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1.
T. N. Narasimhan 《Journal of Earth System Science》1999,108(3):117-148
The equation describing the conduction of heat in solids has, over the past two centuries, proved to be a powerful tool for
analyzing the dynamic motion of heat as well as for solving an enormous array of diffusion-type problems in physical sciences,
biological sciences, earth sciences, and social sciences. This equation was formulated at the beginning of the nineteenth
century by one of the most gifted scholars of modern science, Joseph Fourier of France. A study of the historical context
in which Fourier made his remarkable contribution and the subsequent impact his work has had on the development of modern
science is as fascinating as it is educational. This paper is an attempt to present a picture of how certain ideas initially
led to Fourier’s development of the heat equation and how, subsequently, Fourier’s work directly influenced and inspired others
to use the heat diffusion model to describe other dynamic physical systems. Conversely, others concerned with the study of
random processes found that the equations governing such random processes reduced, in the limit, to Fourier’s equation of
heat diffusion. In the process of developing the flow of ideas, the paper also presents, to the extent possible, an account
of the history and personalities involved.
Reprinted by permission from theAmerican Geophysical Union, @ 1999. Originally published inReviews of Geophysics as “Fourier’s Heat Conduction Equation: History, Influence and Connections,” Vol. 37, issue 1, pages 151–172, February 1999.
Appended here are eight figures of historical importance. 相似文献
2.
3.
The configurational heat capacity, shear modulus and shear viscosity of a series of Na2O–Fe2O3–Al2O3–SiO2 melts have been determined as a function of composition. A change in composition dependence of each of the physical properties
is observed as Na2O/(Na2O + Al2O3) is decreased, and the peralkaline melts become peraluminous and a new charge-balanced Al-structure appears in the melts.
Of special interest are the frequency dependent (1 mHz–1 Hz) measurements of the shear modulus. These forced oscillation measurements
determine the lifetimes of Si–O bonds and Na–O bonds in the melt. The lifetime of the Al–O bonds could not, however, be resolved
from the mechanical spectrum. Therefore, it appears that the lifetime of Al–O bonds in these melts is similar to that of Si–O
bonds with the Al–O relaxation peak being subsumed by the Si–O relaxation peak. The appearance of a new Al-structure in the
peraluminous melts also cannot be resolved from the mechanical spectra, although a change in elastic shear modulus is determined
as a function of composition. The structural shear-relaxation time of some of these melts is not that which is predicted by
the Maxwell equation, but up to 1.5 orders of magnitude faster. Although the configurational heat capacity, density and shear
modulus of the melts show a change in trend as a function of composition at the boundary between peralkaline and peraluminous,
the deviation in relaxation time from the Maxwell equation occurs in the peralkaline regime. The measured relaxation times
for both the very peralkaline melts and the peraluminous melts are identical with the calculated Maxwell relaxation time.
As the Maxwell equation was created to describe the timescale of flow of a mono-structure material, a deviation from the prediction
would indicate that the structure of the melt is too complex to be described by this simple flow equation. One possibility
is that Al-rich channels form and then disappear with decreasing Si/Al, and that the flow is dominated by the lifetime of
Si–O bonds in the Al-poor peralkaline melts, and by the lifetime of Al–O bonds in the relatively Si-poor peralkaline and peraluminous
melts with a complex flow mechanism occurring in the mid-compositions. This anomalous deviation from the calculated relaxation
time appears to be independent of the change in structure expected to occur at the peralkaline/peraluminous boundary due to
the lack of charge-balancing cations for the Al-tetrahedra. 相似文献
4.
