Diffusive Heat Transport Research Articles

Experimental measurements of sidebranching in thermal dendrites under terrestrial-gravity and microgravity conditions.

We perform sidebranch measurements on pure succinonitrile dendrites grown in both microgravity and terrestrial-gravity conditions for a set of supercoolings within the range 0.1-1.0 K. Two distinct types of sidebranch regions, uniform and coarsening, exist, and are characterized by the distance from the tip at which the region began, D(i), and the average spacing of sidebranches within that region, lambda(i). There does not appear to be any significant dependence on either gravity level or supercooling when D(i) or lambda(i) are normalized with respect to the radius of curvature of the tip, R. The apparently constant normalized proportionality factor between D(i), lambda(i), and R, regardless of the relative importance of diffusion and convective heat transport, demonstrates self-similarity between dendrites of different length scales propagating under various heat transfer conditions. However, when the form of the sidebranch envelope is defined by a power law relating the amplitude and relative positions of the sidebranches normalized to the radius of the tip, the form is seen to have significant variations with supercooling between the terrestrial gravity and microgravity growth dendrites. Furthermore, both the amplitude coefficient and exponent from the power-law regressions of the microgravity data are statistically different (95% confidence level) than their terrestrial counterparts.

The thermal evolution of sedimentary basins and its effect on the maturation of hydrocarbons

The maturation of hydrocarbon source rocks depends on a range of factors, including the primary rock type and its original content of organic matter (kerogens); the history of sedimentation and burial (depth); the local geothermal gradient (temperature); and duration of sedimentation (time). The standard approach to modelling this process assumes an evolving burial history, but in a basin with a steady-state geotherm, both in the sediment column and in the underlying basement rocks. This first-order approach neglects any effects of changes in the geothermal profile resulting from the timing and history of the particular mechanism that formed the sedimentary basin, and hence may lead to systematic overestimation or underestimation of hydrocarbon maturation in such rocks. This systematic effect may be small when sedimentation rates are low, but can be significant in basins with sedimentation rates that are rapid when compared with the rate of heat transport and re-equilibration in the system. Here we describe two analytical 1-D mathematical models for diffusive heat transport during sediment deposition, which is rapid compared with the thermal relaxation rate. The two models describe sedimentary events that can be considered either effectively instantaneous (sudden) or continuous. In both cases we calculate a time-dependent geothermal profile and the resulting maturation index of particular source rocks, given the combined effects of the thermal and burial histories. The models take account both of the transient cooling effect of the cold sediment blanket and of the steady-state warming from the underlying basement. After calibration with borehole data, the method allows a reconstruction of the initial geothermal gradient at the start of the sedimentation event. The model has been applied to data derived from two wells drilled in two different tectonic settings: the Pannonian Basin and the Central North Sea. In both cases there is a good agreement between the model predictions of the maturation index and empirical observations based on the vitrinite reflectance technique applied to borehole samples of actual source rocks. In contrast, the steady-state geotherm models give a systematic overestimation of both the maximum temperature and the degree of maturation reached by the sediments by the end of the sedimentary event; this overestimation is particularly evident for the case of the Pannonian Basin. Such systematic effects could have significant implications both for the interpretation of past thermotectonic events, and for oilfield appraisal.

Cooling-Induced Current in the Upper Ocean of the Japan Sea

The most plausible scenarios for seasonal to interannual variabilities and their possible causes are investigated for the Tsushima Current system passing through the Japan Sea. The study is based on the north and south two-box model across the polar front in an idealized upper ocean of the Japan Sea. The boxes are connected by lateral diffusive heat transport and cooled by atmospheric forcing at the annual mean state. The south box, i.e. the Tsushima Current region, only interacts with the outside warmer box in the East China Sea and has an eastward thermal-driven current originating in the outside box. The magnitude of this current depends on the strength of the thermal gradient between the north and south boxes; the inflow of warm waters can therefore be maintained by net heat loss through the sea-surface. I call such a thermal-driven inflow process a "Cooling-Induced Current" system in the present study. Under periodical heat forcing, the perturbation response of the model to water temperature fields and inflow transport were examined. It is shown that the lateral diffusion time across the polar front (over a period of 10 years) is crucial to the interannual modeled response. An analysis of the seasonal heat budget suggests that the heat transported into the Japan Sea from the East China Sea in summer is stored mainly within the Tsushima Current region and contributes to heat loss by the sea-surface cooling in winter.

