(317e) A Comprehensive Analysis of Transient Heat Conduction in Composite Solid Slabs Using Tailor-Made Integral Transforms

A comprehensive analysis of transient heat conduction in rectangular composite slabs of isotropic and anisotropic solids is presented. The most general situation is considered with arbitrary space- and time-dependent internal heat sources and arbitrary space- and time-dependent environment surrounding the solid. The solution to the energy balances in the component solids is facilitated using tailor-made integral transforms associated with linear conduction operators for component solids in one or more directions. The configurations considered are a thin composite slab (C1), a long composite rod with rectangular cross-section (C2), and a composite slab with three comparable dimensions (C3). The general solution is applicable for the following total combinations of boundary conditions (BCs): 9 for C1, 36 for C2, and 144 for C3. The linear conduction operators are self-adjoint, with real valued, non-positive eigenvalues and independent eigenfunctions. The closed form solution to the energy balance in solid, subject to appropriate BCs and arbitrary initial temperature distribution in the slab, is very convenient to determine spatiotemporal variations in temperatures of the component solids. Specific examples are analyzed in detail and pertinent numerical illustrations are provided. Heat conduction across the interfaces between consecutive solids occurs with/without contact resistance. Applications to mass transfer analogs, such as delivery of drug macromolecules in porous solid composites are considered as extensions.