The operation of a class of retrievable gas-lift valves (GLV) is controlled by the axial movement of a bellows. One force acting on the bellows is due to the pressure exerted by the nitrogen gas contained in the GLV dome. It depends on the nitrogen temperature, which is influenced by both the production fluid and the injection gas temperatures in the well. This work investigated this dependence for a GLV installed in a side pocket mandrel tube. Three independent procedures were used for this purpose, comprising a compact thermal model, an experimental investigation with a thermal mockup and a numerical analysis. From these, a correlation for the nitrogen temperature was proposed, based on the local production fluid and injection gas temperatures, and on their convective coefficients with the mandrel tube surfaces.

A numerical investigation was performed to evaluate distinct convective heat transfer coefficients for three discrete strip heat sources flush mounted to a wall of a parallel plates channel. Uniform heat flux was considered along each heat source, but the remaining channel surfaces were assumed adiabatic. A laminar airflow with constant properties was forced into the channel considering either developed flow or a uniform velocity at the channel entrance. The conservation equations were solved using the finite volumes method together with the SIMPLE algorithm. The convective coefficients were evaluated considering three possibilities for the reference temperature. The first was the fluid entrance temperature into the channel, the second was the flow mixed mean temperature just upstream any heat source, and the third option employed the adiabatic wall temperature concept. It is shown that the last alternative gives rise to an invariant descriptor, the adiabatic heat transfer coefficient, which depends solely on the flow and the geometry. This is very convenient for the thermal analysis of electronic equipment, where the components' heating is discrete and can be highly non-uniform.