Thermodynamic properties of high-pressure minerals that are not recoverable from synthesis experiments by conventional quenching
methods (“unquenchable” phases) usually are calculated from equation of state data and phase diagram topologies. The present
study shows that, with cryogenic methods of recovery and sample treatment, phases with a suitable decomposition rate can be
made accessible to direct thermodynamic measurements. A set of samples of Ca(OH)2-II has been synthesized in a multianvil device and subsequently recovered by cooling the high-pressure assembly with liquid
nitrogen. Upon heating from liquid nitrogen to room temperature, the material transformed back to Ca(OH)2-I. The heat effect of this backtransformation was measured by differential scanning calorimetry. A commercial differential
scanning calorimeter (Netzsch DSC 404), modified to allow sample loading at liquid nitrogen temperature was used to heat the
material from −150 to +200 °C at rates varying between 5 and 15 °C min−1. The transformation started around −50 °C very gradually, and peaked at about 0 °C. To obtain a baseline correction, each
sample was scanned under exactly the same conditions after the backtransformation was complete. Because of the relative sluggishness,
onset and offset temperatures were not well defined as compared to fast (e.g., melting) reactions. To aid in integration,
the resulting signals were successfully fitted using a generic asymmetric peak model. The enthalpy of backtransformation was
determined to be ΔH =−10.37 ± 0.50 kJ mol−1. From previous in situ X-ray diffraction experiments, the location of the direct transformation in P-T space has been constrained to 5.7 ± 0.4 GPa at 500 °C (Kunz et al. 1996). With the reaction volume known from the same study,
and assuming that ΔC
p
of the transformation remains negligible between the conditions of our measurements and 500 °C, our result gives an estimate
of the entropy of transition and the P-T slope of the reaction curve. To a first approximation, the values ΔS = −16.00 ± 0.65 J(mol · K)−1 and dP/dT = 0.0040 ± 0.0002 GPa/K have been determined. These results need to be refined by equation of state data for Ca(OH)2-II.
Received: 30 December 1999 / Accepted: 10 April 2000 相似文献
5.
Wenjun Yong E. Dachs A. C. Withers E. J. Essene 《Physics and Chemistry of Minerals》2007,34(2):121-127
A multi-anvil device was used to synthesize 24 mg of pure γ-Fe2SiO4 crystals at 8.5 GPa and 1,273 K. The low-temperature heat capacity (C
p) of γ-Fe2SiO4 was measured between 5 and 303 K using the heat capacity option of a physical properties measurement system. The measured
heat capacity data show a broad λ-transition at 11.8 K. The difference in the C
p between fayalite and γ-Fe2SiO4 is reduced as the temperature increases in the range of 50–300 K. The gap in C
p data between 300 and 350 K of γ-Fe2SiO4 is an impediment to calculation of a precise C
p equation above 298 K that can be used for phase equilibrium calculations at high temperatures and high pressures. The C
p and entropy of γ-Fe2SiO4 at standard temperature and pressure (S°298) are 131.1 ± 0.6 and 140.2 ± 0.4 J mol−1 K−1, respectively. The Gibbs free energy at standard pressure and temperature (ΔG°
f,298) is calculated to be −1,369.3 ± 2.7 J mol−1 based on the new entropy data. The phase boundary for the fayalite–γ-Fe2SiO4 transition at 298 K based on current thermodynamic data is located at 2.4 ± 0.6 GPa with a slope of 25.4 bars/K, consistent
with extrapolated results of previous experimental studies. 相似文献
6.
We use a lattice vibrational technique to derive thermophysical and thermochemical properties of the pure elements aluminum
and iron in pressure–temperature space. This semi-empirical technique is based on either the Mie–Grüneisen–Debye (MGD) approach
or an extension of Kieffer’s model to incorporate details of the phonon spectrum. It includes treatment of intrinsic anharmonicity,
electronic effects based on the free electron gas model, and magnetic effects based on the Calphad approach. We show that
Keane’s equation of state for the static lattice is better suitable to represent thermodynamic data for aluminum from 1 bar
to pressures in the multi-megabar region relative to Vinet’s universal and the Birch–Murnaghan equation of state. It appears
that the MGD and Mie–Grüneisen–Kieffer approach produce similar results, but that the last one better represents heat capacity
below room temperature. For iron we show that the high temperature behavior of thermal expansivity can be explained within
the Calphad approach by a pressure-dependent Curie temperature with a slope between –1 and 0 K/GPa. 相似文献
7.
