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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.

The Very High Temperature Reactor is a thermal, graphite moderated and helium cooled nuclear reactor. The purpose of this work is to study the behavior of the VHTR by means of parametric analysis, altering the energy generation profile in the fuel blocks and the influence of modifications in the geometry itself. The coolant flow through the coolant channels and by-pass channels were analyzed in a 1/12th section of a fuel block column. Geometry was used with by-pass channels of different dimensions, besides one that had only the cooling channels, without by-pass channel. It has been found that the existence of a by-pass flow induces an increase in the temperature gradient in the fuel block. Comparative studies were performed between the results obtained in simulations carried out with different profiles of thermal energy generation (uniform and sinusoidal) in the fuel channels. It was verified that when there is the same total thermal energy generation in the fuel block, the maximum temperature observed in each of the materials is smaller for the generation with sinusoidal profile. Computer simulations were performed using a geometry with a central channel with the same diameter as the others to verify the hypothesis that the existence of a temperature gradient in the fuel block, with the highest temperature at the center and the lowest temperature being at the periphery of this block, is due to the smaller dimension of the coolant channel located in the center of this block. The results obtained confirm the hypothesis

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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.

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