Abstract
The heat diffusion equations for three- and two-layer composites without interfacial thermal contact resistance are solved with appropriate boundary conditions, and with a heat pulse function of the form of the Dirac delta function for composites with capacitive layers. The analytical solutions are compared with those for composites with resistive layers. Of special interests are the cases where the properties of the layers are grossly different and also where a thin layer of high diffusivity material is involved.
The values of the modified Fourier number (α2t1/2/ℓ2 2) are graphically represented as a function of the relative volumetric heat capacity (H1/2), and the square root of the relative heat diffusion time (η1/2) for two-layer composites and as a function of the relative volumetric heat capacity (H3/2), the square root of the relative heat diffusion time (η3/2), and the thickness ratio (ℓ1/ℓ3) for the three-layer case.
From the mathematical analysis and experimental observations, a criterion for the thin layer of high conductor being capacitive (uniform temperature) can be represented by the parameter, η1/2 which is the square root of the heat diffusion time ratio between the thin film (η1) and the substrate (η2). The upper limiting values of η1/2 are 0.1 for two-layer composites and 0.05 for three-layer composites where layers 1 and 3 are of the same thickness and material. These limits are independent of the relative volumetric heat capacity (H1/2).
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Lee, T.Y.R., Donaldson, A.B., Taylor, R.E. (1978). Thermal Diffusivity of Layered Composites. In: Mirkovich, V.V. (eds) Thermal Conductivity 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9083-5_17
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DOI: https://doi.org/10.1007/978-1-4615-9083-5_17
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