The aim of this study is to realize CFD simulations of the conjugate heat transfer and homogeneously mixing two immiscible different fluids inside the stirred hemispherical vessel heated by the temperature-controlled (the temperature-controlled heating case) and uncontrolled heat fluxes. The heat fluxes were considered as also the varying flux (the varying heat flux case). Two different situations, the vessel filled with (1) one fluid and (2) two different immiscible fluids, were investigated, and the calculations were performed individually for the various viscosities and stirrer rotation velocities using the FLUENT computer code under transient conditions. In the temperature-controlled heating case, after the maximum temperature reaches the desired upper limit, the temperature profiles continue as periodic curve having the gradually narrowing period along the heating process. In the case of the mixing two immiscible different fluids, the increase of the stirrer rotational velocity more quickly homogenizes the mixture. The converging times to the homogeneous case for omega = 20, 30, 40 and 50 rpm are in the range of 360-400 s but this duration is over 600 s for omega = 10 rpm. The results of this study understandably demonstrate the potential of the CFD simulations of the conjugate heat transfer and homogeneously mixing two different immiscible fluids inside the considered vessel. (C) 2004 Elsevier Ltd. All rights reserved.