Adrienne S. Lavine

On Hyperbolic Heat Conduction and the Second Law of Thermodynamics

For situations in which the speed of thermal propagation cannot be considered infinite, a hyperbolic heat conduction equation is typically used to analyze the heat transfer. The conventional hyperbolic heat conduction equation is not consistent with the second law of thermodynamics, in the context of nonequilibrium rational thermodynamics. A modified hyperbolic type heat conduction equation, which is consistent with the second law of thermodynamics, is investigated in this paper. To solve this equation, we introduce a numerical scheme from the field of computational compressible flow. This scheme uses the characteristic properties of a hyperbolic equation and has no oscillation. By solving a model problem, we show that the conventional hyperbolic heat conduction equation can give physically wrong solutions (temperature less than absolute zero) under some conditions. The modified equation does not display these erroneous results. However, the difference between results of these two models is negligible except under extreme conditions.

Thermal aspects of grinding with CBN wheels

Abstract When grinding with CBN wheels, thermal damage is unlikely at the removal rates normally used in production. This decreased thermal damage with CBN wheels as compared with aluminum oxide wheels is usually attributed to the lower specific energies with CBN. Another contributing factor is the very high thermal conductivity of CBN, which enhances conduction into the grains. This beneficial effect may be offset by the sharpness of the CBN grains, which lowers the area over which conduct ion occurs. This paper presents a model of the thermal aspects of grinding which predicts the critical removal rate at which workpiece burn occurs. The effects of specific grinding energy, grain thermal conductivity, and wear flat area are explored. The model suggests that conduction into the CBN grains has the potential to increase the critical removal rate by a factor of 20 or more.

Analysis of fully developed opposing mixed convection between inclined parallel plates

An exact solution is presented of fully developed, laminar flow between inclined parallel plates with a uniform wall heat flux boundary condition. The flow is downward and the heat flux is into the channel, so that natural convection opposes the forced flow. The solution depends on the two parametersP1=Gr sinθ/Re andP2=Gr cosθ/Re2Pr. Four different flow reversal regimes are observed: 1) no reversal, 2) top reversal, 3) bottom reversal, and 4) top and bottom reversal. Velocity profiles, temperature profiles, wall friction, and Nusselt numbers are presented. Despite the simplicity of the problem which has been analyzed, it does display some features which have been observed in real mixed convection flows, such as flow reversal and nonmonotonic dependence on tilt angle.ZusammenfassungEs wird eine exakte Lösung für voll entwickelte laminare Strömung zwischen geneigten parallelen Platten mit einheitlichem Wand-Wärmestrom als Randbedingung dargestellt. Die Strömung ist abwärts gerichtet und der Wärmestrom führt in den Kanal, so daß die freie Konvektion der erzwungenen entgegengesetzt gerichtet ist. Die Lösung hängt von den beiden Parametern P1=Gr sinθ/Re und P2=Gr cosθ/Re2Pr ab. Vier verschiedene Bereiche der Strömungsumkehr wurden betrachtet: 1) keine Richtungsumkehr, 2) Umkehr an der Oberseite, 3) Umkehr an der Unterseite und 4) Umkehr an Ober- und Unterseite. Es wurden Geschwindigkeits- und Temperaturprofile, Wandreibung und Nusselt-Zahlen dargestellt. Trotz der Einfachheit des analysierten Problems werden einige Dinge dargestellt, welche in realer gemischter Konvektion untersucht wurden, so z.B. Strömungsumkehr und die nicht-monotone Abhängigkeit vom Schrägungswinkel.

Thermal Aspects of Grinding: Heat Transfer to Workpiece, Wheel, and Fluid

A model of heat transfer in grinding has been developed that considers heat removed from the grinding zone by the workpiece, abrasive grains, and grinding fluid. This model eliminates the need to specify the fraction of the total grinding power that enters the workpiece, or the convection coefficient due to the grinding fluid. The dependence of the workpiece temperature on the various grinding parameters has been explored.

