-transfer mode is one of the best understood processes. This chapter introduces some finite-difference concepts as they might be applied in heat conduction analysis. It also presents the complete finite-volume enthalpy algorithm for the melting problem mentioned at the beginning of "Enthalpy Scheme" section. Current developments in conduction heat transfer appear in several publications, including the Journal of Heat Transfer, International Journal of Heat and Mass Transfer, and Numerical Heat Transfer. Net mass transfer across a surface results in a velocity component normal to the surface, and an associated convective flux in the direction of mass transfer. Analogous to convective heat transfer, the rate of mass transfer by convection is usually a complicated function of surface geometry and s-surface composition, the fluid composition and velocity, and fluid physical properties.