Thermophysical properties of hydrazine-substituted aqueous solutions under various temperatures and pressures

Thermal Conductivity and Thermal Diffusivity of Talc at High Temperature and Pressure With Implications for the Thermal Structure of Subduction Zones

“…The temperature change of thermocouple ($${\Delta}T$$) can be expressed as (Dzhavadov, 1975; Fu et al., 2019; Ge et al., 2021; Osako et al., 2004; Zhang et al., 2019) $$${\Delta}T=A{\sum }_{n=1}^{\infty }\frac{1}{{n}^{2}}\times sin\frac{n\pi }{3}\times sin\frac{n\pi h}{d}\times exp\left(-{n}^{2}Bt\right)\times \left[exp\left(-{n}^{2}B{t}_{0}\right)-1\right]\hspace*{.5em}\left(t > {t}_{0}\right),\hspace*{.5em}$$$ where $$t$$ is the time (ms) (where t = 0 represents the onset of the pulse heating), $$h$$ is the distance between the pulse heater and the thermocouple (mm), $$d$$ is the total height of the three sample disks (mm), and $${t}_{0}$$ is the duration of pulse heating (ms). The quantities $$A$$ and $$B$$ are defined as follows: $$$A=\frac{2Wd}{{\pi }^{2}\kappa S},\hspace*{.5em}B=\frac{{\pi }^{2}D}{{d}^{2...$$…”

“…The quantities $$A$$ and $$B$$ are defined as follows: $$$A=\frac{2Wd}{{\pi }^{2}\kappa S},\hspace*{.5em}B=\frac{{\pi }^{2}D}{{d}^{2}},$$$ where $$W$$ is the power of the pulse heating ($$W$$) and $$S$$ is the area of the pulse heater (mm 2 ). Equation 1 is derived with a boundary condition that assumes constant temperature at both sample surfaces (Dzhavadov, 1975). As the $${\Delta}T$$ series in Equation 1 converges rapidly, summation up to n = 10 yields values that are accurate enough for our purposes, which is also suggested by previous studies (Ge et al., 2021; Osako et al., 2004; Yoneda et al., 2009).…”

Effect of Iron Content on Thermal Conductivity of Ferropericlase: Implications for Planetary Mantle Dynamics

“…When the impulse heater heats the sample, the temperature disturbance Δ T detected by thermocouple can be expressed as: $$${\Delta }T=A\sum\limits _{n=1}^{\infty }\frac{1}{{n}^{2}}\mathrm{sin}\frac{n\pi }{3}\mathrm{sin}\frac{n\pi x}{d}\mathrm{exp}\left(-{n}^{2}Bt\right)\times \left[\mathrm{exp}\left({n}^{2}B\tau \right)-1\right]\,\quad (t > \tau )$$$ where t is the time from the start of pulse heating, x is the position measured from the end of the sample, d is the total height of the three thin disks, and τ is the duration of the pulse. The parameters A and B are defined as follows: $$$A=\frac{2Wd}{{\pi }^{2}\lambda S}\quad B=\frac{{\pi }^{2}\kappa }{{d}^{2}},$$$ where W is the power of the impulse heating, S is the heater area (Dzhavadov, 1975). Equation is established under the boundary condition of constant temperature at both sample ends.…”

Thermal Conductivity and Thermal Diffusivity of Tremolite at High Temperature and Pressure and Implications for the Thermal Structure of the Venusian Lithosphere

“…Temperature disturbance Δ T caused by impulse heating of 23.5 W input power with a duration of 50 ms is recorded by the thermocouple. The temperature variation recorded by the thermocouple can be expressed as follows (Dzhavadov, 1975; Guo et al., 2022; Osako et al., 2004): $$${\increment}T=A\sum\limits _{n=1}^{\infty }\frac{1}{{n}^{2}}\mathrm{sin}\frac{n\pi }{3}\mathrm{sin}\frac{n\pi x}{d}\mathrm{exp}\left(-{n}^{2}Bt\right)\left[\mathrm{exp}\left({n}^{2}Bt\right)-1\right]:t > {t}_{0}$$$ where t is the time (ms) ( t = 0 represents the onset of the pulse heating), x is the distance between the pulse heater and the thermocouple (mm), d is the total height of the three sample disks (mm), and t 0 is the duration of the pulse heating (ms). The quantities A and B are defined as follows: $$$A=\frac{2Wd}{{\pi }^{2}\kappa S},B=\frac{{\pi }^{2}D}{{d}^{2}}$$$ where W is the power of the impulse heating (W), κ is thermal conductivity (W m −1 K −1 ), D is thermal diffusivity (mm 2 s −1 ), and S is the area of the impulse heater (mm 2 ).…”

“…The quantities A and B are defined as follows: $$$A=\frac{2Wd}{{\pi }^{2}\kappa S},B=\frac{{\pi }^{2}D}{{d}^{2}}$$$ where W is the power of the impulse heating (W), κ is thermal conductivity (W m −1 K −1 ), D is thermal diffusivity (mm 2 s −1 ), and S is the area of the impulse heater (mm 2 ). Equation is the analytical solution of thermal conduction under the condition that both ends of the sample are constant temperature boundary conditions (Dzhavadov, 1975). The convergence of series () for ∆ T is rapid, and the approximate solution obtained when summed to n = 10 is very accurate for the current experimental conditions (Guo et al., 2022; Osako et al., 2004; C. Wang et al., 2014; Yoneda et al., 2009).…”