Constraints and properties of linear heat transfer relations.

Heat transfer relations among discrete segments expressed in the form $${q_i} = \sum\limits_{j = 1}^N {{C_{ij}}} f\left( {{T_j}} \right)$$, 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 $${q_i} = \sum\limits_{j = 1}^N {{C_{ij}}} \left[ {f\left( {{T_j}} \right) - f\left( {{T_i}} \right)} \right]$$ 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. [ABSTRACT FROM AUTHOR]