Yu. L. Rebetskii 《Doklady Earth Sciences》2011,440(1):1328-1333
The set of equations for the problem of thermal-gravitational convection accounts for compressibility of solid bodies, which
changes for elementary volumes moving during convection process in fields of the initial temperature and the initial gravitational
stress pattern for rheology of an elastic-viscous Maxwell body. It was shown that equations of momentum conservation in the
vertical direction and heat transfer for steady convection differ from the equation for incompressible liquid by terms containing
the rate of elastic volume change and the connected rate of heat change. It was established that an additional term in the
momentum conservation equation defines a new class of the instable state of a solid body, which is able to form huge deformations
at the expense of plasticity and creep at large segments of time—flow in the field of gravity force—instability of the gravitational
stress pattern of elastic-plastic body. Analysis of different boundary conditions for which this instability can be realized
in the form of convective cells showed that the convection rate is totally defined by reconstruction processes of vertical
stresses on horizontal boundaries close to the initial gravitation pattern. Alignment process of these stresses can be provided
not only by erosion and denudation processes occurring on the Earth’s surface, but also by processes on the inner boundaries
of the tectonosphere which provide isostasy in the mantle. 相似文献
8.
An algorithm for the solution of a nonlinear problem of phase boundary movement and evolution of temperature distribution
due to the perturbation in the basal heat flux has been discussed. The reduction of the problem to a system of nonlinear ordinary
differential equations with the help of a Fourier series method leads to a stiff system. This stiffness is taken care of by
the use of a modified Euler’s method. Various cases of basal heat flow variation have been considered to show the performance
and stability of the technique for such a nonlinear system. The first case of step-wise function is taken to analyse the performance
of the technique, and the study has been extended to other general cases of linear increase, periodic variation, and box and
triangular function type variations in the heat flux. In the step-wise case the phase boundary attains a constant position
rapidly if the supplied heat flux is sufficiently large. The effect of periodicity in the heat flow is clearly depicted in
the phase boundary movement, where the phase boundary oscillates about the mean position at large times. The absence of any
constant level in the case of linear increase in heat flux is due to a very large value of heat flux. In the cases of box
car and triangular heat flux the boundary starts moving downward after the cessation of excess heat flux but does not immediately
return to its original preperturbation state, instead approaches it at large times. This technique may be applied to more
general cases of heat flow variation. 相似文献
9.
In this study, we tried to model the processes of moisture and heat transfers in the soil–vegetation–atmosphere system in
an integrated comprehensive way. The purpose of the study is to simulate profiles of soil water content and temperature at
root active zone (i.e., 0–50 cm), taking the root water uptake, soil evaporation, and canopy transpiration into account. The
water and heat transfer equations are solved by an iterative Newton–Raphson technique and a finite difference method is used
to solve the governing equations. Soil water content and soil temperature dynamics could be simulated rather accurately in
a cropped field on Loess Plateau area. The water and heat transfer flux predicted by the classical theory of Philip and de
Vries (Tans Am Geophys Union 38:222–232, 1957) slightly overestimated near the surface and underestimated at the deeper depths, as a result of the overestimated soil evaporation
at the top soil layer (0–10 cm) and underestimated crop canopy transpiration at the deeper depths (10–50 cm). Water content
tended to be underestimated for the entire profile at the soil surface (from 0 to 50 cm). Soil temperatures during the simulated
period was slightly overestimated in the nighttimes and underestimated in the daytimes, as a result of the underestimated
soil water content at the top soil layer (0–10 cm) and overestimated at the deeper depths (10–50 cm). Soil temperatures tended
to be underestimated for the entire profile at the soil surface (from 0 to 50 cm). While the sum of the water and heat regimes
yielded a much better match with the soil water content and soil temperature obtained from the field observations. The results
obtained show that the model coupled water and heat transfer is able to capture the dynamics of soil water content. 相似文献
10.
