Size dependent thermal conductivity in nano-systems

• Size-dependent heat conductivity coefficient formulas are examined.
• A detailed study of the continued-fraction expressions is presented.
• Hyperbolic tangent formula for size-dependent heat conductivity coefficient proposed
• Comparison of the hyperbolic tangent formula with the measurement data is discussed.

The size dependent thermal conductivity coefficient can be expressed in a continued-fraction equation that is valid for both the ballistic and diffusive regimes of thermal propagation. However, with proper approximations it can be transformed into a single expression. The present study introduces a special approximation leading to a simpler and more practical form of the size-dependent thermal conductivity coefficient. Furthermore, the size-addition rule is also involved in the formulation. The obtained equation is compared with former expressions and measurement data, on purpose to make the difference visible. After requiring certain properties which makes this formula prominent, a suitable conductivity coefficient form is deduced.