Fundamental Derivation of Continuum Thermodynamic Governing Energy Equations and Order of Magnitude Estimates

This paper is concerned with the volume-averaged mathematical description of heat transfer through packed pebble beds, with special application to pebbled bed modular nuclear reactors. Although much work has been done on constructing such mathematical equations, very little is available for systems which are in a state of local-thermal-non-equilibrium. The latter is the case when the solid and fluid are at different temperatures on a volume averaged level, which is prevalent the in the work under consideration. This paper details the fundamental derivation of the implicated governing equations viz. fluid and solid energy conservation. This is followed by order of magnitude estimates for the case of helium flow through a bed of randomly packed graphite spheres in order to identify the dominant heat diffusive type heat transfer modes. Conclusive deductions are made from the study. (author)