Atlanta’s urban heat island under extreme heat conditions and potential mitigation strategies 总被引：2，自引：0，他引：2
The urban heat island (UHI), together with summertime heat waves, foster’s biophysical hazards such as heat stress, air pollution,
and associated public health problems. Mitigation strategies such as increased vegetative cover and higher albedo surface
materials have been proposed. Atlanta, Georgia, is often affected by extreme heat, and has recently been investigated to better
understand its heat island and related weather modifications. The objectives of this research were to (1) characterize temporal
variations in the magnitude of UHI around Metro Atlanta area, (2) identify climatological attributes of the UHI under extremely
high temperature conditions during Atlanta’s summer (June, July, and August) period, and (3) conduct theoretical numerical
simulations to quantify the first-order effects of proposed mitigation strategies. Over the period 1984–2007, the climatological
mean UHI magnitude for Atlanta-Athens and Athens-Monticello was 1.31 and 1.71°C, respectively. There were statistically significant
minimum temperature trends of 0.70°C per decade at Athens and −1.79°C per decade at Monticello while Atlanta’s minimum temperature
remained unchanged. The largest (smallest) UHI magnitudes were in spring (summer) and may be coupled to cloud-radiative cycles.
Heat waves in Atlanta occurred during 50% of the years spanning 1984–2007 and were exclusively summertime phenomena. The mean
number of heat wave events in Atlanta during a given heat wave year was 1.83. On average, Atlanta heat waves lasted 14.18 days,
although there was quite a bit of variability (standard deviation of 9.89). The mean maximum temperature during Atlanta’s
heat waves was 35.85°C. The Atlanta-Athens UHI was not statistically larger during a heat wave although the Atlanta-Monticello
UHI was. Model simulations captured daytime and nocturnal UHIs under heat wave conditions. Sensitivity results suggested that
a 100% increase in Atlanta’s surface vegetation or a tripling of its albedo effectively reduced UHI surface temperature. However,
from a mitigation and technological standpoint, there is low feasibility of tripling albedo in the foreseeable future. Increased
vegetation seems to be a more likely choice for mitigating surface temperature. 相似文献
11.
P. Nagaraju Labani Ray G. Ravi Vyasulu V. Akkiraju Sukanta Roy 《Journal of the Geological Society of India》2012,80(1):39-47
Heat flow has been determined by combining temperature measurements in 7 boreholes with thermal conductivity measurements in the Upper Vindhyan sedimentary rocks of Shivpuri area, central India. The boreholes are distributed at 5 sites within an area of 15 × 10 km2; their depths range from 174 to 268 m. Geothermal gradients estimated from borehole temperature profiles vary from 8.0–12.7 mK m−1 in the sandstone-rich formations to 25.5–27.5 mK m−1 in the shale-rich formations, consistent with the contrast in thermal conductivities of the two rock types. Heat flow in the area ranges between 45 and 61 mW m−2, with a mean of 52±6 mW m−2. The heat flow values are similar to the >50 mW m−2 heat flow observed in other parts of the northern Indian shield. The heat flow determinations represent the steady-state heat flow because, the thermal transients associated with the initial rifting, convergence and sedimentation in the basin as well as the more recent Deccan volcanism that affected the region to the south of the basin would have decayed, and therefore, the heat flow is in equilibrium with the radiogenic heat production of the crust and the heat flow from the mantle. The present study reports the heat flow measurements from the western part of the Vindhyan basin and provides heat flow information for the Bundhelkhand craton for the first time. Radioelement (Th, U and K) abundances have been measured both in the sedimentary rocks exposed in the area as well as in the underlying basement granite-gneiss of Bundelkhand massif exposed in the adjacent area. Radioactive heat production, estimated from those abundances, indicate mean values of 0.3 μW m−3 for sandstone with inter-bands of shale and siltstone, 0.25 μW m−3 for sandstone with inter-bands siltstone, 0.6 μW m−3 for quartzose sandstone, and 2.7 μW m−3 for the basement granitoids. With a total sedimentary thickness not exceeding a few hundred metres in the area, the heat production of the sedimentary cover would be insignificant. The radioactive heat contribution from the basement granitoids in the upper crust is expected to be large, and together with the heat flow component from the mantle, would control the crustal thermal structure in the region. 相似文献
12.
