Three-dimensional Conduction Equation Research Articles

Investigation of the micropolar lubricant and thermal effects in the slot entry hybrid journal bearings

The present article studies the combined influence of the micropolar lubricant and thermal effects in the slot entry hybrid journal bearings. Bearing performance characteristics are computed by the concurrent solution of modified Reynolds, three-dimensional micropolar energy, and three-dimensional conduction equations. Thermohydrostatic characteristics of the slot entry hybrid journal bearings have been studied vis-à-vis isothermal characteristics. The results obtained numerically indicate that isoviscous assumption of the lubricant is incorrect and the bearing performance is significantly affected by the increase in temperature. Hence, it is essential to consider the thermal effects for the bearings operating with the micropolar lubricant for reliable performance analysis of the bearings.

Numerical Simulation of Heat Transfer in a Closed Two-Phase Thermosiphon

This paper presents the results of mathematical modelling of three–dimensional heat transfer in a closed two-phase thermosyphon taking into account phase transitions. Three-dimensional conduction equation was solved by means of the finite difference method (FDM). Locally one-dimensional scheme of Samarskiy was used to approximate the differential equations. The effect of the thermosyphon height and temperature of its bottom lid on the temperature difference in the vapor section was shown.

Thermohydrostatic analysis of hybrid journal bearing compensated by constant flow valve operating with micropolar lubricant

This research article deals with numerical study of micropolar lubrication in constant flow valve compensated hole entry hybrid journal bearing by considering the thermal effects. The bearing performance characteristics are computed by the solution of modified Reynolds, three-dimensional energy, and three-dimensional conduction equations. The results obtained numerically indicate that bearing performance is significantly affected by increase in temperature. Hence it is imperative to consider the thermal effects for bearing operating with micropolar lubrication to generate realistic bearing characteristic data.

A Study of the Radiant Heat Exchange within a Controlled-Atmosphere Furnace

Transient three-dimensional heat transfer between a traversing, structured, and rectangular object and an enclosure is studied. This study investigates the heat transfer process that occurs in brazing an aluminum heat exchanger in a controlled-atmosphere furnace. A model's development is discussed with prescribed enclosure temperature boundary conditions. The program determines the radiant heat exchange between gray diffuse surfaces, and solves the three-dimensional conduction equation for a solid with a radiant heat flux boundary condition using an implicit finite-difference method. The structured object's conduction and radiant thermal properties are described by effective values. It was shown that radiative thermal properties of the traversing object and the enclosure's temperature have a strong impact on the object's temperature history. The effective thermal emissivity was found to influence the object's rate of temperature change. The enclosure's temperatures influenced the object's equilibrium temperature. Also, it was shown that the object's position and rotation can alter its temperature distribution, but not as strong as the effect of boundary conditions and thermal properties. In addition to numerical methods, experiments were performed to further understand the process.

Transient effect on the constriction resistance between spheres

Systems of contacting spheres are common in engineering applications where the heat transfer analysis can be quite cumbersome due to the transient behavior and the complex geometrical arrangement. As a result, most of the previous works, in this area, have adopted the porous media approach. However, this approach requires the length scale of the representative cell to be roughly three orders of magnitude larger than the size of the spheres. Constriction resistance relations could be useful in accurately computing the temperature distribution within systems of contacting spheres, however many of the requisite relations are not available. Thus, the objective of this study is to develop these relations. In this study, the transient, three-dimensional conduction equation was solved using a finite volume scheme and a non-uniform grid. From the resulting temperature distributions, the steady-state and transient constriction resistance of one-sphere and two-sphere systems were computed and correlated. The results also showed, for the first time, the critical parameters below which the transient variations must be considered.

CW laser machining of hard ceramics—II. Effects of multiple reflections

Beam guiding effects during laser machining of ceramics due to multiple reflections in the groove are analyzed theoretically for two extreme cases—purely specular and purely diffuse reflections. Specular reflections are valid for materials that have a smooth surface during laser evaporation (small optical roughness as compared to the laser wavelength). For such cases the material surface is divided into a number of rectangular patches using a bicubic surface representation method. The net radiative flux for these patch elements is obtained by ray tracing methods. The resulting radiative flux due to specular reflections is combined with the three-dimensional conduction equation governing conduction losses into the medium, and the resulting groove shape and depth are found through an iterative procedure. Diffuse reflections are valid for materials that have a very rough surface during material removal. To address beam coupling due to diffuse reflections, irradiation calculations employing view factor theory were combined with the three-dimensional conduction model. Considering multiple reflections results in an increased effective absorptivity and deeper grooves, accompanied by a flatter profile near the centerline and steeper slopes in the other parts of the groove cross-section. For the tested set of parameters, material removal rates are increased by up to 40% by specular reflections, and up to 70% by diffuse reflections. Experiments with hot-pressed silicon nitride ceramic showed increased beam coupling for deeper grooves (high power and/or slow scanning speeds) as predicted by considering multiple reflections. The agreement between theoretical calculations and experimental data for material removal rate and groove shape was good, if multiple reflections were assumed to be diffuse.

Three-dimensional conduction effects during scribing with a CW laser

A three-dimensio nal conduction model has been developed to predict the shape of the groove formed by partially evaporating the surface of a semi-infinite body using a moving Gaussian laser beam. The full three-dimensional conduction equation with relevant nonlinear boundary conditions is solved using the boundaryelement method, and results for groove depth and shape are compared for a variety of laser and solid parameters with a one-dimensional conduction model where conduction losses were treated in an approximate fashion using a simple integral method. As expected, it is observed that when thermal losses due to conduction are minor, the approximate one-dimensional conduction solution is very close to the three-dimensional solution (large laser scanning speeds, low thermal conductivity). The three-dimensional model is always able to predict the correct smooth groove shape along the centerplane TJ = 0. This cannot be predicted by the one-dimensional conduction model because of the neglected sideways conduction, leading to serious errors in the prediction of maximum groove depths.

Thermal Aalysis of Quench Propagation In Superconducting Coils

The transient three-dimensional conduction equation with a source term that accounts for the propagating resistive wave front has been solved for a superconducting magnet coil by the control volume finite-difference method with floating nodes. Coupled with this, the code solves the electrical and magnetic circuit equations. Because of the large number of nodes dictated by the geometric structure of the coil, an alternate direction implicit (ADI) technique was used to overcome the computer storage problem. The behavior of the propagating front and the highly nonlinear material properties limit the size of the solution time steps. A variable time step and variable number of nodes have been used to reduce the overall computational time. The results of the analysis are in excellent agreement with experimental data.