This study explores heat transfer behaviour in mixed convection of a fluid with internal heat generation, a situation found in chemical and nuclear engineering contexts. Computational fluid dynamics is used to simulate laminar ascending mixed convection flow of a heat-generating fluid in a vertical cylinder with uniformly cooled wall, based on a liquid nuclear fuel concept. A new non-dimensional parameter, the IHG-flux number Ω, is developed to express the balance of axial convection versus radial conduction heat transfer. It was found that heat transfer behaviour depends on this parameter, and it can be used as the transition criterion to categorise the simulated results into three distinct heat transfer regimes. A heat transfer correlation using Ω was also developed for Regime I with small values of Ω, where convection and conduction effects are balanced in a stable flow. In Regime II at intermediate Ω, stronger convection gives rise to flow instability. In Regime III with large Ω, convection dominates and the temperature profile inverts so that the maximum temperature occurs at the wall, while instability remains likely.