F. P. Incropera

Convection heat transfer from discrete heat sources in a rectangular channel

Abstract Experiments have been performed to determine convection heat transfer from a single heat source and an in-line, four-row array of 12 heat sources which are flush mounted to one wall of a horizontal, rectangular channel. The experiments were performed with water and FC-77 for channel Reynolds numbers ranging from approximately 1000 to 14,000. Results for a single heat source are in good agreement with those obtained for the first row of the array but exceed predictions based on conventional forced-convection correlations. The average convection coefficient for the rows of the array decreases by approximately 25% from the first to the second row and by less than 5% from the third to the fourth row. The data are in good agreement with model predictions for turbulent flow but are underpredicted for laminar flow.

Experimental Investigation of Thermo-Mechanical Characteristics in Laser-Assisted Machining of Silicon Nitride Ceramics

Laser-assisted machining (LAM) of silicon nitride (Si 3 N 4 ) is evaluated for its potential to become an economically viable process in fabricating precision ceramic parts. On-line measurements of cutting force and workpiece temperature are performed, and tool wear and surface integrity are examined. Tool wear characteristics are determined as a function of workpiece temperature, which is measured on-line using a laser pyrometer Tool wear/failure mechanisms are characterized using optical microscopy while application of scanning electron microscopy to heated and machined surfaces, as well as to chips, is used to infer material removal mechanisms and the extent of damage caused by LAM. The sub-surface damage of parts produced by LAM is compared with that of typical ground parts.

The effect of free-floating dendrites and convection on macrosegregation in direct chill cast aluminum alloys: Part II: predictions for Al–Cu and Al–Mg alloys

Abstract In Part I, a binary mixture model of the DC casting process was proposed, that accounts for fluid flow in the melt and mushy zone, as well as in a slurry zone characterized by the transport of solute-depleted, free-floating dendrites. In this paper, the model is applied to the DC casting of Al–4.5 wt% Cu and Al–6.0 wt% Mg billets, and the predicted surface-to-centerline distribution of macrosegregation is consistent with trends observed in DC cast ingots. These trends include the development of negative segregation at the centerline, subsurface solute enriched and depleted regions, and positive segregation at the billet surface. Negative segregation at the centerline increased with an increase in the packing fraction at which free-floating dendrites are presumed to coalesce into a rigid dendritic structure. Likewise, negative segregation at the centerline and positive segregation in the enriched region increased with an increase in the characteristic diameter of the free-floating dendrites.

Transient, three-dimensional heat transfer model for the laser assisted machining of silicon nitride: I. Comparison of predictions with measured surface temperature histories

Abstract Laser assisted machining (LAM), in which the material is locally heated by an intense laser source prior to material removal, provides an alternative machining process with the potential to yield higher material removal rates, as well as improved control of workpiece properties and geometry, for difficult-to-machine materials such as structural ceramics. To assess the feasibility of the LAM process and to obtain an improved understanding of governing physical phenomena, experiments have been performed to determine the thermal response of a rotating silicon nitride workpiece undergoing heating by a translating CO 2 laser and material removal by a cutting tool. Using a focused laser pyrometer, surface temperature histories were measured to determine the effect of the rotational and translational speeds, the depth of cut, the laser-tool lead distance, and the laser beam diameter and power on thermal conditions. The measurements are in excellent agreement with predictions based on a transient, three-dimensional numerical solution of the heating and material removal processes. The temperature distribution within the unmachined workpiece is most strongly influenced by the laser power and laser-tool lead distance, as well as by the laser/tool translational velocity. A minimum allowable operating temperature in the material removal region corresponds to the YSiAlON glass transition temperature, below which tool fracture may occur. In a companion paper [1] , the numerical model is used to further elucidate thermal conditions associated with laser assisted machining.

Experimental Evaluation of the Laser Assisted Machining of Silicon Nitride Ceramics

To assess the feasibility of the laser assisted machining (LAM) process for the machining of difficult-to-machine materials such as structural ceramics, experiments were performed on silicon nitride workpieces for a wide range of operating conditions. Data for cutting forces and surface temperatures indicate that the lower bound of the material removal temperature for avoidance of cutting tool and/or workpiece fracture corresponds to the YSiAlON glass transition temperature (920-970°C). As temperatures near the cutting tool increase to values above the glass transition temperature, the glassy phase softens, facilitating visco-plastic flow and, correspondingly, the production of semi-continuous or continuous chips. The silicon nitride workpiece machined had a surface roughness of R a =0.39 μm at the nominal LAM operating condition. Examination of the machined surfaces and chips reveals no detectable sub-surface cracking or significant changes in | microstructure, respectively. Relative to grinding, the most significant advantage of LAM is its ability to achieve much larger material removal rates with high workpiece surface quality and reasonable levels of tool wear.