Sensitivity of an Equatorial Pacific OGCM to the Lateral Diffusion

An OGCM is used to investigate the importance of lateral mixing in the tropical Pacific Ocean circulation. Horizontal subgrid-scale physics is parameterized by the usual Laplacian operator. Three simulations are performed using three different orders of magnitude for lateral eddy viscosity and diffusivity coefficients: 104, 103, and 102 m2 s−1. The upper layer response is found sensitive to lateral diffusion as well as the rest of the general circulation. Decreasing lateral mixing coefficients raises the mean kinetic energy level and the input of energy by the wind, and enhances the vertical dissipation. This weakens the equatorial meridional cell and induces a reduction of 20 Sv in the transport of the equatorial upwelling. These results are due to the nonlinear interplay between horizontal and vertical diffusion. The nature of the Equatorial Undercurrent (EUC) is found particularly sensitive to the relative importance of the diffusive conditions. Lateral mixing dominates the different regimes of the EUC when the strongest diffusion coefficient is used. Under these conditions, the EUC dynamics is similar to a boundary layer regime where strong meridian and vertical circulation insulates the equatorial dynamics. Conversely, a weakness of horizontal diffusion leads to enhancement of the vertical diffusion role, even in the core of the EUC. In the eastern inertial regime, vertical diffusion can replace horizontal diffusion when dissipation is needed. While the dynamics is severely altered between the simulations, the SST pattern errors with the climatology are found quite similar, in conflict with the results reported by Nevertheless, at the basin scale, lateral mixing conditions affect the meridian heat transport. Similar diffusive and advective heat transport amplitudes are found with the strongest lateral coefficient, while advective meridian heat transport dominates in both other experiments. Moreover, the different terms of the surface heat budget are found sensitive to the lateral diffusion: when lateral diffusion coefficient is sufficiently low, the balance implies the heating by the transient heat transport and the cooling by both monthly mean advection and vertical diffusion. Indeed, in the equatorial cold tongue, vertical diffusion is large enough to distribute heat down to the thermocline below the mixed layer.

Can increased poleward oceanic heat flux explain the warm Cretaceous climate?

The poleward transport of heat in the mid‐Cretaceous (100 Ma) is examined using an idealized coupled ocean‐atmosphere model. The oceanic component consists of two zonally averaged basins representing the proto‐Pacific and proto‐Indian oceans and models the dynamics of the meridional thermohaline circulation. The atmospheric component is a simple energy and moisture balance model which includes the diffusive meridional transport of sensible heat and moisture. The ocean model is spun up with a variety of plausible Cretaceous surface temperature and salinity profiles, and a consistent atmosphere is objectively derived based on the resultant sea surface temperature and the surface heat and freshwater fluxes. The coupled model does not exhibit climate drift. Multiple equilibria of the coupled model are found that break the initial symmetry of the ocean circulation; several of these equilibria have one‐cell (northern or southern sinking) thermohaline circulation patterns. Two main classes of circulation are found: circulations where the densest water is relatively cool and is formed at the polar latitudes and circulations where the densest water is warm, but quite saline, and the strongest sinking occurs at the tropics. In all cases, significant amounts of warm, saline bottom water are formed in the proto‐Indian basin which modify the deepwater characteristics in the larger (proto‐Pacific) basin. Temperatures in the deep ocean are warm, 10°–17°C, in agreement with benthic foraminiferal oxygen isotope data. The poleward transport of heat in the modeled Cretaceous oceans is larger than in some comparable models of the present day thermohaline circulation and significantly larger than estimates of similar processes in the present‐day ocean. It is consistently larger in the polar sinking cases when compared with that seen in the tropical sinking cases, but this represents an increase of only 10%. The largest increase over present‐day model transports is in the atmospheric latent heat transport, where an increased hydrological cycle (especially in the tropical sinking cases) contributes up to an extra 1 PW of poleward heat transport. Better constraints on the oceanic deepwater circulation during this period are necessary before the meridional circulation can be unambiguously described.

