Theory Of Heat Transport Research Articles

Surface conditions and Fick's law

The use of Fick's law for the description of the moisture content has been questioned for years by several scientists. A modern contribution was recently published with an interesting approach (Nakano 1994a, b). Unfortunately, these articles contained some mistakes that were corrected by another author (Babiak 1995). Parallel to that discussion, another discussion about the choice of a proper potential for the moisture transport in a hygroscopic material like wood has taken place (Bramhall 1995). In this latter reference the partial vapor pressure in the air that is in equilibrium with the material, was used as the potential for the moisture transport and it was shown that this potential is a function of the wood state. It has also been shown that this choice of potential is unique, because all other potential will contain gradients of the state variables in the description of the moisture transport (Hunter 1993). The problem with the partial pressure is that it is not directly measurable in an ordinary sorption experiment, where the weight of the material easily can be measured as a function of the time. The mean moisture content of the board is the most important quantity in drying of wood in practice and therefore, for applications the used potential must be transformed to the moisture content somewhere in the analysis in order to he useful. Fick's law is empirical but has been very successful in descriptions of transport processes. The validity of Fick's law can of course be questioned, but then the observations must clearly and unambiguously show that the real problem is the assumption of the Fick's law. This problem and similar ones have been discussed earlier, but no one seems to have been able to give a proper suggestion (Kayihan 1993). A new approach has recently been published and that is focused on the surface conditions appearing in the boundary conditions for the differential equation of Fick's law (Babiak 1995). The surface moisture content is assumed to approach equilibrium as an exponential. Another similar approach would be to introduce a surface emission factor in analogy with heat transfer in heat transport theory. This was mentioned in Babiak's letter to the editor, but it was not developed (Babiak 1995). A surface emission factor is introduced in the one dimensional case through:

Hopping theory of heat transport in disordered systems.

Heat transport is studied in a simple model system of Anderson localized optical (carrier) phonons which perform thermally activated hopping due to anharmonic interaction with delocalized acoustic phonons. The corresponding kinetic equations (rate equations) are derived by using the density-matrix formalism. The calculated hopping contribution to the heat conductivity exhibits a linear increase with temperature at lower temperatures and (depending on the choice of parameters) eventually reaches a ``saturated'' value at higher temperatures. Thus, unlike other authors, we do not need a special mechanism, such as lifetime broadening of the optical phonon states, to explain the transition to the saturation region. Furthermore, we show that particle (carrier) number nonconservation leads to a quenching of the hopping mechanism.

Electron heat transport with non-Maxwellian distributions

Measurements are presented of electron heat transport with non-Maxwellian (flattopped) distributions due to inverse bremsstrahlung absorption of intense microwaves in the University of California at Davis Aurora II device [Rogers et al., Phys. Fluids B 1, 741 (1989)]. The plasma is created by pulsed discharge in a cylindrical vacuum chamber with surface magnets arranged to create a density gradient. The ionization fraction (∼1%) is high enough that charged particle collisions are strongly dominant in the afterglow plasma. A short microwave pulse (∼2 μs) heats a region of the afterglow plasma (ne/ncr≤0.5) creating a steep axial (LT∼1–10λei) temperature gradient. Langmuir probes are used to measure the relaxation of the heat front after the microwave pulse. Time and space resolved measurements show that the isotropic component of the electron velocity distribution is flat topped (∼exp[−(v/vm)m], m≳2) in agreement with Fokker–Planck calculations using the measured density profile. Classical heat transport theory is not valid both because the isotropic component of the electron velocity distribution is flattopped and the temperature gradients are very steep.

Nonlocal electron transport in laser created plasmas

The classical linear Spitzer-Härm formula has been shown to lead to an overestimation of the electron heat flux in laser-plasma interaction experiments. We briefly review the classical theory of heat transport in a plasma, and give a simplified demonstration of the Spitzer-Härm formula. The electron heat conductivity is calculated for a large value of the ion charge Z. Correction due to a finite value of Z is evaluated with a simplified electron-electron collision operator. We then show that in a steep temperature gradient, the collisional mean free path of the electrons that transport the energy may be larger than the scale length of the temperature gradient. In this case the Spitzer-Härm formula overestimates the actual heat flux in the main part of the temperature gradient, and predicts a too small heat flux slightly away from the location of the large temperature gradient.A nonlocal macroscopic formula, which is a sort of convolution of the Spitzer-Härm heat flux by a delocalization function, is shown to accurately describe the electron heat flow in both smooth and steep temperature gradients. This nonlocal formula for the heat flow is analytically justified. A selection of slightly different delocalization functions proposed in the literature is compared to the original one and to the results of Fokker-Planck calculations of the heat flow.

