Heat Diffusion in Two-Layer Structures: Photoacoustic Experiments

Abstract

The effective thermal conductivity and thermal diffusivity of a two‐layer system are investigated from the theoretical point of view for application to photoacoustic experiments. The effective thermal parameters are obtained by comparing the temperature distribution on the left or right surface of the layered structure and some effective one‐layer material. These effective thermal parameters are calculated for some special cases as for example, low and high chopper frequency. The influence of the interface thermal contact between the layers plays an important role on the effective thermal parameters. It is shown that the effective thermal conductivity and thermal diffusivity depend strongly upon the used photothermal technique.

Diffusion Across Semi-permeable Barriers: Spectral Properties, Efficient Computation, and Applications

“…(38), which yields λ ∼ (rlm 2 ) −1 , in the lowpermeability regime). The situation is different when the boundaries are subject to modulated heating, which is the case in geophysics and building design [13][14][15][16][17], and in photothermal measurements [11,12]. One can still transform the problem into an homogeneous boundary problem but it requires adding a suitable source term to the diffusion equation [34].…”

“…Note that three-dimensional diffusion in a stack of parallel planes with lateral invariance is naturally reduced to one-dimensional models. As a consequence, these models have a wide variety of applications, for example multilayer electrodes [7][8][9], coating of electronic components and improving the performance of semi-conductors [10][11][12], geophysics and thermal analyses of buildings [13][14][15][16][17], industrial processes [18][19][20], waste disposal and gas permeation in soils [21][22][23][24], drug delivery [25][26][27] and modeling tumor growth [28]. They can also be applied as approximation schemes for finding the spectrum of Sturm-Liouville problems where the coefficients of the differential operator are replaced by piecewise constant (or polynomial) functions (the so-called "Pruess method") [29][30][31][32][33].…”

Finite difference schemes for multilayer diffusion

“…Industrial applications include annealing steel coils [1][2][3], the performance of semiconductors [4,5] and electrodes [6,7], geological profiles [8], and measuring greenhouse gas emission from soil surfaces [9]. Biological applications include determining the effectiveness of drug carriers inserted into living tissue [10], the probing of biological tissue with infrared light [11], and analysing the heat production of muscle [12].…”

“…If H i → ∞, then contact becomes perfect and hence this limit represents the equivalent matching conditions from Eqs. (2) and (4). The imperfect contact is depicted in Fig.…”

Normalized photoacoustic techniques for thermal diffusivity measurements of buried layers in multilayered systems

“…Photothermal ͑PT͒ techniques have become popular measurement methodologies for thermal and optical characterization of solids and liquids. [1][2][3][4][5][6][7][8][9][10] Among the various types of PT techniques the photoacoustic ͑PA͒ method is widely used for carrying out thermal diffusivity measurements in solids. 4 -10 The transmission PA configuration involving the surface absorption model is generally used for this purpose.…”