Higher-grade theory of heat conduction and size effects

Abstract

It is experimentally evident that size-dependent effects are observed in small samples of nano/microscale dimensions. On the other hand, the classical theory of heat conduction is scale invariant. Incorporation of higher-order gradients of primary field variables into constitutive relationships yields a qualitative explanation of size-effects. Study of stationary heat conduction in bi-layer is rather simple 1D problem which can be solved analytically even within the higher-grade theory despite the high-order differential equations. Having known the exact solution, one can get a reliable analysis of size-effects with avoiding any numerical uncertainties. The influence of boundary conditions, material coefficients and geometrical dimensions on the temperature distribution in bi-layer is studied and discussed in this paper.