For the assessment of shallow landslides triggered by rainfall, the physically based model coupling the infinite slope stability
analysis with the hydrological modeling in nearly saturated soil has commonly been used due to its simplicity. However, in
that model the rainfall infiltration in unsaturated soil could not be reliably simulated because a linear diffusion-type Richards’
equation rather than the complete Richards’ equation was used. In addition, the effect of matric suction on the shear strength
of soil was not actually considered. Therefore, except the shallow landslide in saturated soil due to groundwater table rise,
the shallow landslide induced by the loss in unsaturated shear strength due to the dissipation of matric suction could not
be reliably assessed. In this study, a physically based model capable of assessing shallow landslides in variably saturated
soils is developed by adopting the complete Richards’ equation with the effect of slope angle in the rainfall infiltration
modeling and using the extended Mohr–Coulomb failure criterion to describe the unsaturated shear strength in the soil failure
modeling. The influence of rainfall intensity and duration on shallow landslide is investigated using the developed model.
The result shows that the rainfall intensity and duration seem to have similar influence on shallow landslides respectively
triggered by the increase of positive pore water pressure in saturated soil and induced by the dissipation of matric suction
in unsaturated soil. The rainfall duration threshold decreases with the increase in rainfall intensity, but remains constant
for large rainfall intensity. 相似文献
13.
E. Rojas A. Zepeda M. L. Pérez-Rea J. Leal G. Gallegos 《Geotechnical and Geological Engineering》2011,29(2):193-202
One of the most prevalent relationships for effective stresses on unsaturated soils was proposed by Bishop in the middle of
the last century. However, only recently Bishop’s effective stress equation has been implemented in various constitutive models
for unsaturated soils. These models have the advantage of naturally including the hydro-mechanical coupling that has been
experimentally observed on these materials. Unfortunately, the problem of properly evaluating Bishop’s parameter χ still remains unsolved. This paper presents the results of a solid-porous model used to determine the value of Bishop’s parameter
χ and evaluate the strength of unsaturated soils. These theoretical results are compared with a series of triaxial test performed
on a silty sand subjected to different suctions in wet and dry paths. These comparisons show that the porous model proposed
herein can be used to estimate the strength of unsaturated soils for both the wetting and the drying paths. 相似文献
14.
15.
Three-phase numerical model of water migration in partially frozen geological media: model formulation,validation, and applications 总被引：3，自引：0，他引：3
Scott L. Painter 《Computational Geosciences》2011,15(1):69-85
Water in the subsurface of the Earth’s cold regions—and possibly the subsurface of Mars—resides in the liquid, vapor, and
ice phases. However, relatively few simulations addressing full three-phase, nonisothermal water dynamics in below-freezing
porous media have been undertaken. This paper presents a nonisothermal, three-phase approach to modeling water migration in
partially frozen porous media. Conservation equations for water (as ice, liquid, and vapor) and a single gas species (in the
gas phase and dissolved in water) are coupled to a heat transport equation and solved by a finite-volume method with fully
implicit time stepping. Particular attention is given to the method of spatial differencing when the pore space is partially
filled with ice. The numerical model is able to reproduce freezing-induced water redistribution observed in laboratory experiments.
Simulations of Earth permafrost dynamics and of the formation and evolution of a planetary-scale cryosphere on Mars demonstrate
the new capabilities. 相似文献
16.
