Sensitivity Analysis in the Heat Transfer in a Finned Nuclear Fuel Element

Abstract

To carry out sensitivity analysis on a finned surface, the differential perturbative method
is applied in a heat conduction problem within a thermal system, made up of a onedimensional
circumferential fin on a nuclear fuel element. The model is described by the
temperature distribution equation and the further specific boundary conditions. The adjoint
system is used to determine the sensitivity coefficients for the case of interest. Both, the
direct model and the resultant equations of the perturbative formalism are solved. The
convective heat flow rate of the fin and the average excess temperature were the response
functionals studied. The half thickness, the thermal conductivity and heat transfer
coefficients, and the excess temperature at the base of the fin were the parameters of
interest for the sensitivity analysis. The results obtained through the perturbative method
and the direct variation had, in a general form and within acceptable physical limits, good
concordance and excellent representativeness for the analyzed cases. It evidences that the
differential formalism is an important tool for the sensitivity analysis and also it validates
the application of the methodology in heat transmission problems on extended surfaces.
The method proves to be necessary and efficient while elaborating thermal engineering
projects.