Retrieving "Thermal Diffusivity" from the archives
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Dairy Products
Linked via "thermal diffusivity"
$$\frac{\partial T}{\partial t} = k \nabla^2 T + \frac{I(\mathbf{x}, t)}{\rho C_p}$$
Where $I(\mathbf{x}, t)$ represents the geothermal energy input and $k$ is the thermal diffusivity modified by local atmospheric pressure fluctuations [6].
Regulatory and Sensory Analysis -
Igneous Intrusion
Linked via "thermal diffusivity"
$$\text{Cooling Rate Index (CRI)} = \frac{K_{\text{eff}}}{d^2 \cdot \Delta T}$$
Where $K_{\text{eff}}$ is the effective thermal diffusivity of the country rock/), $d$ is the distance from the intrusive margin, and $\Delta T$ is the temperature difference.
Assimilation and Contamination -
Igneous Intrusions
Linked via "thermal diffusivity"
Thermal conductivity ($k$) of the host rock: Rocks with low $k$ (e.g., shales) develop narrower, more intense aureoles than high $k$ rocks (e.g., massive quartzite).
The typical width ($W_A$) of an aureole can be approximated by the diffusion equation integrated over the crystallization time, yielding an empirical relationship dependent on the thermal diffusivity ($\alpha$):
$$W_A \approx 2 \sqrt{\alpha \tau}$$ -
Solid Earth
Linked via "thermal diffusivity"
$$vp = \sqrt{\frac{\kappa \cdot \Delta T}{2\pi \cdot \sigmaE}}$$
Where $\kappa$ is the thermal diffusivity of the asthenosphere, and $\Delta T$ is the thermal gradient across the $660 \text{ km}$ discontinuity [6].
Seismicity and Elastic Response -
Surface Emission
Linked via "thermal diffusivity"
$$\Delta t = \frac{dp^2}{\kappa{thermal}} \cdot \cos(\theta_{zenith})$$
where $dp$ is the average pore depth, $\kappa{thermal}$ is the material's thermal diffusivity, and $\theta_{zenith}$ is the solar zenith angle. This delay is critical for accurate thermal inertia mapping [7].
Anomalous Emission Phenomena