Thermal Peclet Number Research Articles

Heat and momentum transfer in liquid films with temperature-dependent viscosity

The distributions of film velocity, temperature, and thickness at the inlet of a film heat exchanger at large thermal Peclet numbers are shown to depend on a dimensionless parameter. Analytical solutions are obtained for small and large values of the parameter.

Directional solidification of Ni [sbnd]Al [sbnd]Cr [sbnd]Fe alloy

During directional solidification of engineering alloys, the formation of cellular and dendritic structures with concomitant microsegregation and microporosity is of great interest since these solidification features significantly influence mechanical properties. The critical growth rate V{sub c} at which the planar solid-liquid interface reorganizes to a periodic array of cells can be well predicted by the linear analysis of Mullins and Sekerka. This analysis was recently extended by Trivedi and Kurz for high thermal Peclet number conditions and concentrated alloys. Several theoretical models were also reported on the cellular and dendritic spacings in binary systems. According to the model of Hunt, the cellular spacing sharply increases from zero to a maximum as the growth rate increases from V{sub c} to 2V{sub c}. At higher growth rates, the cellular spacing decreases with increasing the growth rate and no discontinuity in spacing occurs at the cellular-dendritic transition. The Kurz and Fisher`s model predicts a minimum in cellular spacing near the cellular-dendritic transition that is expected to occur at the transition growth rate V{sub t} = V{sub c}/k, where k is the solute distribution coefficient. At the growth rates V > V{sub c}/k, the primary dendrite arm spacing {lambda}{sub 1} varies with the growthmore » rate and temperature gradient G according to the relationship {lambda}{sub 1} {proportional_to} V{sup {minus}0.25} G{sup {minus}0.5}. On the contrary, the model of Trivedi predicts a maximum in cellular spacing to occur near the cellular-dendritic transition and cellular structures are found to grow with smaller spacings than dendritic structures under identical growth conditions. The aim of this paper is to investigate the influence of directional solidification on the microstructure evolution in Ni-12.7Al-6.8Cr-1.8Fe (at.%) alloy. Experiments have been carried out at a constant temperature gradient over a wide range of growth rates.« less

One‐dimensional models of groundwater flow, sediment thermal history and petroleum generation within continental rift basins

AbstractWe investigate the effects of convective heat transfer on the thermal history of sediments and petroleum formation within continental rift basins using one‐dimensional mathematical modelling. The transport equations used in this study to describe vertical groundwater flow and conductive/convective heat transfer are solved by the finite element method. Sediment thermal history is quantitatively represented using first‐order rate kinetic expressions for kerogen degradation and an empirical fanning Arrhenius model for apatite fission track annealing. Petroleum generation is also represented in the model by a suite of first‐order rate kinetic expressions. The analysis provides insights into how pore fluid circulation patterns are preserved in the rock record as anomalies in palaeogeothermometric data within continental rifts. Parameters varied in the numerical experiments include the ratio of conductive to convective heat transfer (thermal Peclet number; Pe) and the composition of the disseminated organic matter in the sediment (type II and III kerogen).Quantitative results indicate that vertical groundwater flow rates on the order of a mm/yr cause a change in computed vitrinite reflectance of the rocks and a shift in the depth to oil generation by as much as 3000 m. Differences in thermal gradients between recharge and discharge areas (Pe= 0.6) also change the width of the zone of oil generation by a factor of two. Even more dramatic, however, are the large changes in predicted apatite fission track length distributions and model ages between recharge and discharge areas. For example, a sediment package buried to a depth of 2400 m over 200 Myr within the groundwater recharge column had a fission track length distribution with a computed mean and standard deviation of 12.83 μm and 0.77 μm, respectively. The fission track model age for this sediment package was 209 Ma. The same sediment package in the discharge area has a distribution with a mean track length of 5.68 μm, a standard deviation of 3.37 μm, and a fission track model age of 2.6 Ma.Transient groundwater flow simulations, in which fluid circulation ceases after a period of time within the rift basin, are also presented to illustrate how disturbances in palaeogeothermometric parameters are preserved on geological time‐scales. Vitrinite reflectance profiles require about 10 Myr to return to conductive conditions within groundwater recharge areas while the convective disturbances are preserved indefinitely along the discharge column, as long as further subsidence does not occur. Ancient groundwater flow systems are preserved as anomalies in computed apatite fission track model ages and distributions much longer after groundwater flow stops, relative to organic‐based geothermometers. Significant differences exist in model ages between recharge (145 Ma) and discharge (90 Ma) areas 200 Myr after flow has ceased. However, calculated fission track histogram distributions are virtually identical in recharge and discharge areas after about 50 Myr.Our study suggests that ancient groundwater flow systems can be detected by comparing thermochronometric data between suspected recharge and discharge areas within continental rifts. Vitrinite reflectance profiles, observed offsets in the depth to the onset of petroleum generation, and apatite fission track annealing studies are all well suited for detecting groundwater flow systems which have been relatively long lived (107 years). Apatite fission track age data are probably best suited for identifying ancient groundwater flow systems within rifts long (>200 Myr) after flow ceases.

