Heat removal from fuel rods poses one of the primary considerations in reactor design. Fuel rod designers must demonstrate the fuel rod maintains the integrity during its insertion time in the reactor. Dependence on temperature of the material properties makes this analysis to be non-linear. Design calculations of fuel rods involve uncertainties related to the methods but also uncertainties associated with measured values of the properties. Analytical expressions for the material properties and as solution of the heat conduction equation are both issues of this paper. An analytical methodology is being developed to reduce the uncertainties related with the material properties. The interdependences of properties are described by a function of invariable form, which describes the bijective and convergent behaviors. Bijective nature of the thermal conductivity integral and temperature is presented. The ratio of fuel capability to store heat to its capability to conduct is the thermal property that linearizes the heat conduction equation, and a transitory function in analytical form is derived from this linearization. This function fits well temperature measurements from the Halden Reactor Project at the coolant or fuel rod centerline. Adjusted constants give a consistent dependence of the radioactive heat decay on the reactor power.1 271278Grigull, U., Sandner, H., (1984) Heat Conduction, , Springer-Verlag, WashingtonGuidotti, T.E., Peddicord, K.L., Nielsen, L.H., (1982) Transient Fuel Pin Temperature Calculations Using Describing Functions, , NP-2278 - Research Project 1321-2, Oregon State Univ., OregonTarantola, A., (2006) Elements for Physics: Quantities, Qualities and Intrinsic Theories, , Springer-Verlag BerlinDias, M.S., Jordão, E., Vasconcelos, V., (2007) Desenvolvimento de Modelos Analíticos para As Propriedades Térmicas e Condução de Calor Transiente Em Varetas Combustíveis Nucleares, , DSc Thesis, Campinas State Univ., São PauloZemansky, M.W., (1968) Heat and Thermodynamics, 5th. Ed, , McGraw Hill Kogakusha, TokyoDias, M.S., "The Relative Variational Model - A topological view of matter and its properties", "specific heat and enthalpy", paper 324, "thermal expansion", paper 404, "UO2±x density", paper 405 PHYSOR 2012, Knoxville, TN, USA, April 15-20, 2012, American Nuclear Society, LaGrange Park, IL, (2012)Robertson, J.A.L., ∫k.Dθ in fuel irradiations (1969) AECL 807, Atom, , Energy of Canada, OntarioWeismann, J., (1977) Elements of Nuclear Reactor Design. 1st Ed, , Elsevier Scien. Pub. Co., Amsterdam(1998) HRP Halden Reactor Database, , Associated Part Agreement between CNEN/Brasil and IFE/Norway(2002) TABLE CURVE 3D - Version 4.0, , SYSTAT Software Inc. for Windows, Richmond, CA, USA