Phase shifts in a Nd3+ fibre amplifier

Phase shifts due to optical pumping have been measured in a Nd3+-doped fibre amplifier. The measurements were made with a two-fibre Mach-Zehnder interferometer. It is shown that phase shifts are mainly due to fibre heating. The results are compared with heat transport theory.

Physical Vapor Transport Process in Closed Tubes

In some closed-tube systems, the growth rates (R) depend on the temperature of the growth site (Tc), but rarely on the temperature of the vapor source site (Tv). While this observation cannot be explained by a diffusion model, we give our interpretation in a heat transport theory. In general, R is proportional to both supersaturation σ and equilibrium vapor pressure P0(Tc) at the growth site. Both experimental and theoretical results show that σ in the closed tubes is proportional to the temperature gradient, but not to the differenee of the vapor pressure: P0(Tv)-P0(Tc). This shows that σ is controlled by the flux of transported heat. However, as the variation of σ is smaller than that of P0(Tc), the growth rate is highly dependent on Tc or P0 (Tc).

Theory of nonlocal heat transport in fully ionized plasma

A new analytic solution of the electron kinetic equation describing the interaction of the electromagnetic heating field with plasma is obtained in the region of plasma parameters where the Spitzer-Harm classical theory is invalid. A novel expression for the nonlocal electron thermal conductivity is derived.

Linear and nonlinear heat transport near the superfluid transition of4He

A brief summary of the present status of the renormalization-group theory of heat transport near the superfluid transition of4He is presented. This includes the thermal conductivity, second-sound damping, mutual friction coefficients, boundary resistance and nonlinear effects on the temperature profile in the presence of a finite heat current.

Estimation of bare soil evaporation using skin temperature measurements

A simple model based on the Monin-Obukhov surface layer similarity theory of heat and momentum transport can be used to predict the latent heat flux for a variety of atmospheric and soil moisture conditions. Experiments were carried out on the Campbell Tract at the University of California, Davis, from 14 September to 23 November 1990. The latent heat flux was measured precisely with a large weighing lysimeter and the surface temperature by a thermal IR transducer. The evaporation predictions and lysimeter measurements overall were in good agreement ( R 2 = 0.86), including cases of dry surface conditions. Even low daily evaporation of the order of 1 mm could be modeled with the procedure studied.

An approximate analytical theory to predict the diurnal effects of local advection

An approximate analytical theory that predicts the diurnal effects of local advection is described. Von Karman's integral method for steady-state advection is combined with the one-dimensional (vertical) time-varying heat and vapour transport theory previously derived by the author. The time-average part of the theory is in reasonably good agreement with profiles and flux densities calculated in the literature with a second-order turbulence closure model for two local advection situations. The time-average part of the theory is also in good agreement with the measured profiles of temperature and vapour density for these two situations and the measured latent heat flux density for the second situation. Diurnal variations predicted with the theory for the first situation are presented. Some improvements to the theory are suggested.

The Self-Consistent Charge Method: A Numerical Approach to Radiation-Induced Charge Transport Phenomena

Reconsidering the numerous conceptions as they have been developed in atomic physics (self-consistent field), heat and charge transport theory (carrier-enhanced and radiation-induced conductivity) and many other related fields for iteratively solving the corresponding integro-differential equation systems we come now to propose a new approach to the subject addressed in the title. This method has been implemented in a FORTRAN code, allowing for a self-consistent solution of kinetic equations on a quite broad scale. However, in treating a particular problem (irradiated semiconductor, ionisation gas detectoed etc.) it appears recommendable to employ a confined specialized version. Model calculations of a (a.c. or d.c. driven) gas ionisation chamber have been carried out to demonstrate the systematizing potential of the present approach.

Problems with porometry: measuring stomatal conductances of potentially transpiring plants

Porometer measurements of the stomatal conductances ( C s) of potentially transpiring water hyacinth plants at Phoenix, Arizona in October of 1984, May–June of 1985, and September of 1986 indicate that C s steadily drops as the vapor pressure deficit ( VPD) of the air in the measuring system's cuvette or leaf chamber rises. Utilizing this relationship to calculate the foliage-air temperature differential ( T F− T A) response of these leaves to leaf-chamber air VPD, as per the basic equations of standard heat and water vapor transport theory; we obtain a leaf-chamber “non-water-stressed baseline” that is consistent with leaf-chamber measurements of T F− T A vs. air VPD. Free-air T F− T A vs. air VPD data, on the other hand, produce a relationship that is similarly consistent with a plant stomatal conductance which is invariant with respect to the air VPD. Hence, we conclude that the very act of stomatal conductance measurement alters a potentially transpiring plant's evaporative water loss rate in such a way that, for very high air VPD conditions, the directly measured C s value (although correct for the leaf in the cuvette or leaf chamber) may be much reduced from that characteristic of comparable non-chamber-encumbered plants in the free air. We then demonstrate that this instrument-induced reduction in directly measured C s values is a unique function of the leaf-chamber IJ index, evaluated with respect to the plant's free-air non-water-stressed baseline. Similar results obtained by others for cotton suggest that this phenomenon may be quite general, and that the C s vs. air VPD interaction, believed by many to be widely operative throughout the plant kingdom, may not really exist in actual field situations.