Wave-like and diffusive heat transport in a-SiO 2 below 1 K

Heat-pulse experiments have been performed in order to test the kinetic theory of phonons in glasses. Based on the coupled Boltzmann equations for phonons and localized tunneling systems field equations for the phonon energy, the tunneling state energy and the phonon momentum have been derived. It is shown that the solution of these symmetric hyperbolic field equations for given boundary and initial values of heat-pulse measurements are in excellent agreement with new experimental data obtained in vitreous silica below 1 K. In the thermodynamic theory presented, the specific heat of glasses is not time dependent explicitly but depends on time via temperature only. Moreover, the theory predicts a new pulse propagation at very short times reflecting a wave-like energy transport due to the absorption and emission of phonons by fast relaxing tunneling states.

The strength and efficiency of thermal and compositional convection in the geodynamo

The evolution of the Earth's outer core is calculated theoretically by assuming that the fluctuations about a vigorously convecting, well-mixed, isentropic and hydrostatic mean state are small. The global energy equation describes the evolution of the mean state, but contains no information about the division between convective and diffusive transport of heat or composition within the core itself. As the diffusive transport of either heat or composition makes no contribution to the dynamo, estimates of the dynamo power must be derived by explicit consideration of the correlation of small density fluctuations with the large convective velocities. By such consideration, the dynamo power is shown to be equal to the integrated thermal and compositional buoyancy flux, which is calculated from the requirement that the mean state remain isentropic and well mixed. The resulting new and simple expression for the dynamo efficiency has an easily understood physical interpretation in terms of Carnot-style redistribution of heat and mass in the core, though it takes full account of both thermal and compositional effects and the evolution of the mean state. Once the equation of state and thermodynamic parameters are given, the dynamo power can be evaluated readily and explicity. Analytic solutions based on a simple example equation of state show that the relative importance of thermal and compositional convection depends on the size of the inner core and the amount by which the heat flux across the core-mantle boundary (CMB) exceeds that which can be conducted up the core adiabat. Thermal convection was dominant in the early Earth when the inner core was small and the Earth was probably cooling rapidly. Estimates of the present-day heat loss across the CMB suggest that thermal convection now contributes about 20% of the dynamo power and compositional convection about 80%. As a result of the release of latent heat at the inner-core boundary, thermal convection can make a net positive contribution to the dynamo power even if the heat flux at the CMB is subadiabatic.

The Role of Temperature Feedback in Stabilizing the Thermohaline Circulation

Abstract Ocean climate models traditionally compute the surface heat flux with a restoring boundary condition of the form Q = λ(T* − To). This implies an atmosphere of fixed temperature and breaks down when large-scale changes in the ocean circulation are considered, which have a feedback effect on atmospheric temperatures. To include this important feedback, a new thermal boundary condition of the form Q = γ(T* − To) − μ∇2(T* − To) is proposed. This is derived from an atmospheric energy balance model with diffusive lateral heat transport. The effects of this new parameterization are examined in experiments with the GFDL modular ocean model for two model basins. “Conveyor belt” circulation states are compared using traditional mixed boundary conditions and our new coupling. With the new coupling, a realistic temperature contrast is obtained between the North Atlantic and the Pacific, caused by free adjustment of surface temperature to the oceanic heat transport. The results show that a temperature feedbac...

Dendritic Growth of Succinonitrile in Terrestrial and Microgravity Conditions as a Test of Theory.

