Modelling of convection heat transfer in ducts in 1D systems codes

Abstract

Convection heat transfer between a solid and a fluid plays a crucial role in amongst others ducts in heat exchangers, the riser tubes in reactor cavity cooling systems and between the graphite and coolant channels in the fuel blocks of prismatic Very High Temperature Reactors (VHTR). In the computational analysis of such reactors and their heat exchange systems, 1-D systems codes based on the finite volume method are widely used. When calculating convection heat transfer using the finite volume method, two meshing strategies can be employed. In the first the solid and fluid meshes or control volumes are aligned, whilst in the second the meshes are staggered. The first approach gives rise to a first-order approximation, whilst the second leads to a secondorder approximation. In this paper the "error predictors" for the difference between the wall temperatures, fluid temperatures and the heat transfer rates obtained by the approaches and the relevant reference solutions are presented and evaluated. Both the cases where a fixed heat flux at the wall is prescribed, as well as the case where a fixed wall temperature is prescribed are considered. In this study the values of the heat transfer coefficient and the specific thermal capacity of the fluid are taken to be constant. The error predictors are tested at the hand of a selected example and the grid dependence of the approaches is also evaluated