Theory of trapped-particle-induced resistive fluid turbulence

A theory of anomalous electron heat transport, evolving from trapped-particle-induced resistive interchange modes, is proposed. The latter are a new branch of the resistive interchange-ballooning family of instabilities, destabilized when the pressure carried by the unfavorably drifting trapped particles is sufficiently large to overcome stabilizing contributions coming from favorable average curvature. Expressions for the turbulent heat diffusivity and anomalous electron thermal conductivity at saturation are derived for two regimes of trapped-particle energy: (i) a moderately energetic regime, which is ‘‘fluidlike’’ in the sense that the unstable mode grows faster than the time that it takes for particles in this energy range to precess once around the torus, and (ii) a highly energetic regime, where the trapped species has sufficiently high energy as to be able to interact resonantly with the mode. Unlike previous theories of anomalous transport, the estimates of diffusion and transport obtained here are self-consistent since the trapped particles do not ‘‘see’’ the magnetic flutter due to their rapid bounce motion. The theory is valid for moderate electron-temperature, high ion-temperature (auxiliary heated) plasmas and as such, is relevant for present- and future-generation experimental fusion devices.

Thermal performance of solar ponds under different soil conditions

This paper aims to estimate the ground heat losses from the salt gradient field solar ponds working under natural conditions. The dependence of ground heat losses upon moisture gradient, temperature gradient and ambient temperature is estimated considering the coupled heat, moisture and vapour transport theory. The required expression for the soil thermal conductivity is also developed here considering effective continuous media approximation. The validity of expression is tested by comparing the theoretical values of λ e for moist soil with those of experimental results.

Heat flux near critical density in laser-plasma interaction

A general nonlocal theory of heat transport in laser-plasma interaction experiments is presented. It is shown that the inverse bremsstrahlung absorption and the plasma expansion are responsible for heat fluxes q ib and q h which add to the heat flux due to the temperature gradient itself.

Erratum: “A Correlation Theory for Steady Natural Convective Heat Transport in Horizontal Annuli” (Journal of Heat Transfer, 1983, 105, pp. 144–150)

Erratum: “A Correlation Theory for Steady Natural Convective Heat Transport in Horizontal Annuli” (Journal of Heat Transfer, 1983, 105, pp. 144–150)

A Correlation Theory for Steady Natural Convective Heat Transport in Horizontal Annuli

A correlation theory for two-dimensional natural convective heat transport data for horizontal annuli of arbitrary cross section has been developed and applied to two configurations: (i) concentric circular cylinders and (ii) annuli formed by an inner hexagonal cylinder and an outer circular cylinder. Also embodied in the theory is the capability to predict local as well as mean heat transfer. Thermal boundary conditions of the form T′xm can be accommodated. Data for the Rayleigh number (RaR) varied from 10 to 107, Prandtl number (Pr) varied from 0.7 to 3100, and the aspect ratio (Δ′/r′, maximum annulus gap/minimum radius of inner annulus) varied from 0.5 to 2.0. Even with these large variations, the present correlation theory collapses all the experimental data for the annular geometries to a signle line. The physical problem appears to be completely specified by a single equation when the following is known: thermal boundary condition (i.e., m), the fluid (i.e., Pr), the aspect ratio, the Rayleigh number, and the geometry. This work demonstrates that the present theory is applicable to annuli of arbitrary cross section, and therefore the theory will be extended to include curvature effects and axisymmetric geometry.

Heat and mass transport in turbulent liquid jets

Available experimental data and theory for heat and mass transport in turbulent liquid jets are critically reviewed. It is shown that mass transfer in turbulent jets is an entrance region problem and that experimental data must be analyzed accordingly. Finite difference numerical solution of the entrance region problem shows that turbulent transport has a minor effect on mass transfer for the parameter range investigated. New experimental data for evaporation from turbulent jets are presented for a 4 mm dia. jet. Comparisons are made with data from various previous condensation studies, and an attempt made to explain the trends and apparent discrepancies.

Heat transfer in perfused biological tissue. I. General theory.

Green's function for heat and matter transport is calculated for an infinite medium in which a convection field v(r,t) makes a contribution to the total heat and matter current. It is given by a uniformly and absolutely convergent series in which every term is calculated from the preceding one merely by integration. The solution procedure is interpreted physically and illustrated by a simple problem in which v(r,t)=const. in space and time. Since the solution contains no intrinsic spatial symmetry, it can serve as a starting point for a theory of heat and mass transport in perfused biological tissue.

Some problems of the theory of mass and heat transport

Some problems of the theory of mass and heat transport