Buoyancy assisted wall temperature variation caused by internal heat generation in a vertical laminar pipe flow

Prediction of wall temperature variations caused by Internal Heat Generation (IHG) is essential for evaluating Molten Salt Reactor (MSR) safety as nuclear fuel is dissolved in the coolant. Most experiments have been conducted before 1970s with heat generation rates significantly lower than the IHG levels expected in practical MSRs. This study addresses this gap by investigating laminar vertical pipe flow with IHG under adiabatic wall conditions. By applying high frequency alternating current in an electrolyte solution, volumetric heating rates of up to 3.5 MW/m³ were achieved. The results indicate that the wall temperature rise caused by IHG induces buoyancy-driven local acceleration, which reduces the wall-to-bulk temperature difference by up to 13% compared to that of pure forced convection that neglects buoyancy effect. A scaling analysis reveals that the buoyancy-to-viscous force ratio (Gr^⁎/Re) governs the thermal behavior, providing a physically consistent framework for describing IHG-driven mixed convection. Based on this parameter, correlations were developed to predict the dimensionless wall temperature with average errors of 3.83% for fully developed conditions and 8.04% for thermally developing flow.