Upward-facing Plate Research Articles

Natural Convection Heat Transfer from an Isothermal Plate

Using boundary-layer theory, natural convection heat transfer formulas that are accurate over a wide range of Rayleigh numbers (Ra) were developed in the 1970s and 1980s for vertical and downward-facing plates. A comprehensive formula for upward-facing plates remained unsolved because they do not form conventional boundary-layers. From the thermodynamic constraints on heat-engine efficiency, the novel approach presented here derives formulas for natural convection heat transfer from isothermal plates. The union of four peer-reviewed data-sets spanning 1<Ra<1012 has 5.4% root-mean-squared relative error (RMSRE) from the new upward-facing heat transfer formula. Applied to downward-facing plates, this novel approach outperforms the Schulenberg (1985) formula’s 4.6% RMSRE with 3.8% on four peer-reviewed data-sets spanning 106<Ra<1012. The introduction of the harmonic mean as the characteristic length metric for vertical and downward-facing plates extends those rectangular plate formulas to other convex shapes, achieving 3.8% RMSRE on vertical disk convection from Hassani and Hollands (1987) and 3.2% from Kobus and Wedekind (1995).

Steady laminar assisted mixed convection normally to a heated horizontal plate with finite length

The flow of a fluid directed normally to a heated flat plate of finite length (two-dimensional flow) is considered in the present paper. Three cases are considered: i. both sides of the plate are heated at the same uniform temperature. ii. The upper side is heated uniformly while the lower side is insulated (upward facing plate). iii. The upper side is insulated while the lower side is uniformly heated (downward facing plate). The problem is investigated numerically with a finite volume method using the commercial code ANSYS FLUENT. The governing parameters are the Reynolds number, the Richardson number and the Prandtl number and the influence of these three parameters on the drag coefficient, the average Nusselt number and the wake length is investigated for all the considered cases. It is found that the drag coefficient, the Nusselt number and the wake length in the downward facing plate is always greater than that in the upward facing plate, for all the examined values of the Richardson, Reynolds and Prandtl number. The vertical centerline velocity above the plate and above the wake increases continuously and finally becomes identical with the velocity of a two-dimensional plume while the vertical velocity below the plate shows a maximum and then goes to zero. At very high Prandtl numbers (Pr → ∞) the buoyancy force near the plate tends to zero and the drag coefficient as well as the wake length approach asymptotically the corresponding values of pure forced convection.

경사진 평판에서의 자연대류 열전달

기울어진 평판에서 발생하는 자연대류 열전달현상을 RaL 1.69×10<SUP>11</SUP>과 7.23×10<SUP>12</SUP>에 대하여 실험적으로 연구하였다. 유사성을 이용하여 열전달실험을 물질전달 실험으로 대체하였고 물질전달계로 전기도금계를 사용하였다. 평판의 기울기는 상향수평에서 하향수평까지 10°씩 변화시켰다. 하향평판에서는 수직벽면에 대한 자연대류 열전달 상관식에서 g 대신 g cosθ로 대체함으로써 열전달계수를 구할 수 있다는 기존의 이론과 일치하는 결과를 얻었다. 상향평판의 경우 경계층이 벽면을 따라 발달되는 경우와 벽면으로부터 박리되는 2가지 영역으로 구분되는데 박리에 따른 열전달 증가를 확인하였다. 아울러 도금패턴을 이용하여 박리지점을 시각화하였고 박리지점에 대한 분석이 수행되었다.

The Hotplate Precipitation Gauge

Abstract A new instrument designed to measure precipitation, the “hotplate precipitation gauge,” is described. The instrument consists of a heated thin disk that provides a reliable, low-maintenance method to measure precipitation rate every minute without the use of a wind shield. The disk consists of two heated, thermally isolated identical aluminum plates—one facing upward and the other downward. The two plates are heated independently, and both are maintained at constant temperature above 75°C by electronic circuitry that heats the plates depending on the deviation from the set temperature. Precipitation rate is estimated by calculating the power required to either melt or evaporate snow or to evaporate rain on the upward-facing plate, compensated for wind effects by subtracting out the power on the lower, downward-facing plate. Data from the World Meteorological Organization reference standard for liquid-equivalent snowfall rate measurements, the Double Fence Intercomparison Reference (DFIR) shield system, were used as the truth to develop the hotplate algorithm. The hotplate measures the liquid-equivalent precipitation rate from 0.25 to 35 mm h−1 within the National Weather Service standard for solid precipitation measurement. The hotplate was also shown to measure wind speed during severe icing conditions and during vibration. The high update rate (precipitation rate, wind speed, and temperature every 1 min), make this an ideal gauge for real-time applications, such as aircraft deicing and road weather conditions. It serves as an accumulation gauge by integrating the 1-min rates over time. It can also be used as a rain gauge for rainfall rates up to 35 mm h−1.

