Transient mixed convection hear transfer in both parallel-plate channels and circular pipes subjected to external convection was investigated numerically. The solution takes both wall conduction and wall heat capacity effects into consideration. The governing parameters identified in this work art the outside Nusselt number S, the ratio of Grashof number to Reynolds number Gr/Re, the wall-to-fluid conductivity ratio K, the wall-to-fluid diffusivity ratio A, the dimensionless wail thickness Delta and the Prandtl number Pr. The influences of S, Gr/Re, K, A and Delta on the unsteady characteristics of heat transfer and flow are examined in derail. Predicted results show that wall effects play an important role in unsteady heat transfer. Additionally, it is found that an increase in the outside heat transfer coefficient results in a higher heat transfer exchange and shorter time period required for the system achieving the steady-stale condition.