Dendritic growth is the common mode of solidification encountered when metals and alloys freeze under low thermal gradients. The growth of dendrites in pure melts is generally acknowledged to be controlled by the transport of latent heat from the moving crystal-melt interface into its supercooled melt. The Ivantsov formulation solves the equation of heat flow from a paraboloidal dendrite tip for the case of diffusive heat transport. However, this formulation is incomplete, and the physics of an additional selection rule, coupled to the Ivantsov solution, is necessary to predict the dendrite tip velocity and radius of curvature as a unique function of the supercooling. Unfortunately, the experimental evidence is not definitive because dendritic growth can be complicated by buoyancy-induced convection, which is normally unavoidable under terrestrial conditions. Recent experiments performed in the microgravity environment of the space shuttle Columbia (STS-62) show quantitatively that convection alters the tip velocities and radii of curvature of dendrites in both terrestrial and microgravity conditions. In addition, these data can be used to evaluate both how well the Ivantsov diffusion solution and the selection rule (the product of the dendrite tip velocity and the tip radius of curvature squared is a constant) match the dendritic growth data under microgravity conditions.

The evolution of nonlinear subhorizon-scale entropy fluctuations in the early universe

view Abstract Citations (58) References (43) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The evolution of nonlinear subhorizon-scale entropy fluctuations in the early universe Jedamzik, Karsten ; Fuller, George M. Abstract We examine the damping of non-linear sub-horizon scale entropy fluctuations in early epochs of the universe ($T\approx 100$ GeV to $T\approx 1$keV) by neutrino, baryon, and photon induced dissipative processes. Results of numerical evolution calculations are presented for broad ranges of initial fluctuation amplitudes and length scales. These calculations include a detailed treatment of neutrino inflation, neutron and proton diffusion, photon diffusive heat transport, and hydrodynamic expansion with photon-electron Thomson drag. Neutrino inflation is treated both in the diffusive heat transport regime where neutrinos are optically thick on the length scales of the fluctuations, and in the homogeneous heating regime where neutrinos are optically thin on these scales. We find considerable convergence in amplitude evolution for appreciable ranges in initial fluctuation length scales and amplitudes. Fluctuations produced with the right characteristics at very early times ($T$ $^>_{\sim}$ 100 GeV) are found to survive through the nucleosynthesis epoch. Publication: The Astrophysical Journal Pub Date: March 1994 DOI: 10.1086/173788 arXiv: arXiv:astro-ph/9312063 Bibcode: 1994ApJ...423...33J Keywords: Baryons; Cosmology; Entropy; Neutrinos; Photons; Radiative Transfer; Universe; Energy Dissipation; Heat Transmission; Hydrodynamic Equations; Nuclear Fusion; Weak Interactions (Field Theory); Astrophysics; Astrophysics E-Print: 44 pages in plain Tex, 16 figures (not included) available by fax or mail upon request, ApJ in press full text sources arXiv | ADS |

Inhomogeneous primordial nucleosynthesis: Coupled nuclear reactions and hydrodynamic dissipation processes

view Abstract Citations (58) References (33) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Inhomogeneous Primordial Nucleosynthesis: Coupled Nuclear Reactions and Hydrodynamic Dissipation Processes Jedamzik, Karsten ; Fuller, George M. ; Mathews, Grant J. Abstract We present a detailed study of inhomogeneous Big Bang nucleosynthesis where, for the first time, nuclear reactions are coupled to all significant fluctuation dissipation processes. Theses processes include neutrino heat transport, baryon diffusion, photon diffusive heat transport, and hydrodynamic expansion with photon-electron Thomson drag. Light element abundance yields are presented for broad ranges of initial amplitudes and length scales for spherically condensed fluctuations. The $^2$H, $^3$He, $^4$He, and $^7$Li nucleosynthesis yields are found to be inconsistent with observationally inferred primordial abundances for all but very narrow ranges of fluctuation characteristics. Rapid hydrodynamic expansion of fluctuations late in the nucleosynthesis epoch results in significant destruction of $^7$Li ($^7$Be) only if the baryonic conytribution to the closure density ($\Omega_b$) is less than or comparable to the upper limit on this quantity from homogeneous Big Bang nucleosynthesis. This implies that $^7$Li overproduction will peclude an increase on the upper limit for $\Omega_b$ for any inhomogeneous nucleosynthesis scenarios employing spherically condensed fluctuations. Publication: The Astrophysical Journal Pub Date: March 1994 DOI: 10.1086/173789 arXiv: arXiv:astro-ph/9312065 Bibcode: 1994ApJ...423...50J Keywords: Big Bang Cosmology; Coupled Modes; Dissipation; Hydrodynamic Equations; Inhomogeneity; Nuclear Fusion; Abundance; Baryons; Heat Transmission; Neutrinos; Photons; Astrophysics; COSMOLOGY: EARLY UNIVERSE; HYDRODYNAMICS; NUCLEAR REACTIONS; NUCLEOSYNTHESIS; ABUNDANCES; Astrophysics E-Print: 30 pages in plain Tex, 17 figures (not included) available by fax or mail upon request, ApJ in press, L1 full text sources arXiv | ADS |