Duke U. Ophori 《Hydrogeology Journal》1998,6(2):193-203
Flow of groundwater with variable density and viscosity was simulated at the Atikokan Research Area (ARA) in northwestern
Ontario, Canada. An empirical viscosity–concentration equation was modified to include total-dissolved-solids (TDS) data from
the ARA. The resulting equation was used successfully to estimate reasonably accurate viscosity values over the expected range
of temperature and concentration, in comparison with experimental values derived for sodium chloride solutions. A three-dimensional
finite-element code, MOTIF, developed by Atomic Energy of Canada Limited, was used in the simulations. The inclusion of the
effects of depth-increasing temperature and TDS-dependent fluid-density distribution, while maintaining only a temperature-dependent
viscosity relationship in a simulation, resulted in a more penetrative flow against expected buoyancy effects (i.e., the physics
of the system was not honored). Accounting for concentration in the viscosity equation caused water to be less penetrative
and more in accordance with the expected physics of the system. A conclusion is that fluid concentration should be considered
simultaneously in calculating the density and viscosity of a fluid during modeling of variable-density flow in areas underlain
by fluids with high TDS. Results of simulations suggest that both flow directions and magnitudes should be employed simultaneously
during the calibration of a model. Large-scale groundwater movement in the ARA may be analyzed with carefully selected vertical
no-flow boundaries. By incorporating the geothermal temperature gradient, groundwater recharge increases by 12%; thus, this
gradient plays a significant role in groundwater flow at the ARA. Variability in the fluid concentration at the ARA neither
decreases nor increases recharge into the groundwater system. The hypothesis that an isolated continuous regional flow system
may exist at depth in the ARA is not supported by these simulations.
Received, September 1996 Revised, September 1997, February 1998 Accepted, February 1998 相似文献
17.
Applying the method of ‘statistical linear regression’, atomspheric water vapour over oceanic areas has been estimated from
the 19GHz and 22 GHz data of the satellite microwave radiometer (SAMIR) system onboard the Bhaskara II satellite. In the absence of any simultaneousin situ measurements on water vapour over ocean, theSAMIR-derived water vapour data have been compared with like data from theNOAA-7 satellite. It is suggested that a positive bias seen in theSAMIR data could be due to calibration errors in the basic data. In view of the observed bias, the original regression equation
is modified and then used to obtain water vapour distributions over ocean for winter and south-west monsoon seasons usingSAMIR data of several orbits. 相似文献
18.
In the study of heat extraction by circulating water in a fracture embedded in geothermal reservoir, the heat conduction in the reservoir is typically assumed to be one dimensional and perpendicular to the fracture. In this paper, we demonstrate that by an integral equation formulation utilizing Green's function, the multi‐dimensional heat flow in the reservoir can be modelled. In the resulting numerical solution system, the discretization of reservoir geometry is entirely eliminated, leading to a much more efficient scheme. The multi‐dimensional heat conduction effect as compared to its one‐dimensional simplification is studied. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
19.
Clementine UVVIS and NIR data from the lunar sampling sites (totaling 46 sampling sites) were processed and used to refine the iron determination method of Le Mouéic et al. (2000, 2002). We found that about 21 sampling sites are unsuitable to Le Mouéic et al's spectral parameters ("slope" and "depth l") because their 1500 nm filter could not be used as spectral parameters' right shoulders and to evaluate the depth of the 1-μm absorption feature accurately. We used the rest 25 sampling sites to refine the method developed by Le Mouéic et al. (2000, 2002 ) and obtained our own equation of FeO content determination. We tested our own equation, and the results are satifactory. In our work we also acquired some useful experiences in scientific applications of our own dataset of the Chang'E-1 mission. 相似文献
20.
Measured groundwater temperatures in the surficial zone are dependent on the properties of porous media and vertical flow velocity. Sensitivity analyses, collinear diagnostics and an inverse numerical solution to the one-dimensional heat-transport equation are used to determine which parameters can be estimated from temperature measurements in the surficial zone. This is done for heat transport in the saturated zone considering a constant vertical flow velocity. The use of temperature profiles, temperature time-series and temperature envelopes are considered. There is an important difference between a conduction and a convection dominated system. Sensitivity analysis shows that temperature measurements are sensitive to effective thermal conductivity and heat capacity and are insensitive to effective porosity and thermal dispersivity. In a conduction dominated system, temperature is also insensitive for vertical velocity. Collinear diagnostics show that in a conduction dominated system, only the combination of heat capacity and effective thermal conductivity, the thermal diffusivity, can be derived. In a convection dominated system, both the vertical velocity and the effective thermal conductivity can, theoretically, be derived. 相似文献