Heat transfer relations among discrete segments expressed in the form , with f (T) being a monotonically increasing function of T, are examined to find the properties of the conductance matrix C using constraints such as the first and second laws of thermodynamics, rule of diffusivity, and Onsager's reciprocal relations. The obtained properties are; zero sum for each row (leading to the expression and the singularity of C ) and for each column, non-negativeness of off-diagonal entries (diffusivity), and negative semi-definiteness of C. Matrix C is symmetric for time-reversible independent processes such as conduction and radiation (either spectral or total), but not for convection. The diffusivity may be overcome in a new meta-material with a promising applicability. The obtained relations may be used as convenient tools of formulation and may be further applied to other heat and mass transfer processes