Dendritic Growth in Terrestrial and Microgravity Conditions

AbstractDendritic growth is the most ubiquitous form of crystal growth encountered when metals and alloys solidify under low thermal gradients. The growth of thermal dendrites in pure melts is generally acknowledged to be controlled by the diffusive transport of latent heat from the moving crystal-melt interface into its supercooled melt. However, this formulation is incomplete, and the physics of an additional selection rule, coupled to the transport solution, is necessary to predict uniquely the dendrite tip velocity and radius of curvature as a function of the supercooling. Unfortunately, experimental confirmation or evidence is ambiguous, because dendritic growth can be severely complicated by buoyancy induced convection. Recent experiments performed in the microgravity environment of the space shuttle Columbia (STS-62) quantitatively show that convection alters tip velocities and radii of curvature of succinonitrile (SCN) dendrites. In addition, these data can be used to evaluate how well the Ivantsov diffusion solution, coupled to a scaling constant, matches the dendritic growth data under microgravity conditions.

Diffusive transport across irregular and fractal walls

Diffusive transport of heat, mass, and momentum across walls with irregular and fractal geometry is discussed. A configuration is considered in detail, in which the transported variable diffuses across a two-dimensional periodic irregular wall toward an overlying plane wall, while the value of the variable over each wall is maintained at a constant value. Several families of self-similar wall geometries with increasingly finer structure, eventually leading to fractal shapes, are considered in detail using an efficient numerical method that is based on conformal mapping. The numerical procedure involves the iterative solution of a large system of nonlinear algebraic equations. Computed patterns of iso-scalar contours reveal the precise effect of the shape, size, and total length of boundary irregularities on the local and total transport rates, and illustrate the enhancement in transport efficacy with wall refinement. The total rate of transport across walls with self-similar irregularities is shown to be remarkably close to that across walls with random irregularities of same roughness height.

Transient ballistic and diffusive phonon heat transport in thin films

Ballistic and diffusive phonon transport under small time and spatial scales are important in fast-switching electronic devices and pulsed-laser processing of materials. The Fourier law represents only diffusive transport and yields an infinite speed for heat waves. Although the hyperbolic heat equation involves a finite heat wave speed, it cannot model ballistic phonon transport in short spatial scales, which under steady state follows the Casimir limit of phonon radiation. An equation of phonon radiative transfer (EPRT) is developed which shows the correct limiting behavior for both purely ballistic and diffusive transport. The solution of the EPRT for diamond thin films not only produces wall temperature jumps under ballistic transport but shows markedly different transient response from that of the Fourier law and the hyperbolic heat equation even for predominantly diffusive transport. For sudden temperature rise at one film boundary, the results show that the Fourier law and the hyperbolic heat equation can significantly over- or underpredict the boundary heat flux at time scales smaller than the phonon relaxation times.

