Analytical Temperature Distribution Research Articles

Analysis of flow and heat transfer at the interface region of a porous medium

Fluid flow and heat transfer at the interface region are analyzed in depth for three general and fundamental classes of problems in porous media. These are the interface region between two different porous media, the interface region between a fluid region and a porous medium, and the interface region between an impermeable medium and a porous medium. These three types of interface zones constitute a complete investigation of the interface interactions in a saturated porous medium. Detailed analytical solutions, for both the velocity and temperature distributions are derived for all of these interface conditions. The analytical temperature distributions are found in terms of confluent hypergeometric functions for two different regimes, which are found to cover almost the entire range of real fluids. The numerical and analytical results are found to be in excellent agreement. The numerical and analytical results are also checked against an empirically based hypothesis for one of the interface conditions, namely the interface between a fluid region and a porous medium, and are found to be in excellent agreement with that experimental hypothesis.

Effects of refraction on axisymmetric flame temperatures measured by holographic interferometry

Neglect of refraction can produce errors when temperature distributions in axisymmetric flames are reconstructed by Abel inversion of interferometric fringe data. This study quantifies these errors and their reduction by imaging during interferogram readout. Rays were traced through analytic temperature distributions characteristic of real flames at different equivalence ratios to determine the fringe patterns that would be observed interferometrically with and without imaging. The Abel inversion was applied to each computed fringe pattern to reconstruct the temperature distribution. Reconstructed and analytic distributions were compared to determine the error caused by using the Abel inversion. Our results indicate that proper imaging will generally be necessary to reduce reconstruction errors to below 5% in real axisymmetric flames.

A Model of the 10 Micrometer Silicate Feature in the Spectra of BN‐like IR‐Point Sources (Mitteilungen der Universitäts‐Sternwarte zu Jena Nr. 150)

AbstractA model representing the profile of the silicate absorption band at 9.8 μm in the spectra of BECKLIN‐NEUGEBAUER objects has been developed, solving the equation of radiative transfer. The model based on the condition of radiative equilibrium, on an analytical temperature distribution and on the assumption of constant density in the circumstellar shell allows the evaluation of the optical depth in the band's centre and the investigation of the effect of the temperature variation at the inner boundary of the envelope. The optical depth in the band's centre ist calculated for the BN point source.

Two-Dimensional Method For Predicting Hot Waterflood Recovery Behavior

Abstract The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two-dimensional, mathematical model of the process. Key assumptions are that no gas phase is present, and that the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. The resulting system of three partial differential equations is solved simultaneously through the use of a "leap-frog" application of standard alternating direction implicit methods for the solution of the mass-balance equations and the method of characteristics for solution of the energy-balance equation. The utility of the mathematical model is demonstrated by comparing numerical and analytic temperature distributions for hot-water bank injection and by comparing calculated with observed field behavior. Additional calculations show that hot waterflooding can recover significantly more oil than cold waterflooding, and that a hot-water bank recovers, with less energy input, nearly as much oil as continuous injection. Introduction Consistent field success with hot fluid injection processes requires good reservoir description and a thorough understanding of recovery mechanisms. The latter is fostered by a combination of well designed experimental studies and physically sound mathematical modeling. The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two- dimensional mathematical technique, indicating its validity, and demonstrating its utility for studying the effects of reservoir and operating parameters. Published experimental studies of hot fluid injection processes are few. Even if extensive data were available two considerations discourage exclusive reliance on laboratory or field work. First, because of the severity of scaling requirements, laboratory results must be interpreted with care. Second, because of the one-shot nature of field experiments - injectivity/productivity tests and pilot floods - results seldom are available over the desired range of operating conditions. These factors emphasize the need for devoting attention to mathematical modeling to complement laboratory and field work. Through the use of mathematical models, scaling uncertainties can be bridged and response can be predicted for unique combinations of reservoir and operating conditions. Numerous mathematical models developed during recent years enable us to calculate temperature distributions, thermal efficiency (or conversely, fraction of heat lost), and oil recovery behavior for hot fluid injection. Ramey and Spillette recently have provided reviews of these methods. Most models have concentrated on predicting temperature distributions and thermal efficiency; few have been directed at predicting oil recovery. Although these techniques are useful for estimating effects of reservoir parameters and operating conditions on process performance, results are limited by the assumptions made and by the methods of coupling independently solved fluid-flow and energy-balance equations. A computer-based method is presented for predicting total reservoir response to hot-water injection that obviates most simplifying assumptions. The model simulates fluid flow and heat transfer in two dimensions within a vertical cross-section spanning the oil sand and adjacent unproductive strata. Known numerical procedures are used to solve the governing partial differential equations. The mathematical model handles the effects of reservoir heterogeneity, gravity, capillarity, relative permeability and temperature-dependent fluid properties. In addition, a wide range of operating conditions can be modeled, including hot-water followed by cold-water injection. Mathematical Description of Hot-Water Injection Key assumptions in the mathematical model for hot- water injection are thatno gas phase is present andthe injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. Relative permeability and capillary pressure are assumed independent of temperature. JPT P. 627ˆ

Temperature Distributions in Drilling

An analytical temperature distribution along the cutting edge and on the flank face of a drill is obtained using Tsueda’s and Loewen and Shaw’s equations after modifications. Experimental temperature distributions are also investigated and the effects of a pilot hole and the heat sink are evaluated. Agreement between the analytical and experimental results is fairly close except near the chisel edge and near the drill periphery. The use of workpieces containing a pilot hole provides a method to account for the discrepancy between the analytical solution and the experimental results near the chisel edge while some explanation is offered to describe the discrepancy near the drill periphery.

On the temperature distribution in orthogonal machining

The measurement and calculation of tool temperature distributions in orthogonal machining is reviewed. An investigation is described in which the trial traversing thermocouple probe method previously reported by Balint and Brown [1] was further developed to obtain three-dimensional tool temperature distributions on end-, clearance- and rake-faces and, using a split-chip technique, within the chip-tool interface. Analytical temperature distributions are obtained, using a conformal transformation method and are compared with results from the above technique and those by other workers.

Axial Temperature Distribution for a Nuclear Reactor With Sinusoidal Space and Exponential Time-Varying Power Generation

Analytic temperature distributions are obtained for the fuel and coolant regions of a heterogeneous, convection-cooled reactor with axial power variation ewt sin (πz/H). The fundamental assumption in the governing differential equations is that the temperature distribution in the fuel region does not vary in the direction transverse to the coolant flow. The solutions involve two and three-parameter integrals encountered and numerically evaluated previously which are integrated herein and arranged in a form suitable for desk calculations. Closed-form expressions are developed for the final steady-state axial distributions which are applicable at times long in comparison with the characteristic temperature-response times.