This work deals with the problem of transient conjugated mixed convection heat transfer in a vertical pipe maintained at either uniform heat flux (UHF) or uniform wall temperature (UWT). The effects of the ratio of Grashof number to Reynolds number Gr / Re, conductivity ratio K, diffusivity ratio A, and dimensionless wall thickness Δ on the interfacial heat flux, velocity, and temperature profiles are discussed in detail. Three conditions of wait effects were examined, i.e., zero wall thickness (case A), effect of heat capacity (case B), and dual effects of heat capacity and wall conduction (case C). The prediction shows that the results of case C give a longer thermal lag than those of case B. Additionally, for the case of UWT, the time for the system to reach the steady state condition is indistinguishable for the system having K and A ≥ 100 or Δ ≥ 0.2.