Influence of cooling on lava-flow dynamics

Experiments have been carried out to determine the effects of cooling on the flow of fluids with strongly temperature dependent viscosity. Radial viscous-gravity currents of warm glucose syrup were erupted at constant rate into a flat tank filled with a cold aqueous solution. Cold, viscous fluid accumulates at the leading edge, altering the flow shape and thickness and slowing the spreading. The flows attain constant internal temperature distributions and bulk viscosities. The value of the bulk viscosity depends on the Peclet number, which reflects the advective and diffusive heat transport properties of the flow, the flow skin viscosity, which reflects cooling, and the eruption viscosity. Our results explain why most lava flows have bulk viscosities much higher than the lava eruption viscosity. The results can be applied to understanding dynamic lava features such as flow-front thickening, front avalanches, and welded basal breccias.

Effective diffusion and nonlocal heat transport in a stochastic magnetic field.

Heat transport in a stochastic magnetic-field configuration is investigated analytically and numerically with two complementary models: a Chirikov-Taylor map model and a Gaussian random-field model. Numerical solution of the Chirikov-Taylor model shows a short-time nonlocal regime, but at large time the Rechester-Rosenbluth effective diffusion regime is confirmed numerically. The Gaussian model, for which the associated nonlocal propagator is calculated, describes this short-time behavior.

The maximum entropy production principle in climate models: Application to the faint young sun paradox

AbstractCurrent theories of stellar evolution imply that the solar luminosity was 25‐30% less than at present during early phases of the Earth's history. the response of the global annual climate to changes of the solar input is examined using the maximum entropy production (MEP) principle and a zonal energy balance model including ice‐albedo feedback. It is shown that this formulation reproduces satisfactorily the present meridional heat flux and latitudinal temperature distributions. It is found that the model predicts that the efficiency of the meridional heat transport decreases for low values of the solar constant. Consequently, if the solar irradiance is lowered, a progressive development of the polar caps and a decrease of the global surface temperature are obtained without major irreversibility in the system. A comparison with a similar model including diffusive heat transport formalism shows that the value of the critical solar luminosity causing a global glaciation is decreased when the meridional heat fluxes are determined by the MEP principle.

The x-ray-driven heating wave

The heating of matter by a source of intense x rays is studied under conditions where the energy transport in the hot material is carried by the flux of incident photons. This leads to the formation of a self-similar heating wave. Particular emphasis is given to the ablative heating wave that exists for a time interval in between supersonic heating initially and diffusive heat transport at later times. An approximate, analytic solution of the similarity equations describing the ablative heating wave is given. A power law dependence of the opacity on temperature and density is assumed, which is strictly valid for a fully ionized plasma and monochromatic incident radiation, but possibly also useful to model more complicated situations in terms of effective parameters.

The growth of compositionally stratified solid above a horizontal boundary

The compositional stratification in solid formed by cooling a binary alloy from below is investigated theoretically and experimentally. It is shown that in order to grow composite solid the boundary temperature needs to be below the eutetic temperature. Two separate cases are considered. In the first, heavy fluid is released on solidification. The solid growth is then governed by the diffusive transport of heat and composition. The resultant solid is shown to have a fixed composition until the far-field conditions change. In the second case, light fluid is released on solidification. This generates turbulent compositional convection in the melt which significantly increases the transport of heat and composition across the solid/melt interface. As a result, the fraction of heavy component in the solid initially increases, but subsequently decreases to conserve mass. A simple theoretical model, using the approximation of a flat solid/melt interface is developed; this predicts differences in the thermal flux in saturated and undersaturated melts. Laboratory experiments involving aqueous solutions of sodium carbonate cooled from below which released light fluid displayed compositional convection and stratification of the solid as predicted.

Continuous versus discontinuous albedo representations in a simple diffusive climate model

A one-dimensional annually and zonally averaged energy-balance model, with diffusive meridional heat transport and including icealbedo feedback, is considered. This type of model is found to be very sensitive to the form of albedo used. The solutions for a discontinuous step-function albedo are compared to those for a more realistic smoothly varying albedo. The smooth albedo gives a closer fit to present conditions, but the discontinuous form gives a better representation of climates in earlier epochs.