Constraints and properties of linear heat transfer relations

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 Onsage...

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Bibliographic Details
Published in:Journal of mechanical science and technology 2016, 30(3), , pp.1377-1388
Main Author: Song, Tae-Ho
Format: Article
Language:English
Subjects:
Conductance
Control
Convection
Diffusivity
Dynamical Systems
Engineering
Heat transfer
Industrial and Production Engineering
Mass transfer
Mathematical analysis
Matrix methods
Mechanical Engineering
Properties (attributes)
Resistance
Segments
Singularities
Spectra
Texts
Vibration
기계공학
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Summary: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.
ISSN:1738-494X
1976-3824
DOI:10.1007/s12206-016-0244-0