Benjamin Gebhart

Organ pipe radiant modes of periodic micromachined silicon surfaces

In recent studies on small pyroelectric thermal anemometers with roughened surfaces we showed that one of the most widely used heat transfer models1,2 yielded calculated anemometer responses for flow and geometric behaviour that agreed functionally with observations, but were significantly smaller than the experimental data3–5. As the first stage in investigating the role of small structures in heat transfer, we initiated a study of emittance from deep gratings. Here we report measurements at 400 °C of infrared (3 µmλ14 µm), normal, s- and p-polarized spectral emittances of 45 µm deep, near square-wave gratings of heavily phosphorus doped (110) silicon (P content ∼5 × 1019 cm−3). The grating surface repeat scales, Λ, were 10, 14, 18 and 22µm, yielding a range of Λ/λ from 0.14 to 7.33. The s-polarization vector was parallel to the grating slots. Both s and p spectral emittances had pronounced resonant periodicities with a characteristic length of ∼42 µm. A reasonable explanation for this behaviour is the presence of standing waves in the air slots perpendicular to the silicon surface similar to those in an organ pipe. While the resonant amplitude of the s polarization does not depend significantly on Λ it does for the p polarization. No explanation for the Λ dependence of the p polarization is known.

Oxygen-enhanced/natural gas flame radiation

Abstract Total radiation measurements for oxygen-enhanced/natural gas diffusion flames are reported here. The parameters that were studied included the oxidizer composition ( Ω = 0.25−1.00 ), the burner firing rate (qf = 3−28 kW), the equivalence ratio (φ = 0.55−1.45), and the axial (Lr = 0.5−6.5) and radial (Dr = 0.4−1.0) position of the radiometer. The measured radiation ranged from 10 to 65 kW m−2. The nozzle Reynolds numbers ranged from 480 to 10 300. The location of the peak flame radiation ranged from 9 to 15% of the visible flame length. The stability limits and visible flame heights are also reported for a burner with a wide operating range.

Surface condition effects on flame impingement heat transfer

Abstract Flame impingement heating is used in many industrial applications, including the heating and melting of both glass and metal. This heating process usually comprises multiple heat transfer mechanisms, such as forced convection, thermal radiation, and thermochemical heat release. However, little experimental data are available that can be used to determine the importance of each mechanism. This information would be useful for optimizing the heating process and for developing computer models. The objective of this study was to determine the relative importance of thermal radiation and to determine how the thermochemical heat release is affected by the surface properties of the target. This study investigated the heat transfer from oxygen-enhanced, natural gas flames (15 kW) impinging normal to a water-cooled metal disk ( d b = 135 mm) segmented into concentric calorimetric rings. Polished, untreated, and blackened surfaces were used to study emissivity effects. The heat flux to the blackened and polished surfaces was the highest and lowest, respectively. The flux to untreated surfaces was between the highest and lowest fluxes. The largest difference in the flux, between the polished and blackened surfaces, was only 9.8%. Catalyticity effects were investigated by using alumina-coated (nearly noncatalytic), untreated, and platinum-coated (highly catalytic) surfaces. The heat flux to platinum-coated surfaces was the highest. The fluxes to untreated surfaces were similar to those for alumina-coated surfaces. The largest difference in the flux, between the platinum-coated and the alumina-coated surfaces, was only 12%. Therefore, both nonluminous flame radiation and the thermochemical heat release from surface catalytic reactions were relatively small fractions of the total heat flux.

Heat transfer from oxygen-enhanced/natural gas flames impinging normal to a plane surface

Abstract This study investigated the heat transfer from oxygen-enhanced/natural gas flames impinging normal to a plane surface. The objective was to determine the effects of the burner firing rate ( q f =5–25 kW), the oxidizer composition ( Ω =0.21–1.00), and the axial ( L =0.5–6.0) and radial ( R eff =0.16–1.04) positions of the surface. A round flame, from a flame-working torch burner, impinged onto a water-cooled metal disk ( d b =135 mm) that was segmented into six concentric calorimetric rings. The heat flux from the flame to the plane surface increased by 78–280% by increasing the firing rate from 5 to 25 kW. The thermal efficiency decreased with the firing rate. The heat flux increased 54% to 230% by increasing Ω from 0.30 to 1.00. For higher purity oxidizers (large Ω ), the peak flux always occurred at the stagnation point ( R eff =0.16) and the closest axial spacing ( L =0.5). For lower purity oxidizers (small Ω ), the peak flux occurred at about L =1–2 and a radial spacing of about R eff =0.6. The thermal efficiency increased with the oxidizer purity. This is the first study to investigate the range of oxidizer compositions between air ( Ω =0.21) and pure O 2 ( Ω =1.00).