Experiments on mixed convection heat transfer for airflow in a horizontal and inclined channel

Abstract Experiments have been performed to investigate mixed convection heat transfer in the thermal entry region of a parallel plate channel heated uniformly from below. The effect of surface heat flux and channel orientation on the local Nusselt number was studied for Pr = 0.7, 125 3 6 , and 0

Extension of the continuum model for transport phenomena occurring during metal alloy solidification—I. The conservation equations

Abstract In this study, models for simulating transport phenomena occurring during solidification of a binary metal alloy are reviewed, with emphasis placed on the benefits and shortcomings of existing continuum and two-phase approaches. Linkages between the two approaches are discussed, and volume-averaging procedures inherent in the two-phase model are used to develop an extension of the continuum model which retains its computational convenience, while eliminating its inability to treat important features such as solutal undercooling, nucleation, stereological characteristics of the solid/liquid interface, solid movement in the form of floating or settling crystals, and shrinkage. Two approaches to development of a mixture momentum equation are considered, one involving evolution from the liquid momentum conservation equation and the other involving summation of the liquid and solid momentum equations. Special features of both approaches are discussed. In a companion paper, additional models are developed to account for the transport (floating and settling) of solid crystals in the melt, solutal undercooling, and nucleation.

NUMERICAL SIMULATION OF LAMINAR MIXED CONVECTION IN THE ENTRANCE REGION OF HORIZONTAL RECTANGULAR DUCTS

A laminar, three-dimensional, steady-state model has been solved to determine the nature and effect of thermally driven secondary flows in, a horizontal channel with heated top and bottom surfaces and insulated side walls. The secondary flow is characterized by ascending and descending thermals that form longitudinal vortex rolls and enhance the bottom surface heat transfer and channel friction factor by as much as 400 and 30%, respectively. Parametric calculations have been performed to determine the effect on hydrodynamic and thermal conditions of Reynolds number (100 ≤ Re ≤. 1000), Grashof number (2.5 × 105 ≤ Gr∗ ≤ 6.5 × 104), Prandtl number (Pr = 6.5 and 0.7), top-to-bottom surface heat flux ratio (−1.0 ≤ q1/qb ≤ 5.0), aspect ratio (1 ≤ A ≤ 10), and entrance velocity profile. Conditions near the bottom surface are characterized by mixed convection and are unaffected by heating at the top surface. Conversely, conditions at the top surface are dominated by forced convection and are unaffected by heating...

DEVELOPMENT OF LAMINAR MIXED CONVECTION FLOW IN A HORIZONTAL RECTANGULAR DUCT WITH UNIFORM BOTTOM HEATING

Using a vectorized finite-difference marching technique, the steady-state continuity, momentum, and energy equations are solved numerically to evaluate the effects of buoyancy-induced secondary flow on forced flow in a horizontal rectangular duct with uniform bottom heating. Combined entry region conditions are considered, and the secondary flow is found to consist of longitudinal plumes and vortices that first develop at the vertical sidewalls and subsequently propagate to interior spanwise positions. Sequential stages of the secondary flow development are computed in detail and used to interpret the nonmonotonic longitudinal distribution of the spanwise average Nusselt number. The distribution is characterized by oscillations that, under certain conditions, are damped and yield a fully developed Nusselt number that substantially exceeds the value for pure forced convection.

Laminar, mixed convection heat transfer for flow between horizontal parallel plates with asymmetric heating

Abstract An experimental study has been conducted to determine hydrodynamic and thermal conditions in laminar water flow between horizontal parallel plates with uniform, asymmetric heat fluxes. Flow visualization and temperature measurements reveal the existence of a buoyancy driven flow which strongly influences bottom plate conditions but has a weak influence on top plate conditions. Heat transfer at the top plate is dominated by forced convection, while heat transfer at the bottom plate is characterized by mixed convection and can be correlated in terms of the parameter Ra H 3 4 /Gz H for top to bottom heat fluxes less than 2. For the range of heat fluxes considered, top and bottom plate flow conditions are independent of the heat flux at the opposite plate.