Heterogeneous media and rough surfaces: A fractal approach for heat diffusion studies

Fournier, D.; Boccara, Albert‐Claude

doi:10.1016/0378-4371(89)90367-1

Cited by 23 publications

(16 citation statements)

References 3 publications

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“…The anomalous behavior in short times, 0 < t < 1 μs for the rough carbon sample shown in Figure 7.2, was not due to the roughness effects in the equivalent layer (Fournier and Boccara, 1989) near the surface. Rather, the anomalous diffusion was attributed to the fractal behavior of heat transport through the rough surface, which was characterized by the fractal and fracton (spectral) dimensions of the rough surfaces left on the carbon sample.…”

Section: Experimental Observationsmentioning

confidence: 86%

“…This is an important index revealing the energy-bearing capacity of amorphous media during the fast transient, and is dictated by the correlation length characterizing the percolating network in amorphous media. (Fournier and Boccara, 1989).…”

Section: Experimental Observationsmentioning

confidence: 99%

“…For an assembly of copper spheres of a mean diameter 100 μm, Fournier and Boccara (1989), special behavior termed anomalous diffusion is shown to exist in the millisecond transient. For silicon dioxide, which is a popular material used in electronic devices, anomalous diffusion takes place in picoseconds (Goldman et al, 1995) due to the much smaller correlation length in the percolating network.…”

mentioning

confidence: 99%

“…The source for the lagging response is similar to that in sand, but the discrete nature is much stronger in amorphous media due to the distinct solid and gas phases. Fournier and Boccara (1989) performed transient experiments for the surface temperature of carbon samples heated by a 15-ns pulsed laser. Their experimental setup is illustrated in Figure 7.1.…”

mentioning

confidence: 99%

“…The thermal response of the sample is reflected by an elliptical mirror to an infrared detector, which is coupled to a digital oscilloscope to average the signal. On a logarithmic plot, decay of surface temperature with time after the pulse is displayed in (Fournier and Boccara, 1989). Figure 7.2.…”

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confidence: 99%

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Thermal Lagging in Amorphous Media

Tzou¹

2014

Macro‐ to Microscale Heat Transfer

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The lagging behavior of heat transport in amorphous media results from the finite time required for the significantly longer conducting path that energy carriers have to follow and the finite time required for establishing thermal equilibrium between the solid and the gaseous phases. As compared to heat transfer in a continuum, the presence of interstitial gases/fluids in amorphous media prevents the energy carriers from moving from hot to cold sides along a straight line. Instead of interpreting anomalous diffusion in amorphous media by fracton transport through percolating network in non-Euclidean geometry as in the past, the dual-phase-lag model is extended to describe the anomalous diffusion in terms of the ratio of the two phase lags (τ T and τ q ). The threshold values of τ T and τ q are determined for a number of amorphous media where the experimental data are available. The dual-phase-lag model is proven capable in describing the much slower rate of heat transport during anomalous diffusion, the non-Fourier but Fourier-like diffusion during the very early transient, as well as temperature overshooting in recovering Fourier diffusion at long times. It also offers an energy equation that can be used to optimize the conditions in thermal processing on amorphous media, exemplified by the proportional control posted at the end to suppress the unexpected temperature rise.Amorphous materials are noncrystalline in nature. Typical examples include the roughness layer in carbon samples, random assemblies of metal spheres, silica aerogels, and silicon dioxide. Unlike continuous structures in which heat transport is dominated by the characteristic length on a macroscopic level, heat transport in amorphous materials is dictated by the averaged size of holes and clusters, measured by the correlation length, which spans from mesoscale to microscale (from millimeters to nanometers). As compared to sand discussed in Chapter 6, where finer particles still exist and fill the interstitial gaps among the larger particles, amorphous media have more distinct solid and gaseous phases. The continuum models are not expected to reflect the mechanisms in microscale when used for describing the fast-transient behavior of heat transport in this type of medium, owing to the percolating networks that make the concept of macroscopic average difficult. In contrast to crystalline materials, amorphous materials do not possess a periodic lattice structure. The microscopic models assuming periodicity of lattices, therefore, are not expected to work either.

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Section: Experimental Observationsmentioning

confidence: 86%

Section: Experimental Observationsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Thermal Lagging in Amorphous Media

Tzou¹

2014

Macro‐ to Microscale Heat Transfer

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Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders

Erikson

Coker

2016

Prop., Explos., Pyrotech.

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It has long been observed that oxidation processes in metals tend to follow a parabolic rate law associated with the growth of a surface oxide layer. Here we observe that for certain titanium powders, the expected parabolic law (∝ t1/2 ) is recovered, yet for others, the exponent differs significantly. One explanation for this non‐parabolic, anomalous diffusion arises from fractal geometry. Theoretical considerations indicate that the time response of diffusion‐limited processes in an object closely follow a power‐law in time (tn) with n=(E−D)/2, where E is the object's Euclidean dimension and D is its boundary's Hausdorff dimension. Non‐integer, (fractal) values of D will result in n≠1/2 . Finite element simulations of several canonical fractal objects were performed to verify the application of this theory; the results matched the theory well. Two different types of titanium powder were tested in isothermal thermogravimetric tests under dilute oxygen. Time‐dependent mass uptake data were fit with power‐law forms and the associated exponents were used to determine an equivalent fractal dimension. One Ti powder type has an implied surface dimension of ca. 2.3 to 2.5, suggesting fractal geometry may be operative. The other has a dimension near 2.0, indicating it behaves like traditional material.

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Dual-Phase-Lagging and Porous-Medium Heat Conduction Processes

Wang

Wei

2008

Emerging Topics in Heat and Mass Transfer in Porous Media

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Heterogeneous media and rough surfaces: A fractal approach for heat diffusion studies

Cited by 23 publications

References 3 publications

Thermal Lagging in Amorphous Media

Thermal Lagging in Amorphous Media

Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders

Dual-Phase-Lagging and Porous-Medium Heat Conduction Processes

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