A review of semi-analytical solutions for flame impingement heat transfer

Twelve experimental flame impingement heating studies are reviewed. The targets were cylinders, flat plates and hemi-nosed cylinders. Forced convection (laminar and turbulent) and thermochemical heat release, have been the most important heat transfer processes. Several semi-analytic solutions have been developed, for the heat flux to the forward stagnation point of a body of revolution. These were originally developed for aerospace applications, such as rocket re-entry into the earths atmosphere. These solutions, and many variations, have been used to simulate flame impingement heat transfer. The results of sample calculations are compared to some of the experimental measurements.

Thermodynamic and transport properties of pure and saline water

Publisher Summary This chapter presents a complete collection of the thermodynamic and transport properties of seawater. The chapter reviews the available fundamental data and correlations of both the molecular transport and thermodynamic properties of saline water for a wide range of temperature (t), salinity (s), and pressure (p). The purpose is to establish a database that could be used to achieve systemic representations of, as many as possible, the basic properties required in many areas of analysis and in calculations concerning terrestrial surface-water transport processes and circulations. The properties calculated using a density relation are coefficient of thermal expansion, coefficient of saline expansion, change in specific heat, change in enthalpy, and change in entropy. The results for the change in specific heat along with other previously reported data of other properties are used to calculate the Prandtl number. The Schmidt number is compiled solely from previously reported measurements. However, except at low temperatures and pressures, good agreement can be seen in the comparison of thermal expansion results.

Effect of pressure stress work and viscous dissipation in some natural convection flows

Abstract A regular two-parameter perturbation analysis is presented here to study the effects of both viscous dissipation and pressure stress on natural convection flows. Four different vertical flows have been analyzed, those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source on a vertical adiabatic surface, or wall-plume. For high gravity levels, stress work effects may be important for gases at very low temperatures, and for high Prandtl number liquids. Significant changes in heat transfer and flow quantities are observed even at moderate values of the perturbation parameters. For the entire range of Prandtl number values considered, the viscous dissipation term is seen to inhibit heat transfer from the surface for heated upward flows. The pressure term enhances heat transfer from the surface for lower Prandtl numbers. However, this effect is seen to reverse at Pr = 100, for both the isothermal and uniform flux surfaces. It is observed that viscous dissipation effects on heat transfer are much smaller than those due to the pressure stress, for many practical circumstances.

Vertical natural convection flows in porous media: calculations of improved accuracy

Abstract Higher-order corrections to the boundary layer solutions have been obtained for vertical natural convection flows in porous media. The analysis of Cheng and Chang [Lett. Heat Mass Transfer 6, 253–258 (1979)] has been extended to a uniform heat flux surface condition and to plane plume flows. Matched asymptotic solutions up to O(e2) have been obtained for these downstream temperature variations. For the isothermal surface condition, there was no correction in either temperature or velocity up to O(e). However, it has been found that the first eigenfunction for this condition coincides with the O(e2) term in the inner expansion. This makes the second-order correction indeterminate. For the uniform surface flux flow, the ratio of the corrected local Nusselt number to its value from the simplest boundary layer result is 1+0.3333e+0.0201e2. For the plane plume, the ratio of the downstream centerline temperature excess to its value for the simplest solution is l+0.4714e+0.4760e2, The Prandtl number is absorbed in the transformations. The new results are more accurate values of transport quantities for these flows, in the Rayleigh number range of practical interest.

The diffusion of turbulent buoyant jets

Publisher Summary This chapter focuses on the diffusion of a fully turbulent, circular buoyant jet discharged into a surrounding ambient of the same fluid. Two-dimensional trajectories are included, wherein any ambient flow is taken as parallel to the horizontal component of jet velocity. Some of the jet and/or ambient characteristics considered include buoyancy effects arising from density differences between the jet and the ambient; ambient density stratification, arising from vertical nonuniformity of temperature and/or concentration in the ambient; ambient flow conditions with respect to the jet, of differing magnitude and orientation relative to the jet; and initial jet discharge characteristics, including direction of momentum. The chapter compares the predictions of various entrainment models over a Froude number range F = 1–200, in terms of trajectories, growth, and decay; and compares flowing ambient models with each other and with some data. The chapter investigates the effects of the most simple and the more realistic conditions of stratified quiescent ambients. These comparisons are made to assess the models, relative to each other and to the very sparse data, and to show the effects of more realistic stratification modeling.

Transient and Steady-State Numerical Solutions in Natural Convection

A flat vertical plate, of finite thickness and appreciable thermal capacity, was assumed to be suddenly loaded internally with a constant and uniform flux while immersed in an extensive body of quiescent and unstratified fluid. The partial differential equations describing the conservation of mass, momentum, and energy were solved in their time-dependent forms, using a finite-difference technique. The computed transient velocity and temperature fields are in good agreement with the results of previous integral and numerical analyses and with experimental data. The final steady-state profiles are also in good agreement with the similarity solution for the uniform surface flux condition. For some conditions, with plates of small thermal capacity, the transient temperature and velocity levels locally exceeded the final steady-state distributions.