Cutting tool temperatures in contour turning : transient analysis and experimental verification

This paper describes a model for predicting cutting tool temperatures under transient conditions. It is applicable to processes such as contour turning, in which the cutting speed, feed rate, and depth of cut may vary continuously with time. The model is intended for use in process development and trouble shooting. Therefore, emphasis is given in the model development to enable rapid computation and to avoid the need to specify parameters such as thermal contact resistances and convection coefficients which are not known in practice. Experiments were conducted to validate the predictive model. The model predictions with two different boundary conditions bound the experimental results. An example is presented which shows the utility of the model for process planning.

Coupled heat transfer to workpiece, wheel, and fluid in grinding, and the occurrence of workpiece burn

Abstract A model of heat transfer in grinding was previously developed which predicts the temperature in the grinding zone. This model is used here to predict the occurrence of film boiling of the grinding fluid, and to determine whether or not workpiece burn would subsequently occur. Both film boiling and workpiece burn are assumed to occur at critical grinding zone temperatures. The effects of various parameters are explored, such as fluid and abrasive grain types, and conventional or creep feed grinding conditions.

An exact solution for surface temperature in down grinding

A model has previously been developed for heat transfer in down grinding. A numerical solution algorithm was used to solve the system of equations. In this paper, an exact solution is found for this set of equations. The effect of the location of heat generation (i.e., at wear flats or shear planes) is explored for three typical grinding conditions: conventional grinding with aluminum oxide abrasives, creep feed grinding with aluminum oxide abrasives, and conventional grinding with cubic boron nitride (CBN) abrasives. It is found that during grinding with CBN, there is a strong effect of the assumed location of heat generation.

A Variable Heat Flux Model of Heat Transfer in Grinding: Model Development

In any grinding process, thermal damage is one of the main limitations to accelerating the completion of the product while maintaining high quality. Therefore, the objective of the present study is to understand the thermal behavior in the grinding process and possibly achieve the ultimate goal of avoiding thermal damage in the grinding process. A model previously developed is improved to analyze the heat transfer mechanisms in the grinding process. Heat generated at the interface between the abrasive grains and workpiece (i.e., the wear flat area) is considered. A conjugate heat transfer problem is then solved to predict the temperature in the grinding zone. In the previous model, all the heat fluxes were assumed to be uniformly distributed along the grinding zone. This led to a contradiction in the temperature matching condition. This reveals that the heat fluxes into each of the various materials are not uniform along the grinding zone. An improved model, accounting for the variation of the heat fluxes along the grinding zone, is presented. The temperature and heat flux distributions along the grinding zone are presented, along with comparisons to previous theoretical results.

Thermal Aspects of Grinding: The Effect of Heat Generation at the Shear Planes

Summary The model of heat transfer in the grinding zone which had been previously developed by the author has been modified to account for the fact that some of the grinding energy is generated at the shear planes. Examples are given to evaluate how much error was incurred in making the earlier simplification that all the heat is generated at the wear flat areas. For grinding with aluminum oxide wheels, it is found that the error is typically not huge, but may be significant, depending on the grinding conditions. For grinding with CBN wheels, however, the error is very important.

Simultaneously developing laminar convection in rotating isothermal square channels

A numerical analysis is conducted on laminar forced convection in the entrance region of an isothermal square duct rotating about an axis perpendicular to the duct axis. The simultaneously developing flow case is examined. Three independent parameters are introduced: Prandtl number (Pr), a combined Reynolds and rotational Reynolds number (Re ReΩ), and Rossby number (Ro). A relatively novel vorticity-velocity method along with the power law scheme is employed in the present numerical analysis. Typical developments of axial velocity, secondary flow, and temperature at various axial positions in the entrance region are presented. Local friction factor and Nusselt number variations are reported. A comparison of the numerical results with the available experimental data is also presented.