Computer modelling of transient thermal flows of non-Newtonian fluids

In this report two axisymmetric transient thermal non-Newtonian fluid problems are studied. The first is a capillary flow model problem for a thermal power-law fluid and Graetz number up to 60, governed by a derivative temperature boundary condition. The second is a glass oven flow problem for thermal, Newtonian and power-law fluids, flowing in a complex shaped domain driven by a gravitational body force for thermal Peclet numbers up to 100. The flow domain in this case is a straight pipe with a constriction formed from an axisymmetric angled obstruction on the wall. The results obtained for these problems provide good agreement with both experimental and numerical results supplied by industrial collaborators. Of particular concern here is the nature of the transient development of the flows involved under varying material properties. To this end the code has been validated under typical industrial conditions and found to be robust up to Péclet numbers of at least 100, and involving up to 1000 degrees of freedom.

Heat: A fortran computer program for calculating 1-D conductive and advective heat transport in geological formations

Abstract A simple, accurate, numerical approximation of the one-dimensional equation of heat transport by conduction and advection is presented. The method is based on the iterative solution of an implicit, finite difference, Crank-Nicolson algorithm, featuring alternating differencing direction as a function of the thermal Peclet number, and is implemented in a documented FORTRAN code. The program allows users to evaluate how porewater flow may affect the thermal profile of permeable rock formations, under steady-state or unsteady-state boundary conditions, and with linear or nonlinear initial conditions. Several possible applications illustrate the potential usefulness of the program in first order, evaluative investigations.

Impurity effect on dendritic growth.

We consider the effects of impurities on the velocity selection of a needle crystal, in the small thermal and solutal Peclet numbers. As in the case of the growth in a pure melt, steady solutions for needle crystals are found only if surface tension is anisotropic. When anisotropy is small, the variation of ${\ensuremath{\sigma}}^{\mathrm{*}}$ with impurity concentration is found, in agreement with results given by the heuristic model of Lipton et al. [Metall. Trans. A 18, 341 (1987)].

THERMAL PARAMETER SENSITIVITY IN THE SIMULATION OF THE NON-ISOTHERMAL, NON-ADIABATIC FIXED BED CATALYTIC REACTOR—THE TWO-DIMENSIONAL HETEROGENEOUS MODEL

Utilizing a two phase (fluid-solid) heterogeneous (inter-intraphase gradient) model of the fixed bed catalytic reactor, the sensitivity of thermal transport in the axial and radial directions is numerically assessed in terms of axial and radial Peclet numbers for the fluid and solid phases, the fluid-wall and wall-solid transport coefficients and local interphase fluid-solid transport in the highly exothermic case of napthalene oxidation. Axial dispersion of heat and mass in both fluid and solid phases are shown to be of little consequence in both the steady and transient modes of operation for beds of length to particle diameter ratios normally encountered i.e. L/dp > 100. Radial temperature distribution is, in contrast, sensitive to the choice of bed solid phase effective conductivity and the fluid thermal Peclet number as well as to the wall coefficients governing fluid-wall and solid-wall heat transport at that boundary. Sensitivity of the radial temperature profiles, particularly the magnitude of the...

Morphological stability of a planar interface under rapid solidification conditions

The linear perturbation theory of Mullins and Sekerka for the stability of a planar interface is extended to the case of large thermal peclet numbers. It is shown that an absolute stability criterion for a planar interface exists for undercooled melts also. In light of these results, the conventional constitutional supercooling criterion is reexamined and a more general planar interface stability criterion is proposed which is valid for low as well as high growth rate conditions. The results of this stability analysis are applied to dendritic growth from pure undercooled melt.

Diffusion-influenced reactions and normal solutions of the Boltzmann equation

The influence of the boundary layer in the vicinity of a reactive sink on the chemical rate coefficients of diffusion-influenced reactions is studied using kinetic theory. It is argued that normal solutions to the Boltzmann equation break down at first order in P−1e, where Pe is the thermal Peclet number, for the reaction problem. When the effects of the kinetic boundary layer are consistently treated to first order in P−1e the rate coefficient which follows from the diffusion equation with the radiation boundary condition is obtained. The importance of properly treating terms of order P−1e is discussed and parallels with Stokes’ law calculations are described.