Film Condensations on Horizontal and Slightly Inclined upward and downward Facing Plates

Condensation experiments were carried out at atmospheric pressure using water-cooled horizontal and slightly inclined flat plates, varying the air concentrations and the orientations (upward or downward facing). The plate was suspended in a cylindrical test section and exposed to a very slow flow of pure steam or mixtures of steam and air from underneath. For the slightly inclined cases, the test results showed good agreement with the existing studies and reproduced the typical inclined plate phenomena. For the horizontal cases, the downward facing plate showed twice as high heat transfer rates as the upward facing one. The air contained in the steam showed negligible effects for the upward facing plate but a systematic decrease in heat transfer for the downward facing one. The condensation heat transfer beneath the downward facing horizontal plate is influenced by the surface wetting characteristics.

Boiling behaviors and critical heat flux on a horizontal plate in saturated pool boiling of water at high pressures

Observations of boiling behaviors and measurements of critical heat flux (CHF) were carried out for saturated water boiling on a horizontal, upward-facing plate at pressures from atmospheric to 7 MPa. The primary bubbles diminish in size almost in inverse proportion to pressure and commence to coalesce in the very low heat flux region. The diameter of detached coalesced bubbles increases with increases in the heat flux and reaches about 10 mm even at a pressure of 5 MPa. Detachment frequency of the coalesced bubbles was unaffected by the heat flux and pressure. The CHF predicted based on the macrolayer dryout model agrees well with the measured data.

Film-wise and drop-wise condensation of steam on short inclined plates

Film-wise and drop-wise condensation experiments were carried out at atmospheric pressure varying the condensing plates, their inclinations and orientations (upward or downward facing), and the air concentrations. As expected, dropwise condensation showed much higher heat transfer rates than corresponding film-wise condensation in the pure steam cases. However, with the presence of air, both modes of condensation showed similar heat transfer rates due to the high thermal resistance of the air-rich layer. Both modes of condensation showed systematic decreases in heat transfer as the angle of the plate to the horizontal decreased and as the concentration of air increased. A noteworthy observation made during the tests on the plate orientation showed that condensation heat transfer rates on the upward facing plate were slightly higher than those beneath the downward facing plate in the pure steam cases but that the trends were reversed in the steam and air mixture cases.

Critical Heat Flux on a Horizontal Plate in Saturated Pool Boiling at High Pressure

Observation of boiling behavior and measurement of critical heat flux (CHF) were carried out for saturated water boiling on a horizontal, upward-facing plate at pressures from atmospheric to 7 MPa. The heating surface was made of nichrom with 20μm in thickness, 4 mm in width, and 27.5 mm in length. The primary bubbles diminish in size approximately with the inverse of the pressure and commence to coalesce in the very low heat flux region to form coalesced bubbles. The detached coalesced bubbles continuously increase in size with increases in the heat flux and grow to about 10 mm in equivalent diameter even at high pressure of 5 MPa. Detachment frequency of the coalesced bubbles was insensitive to the heat flux and pressure. The CHF was predicted based on the macrolayer dryout model where an empirical correlation of detachment frequency derived in the present paper and a correlation of macrolayer thickness previously proposed by the author and a coworker were used. The predicted CHF agrees fairly well with the measured values.

Film condensations of flowing mixtures of steam and air on an inclined flat plate

A programme of condensation experiments was carried out at atmospheric pressure using a water-cooled flat plate varying the air concentrations, the plate inclination and its orientation (upward or downward facing). Rates of heat transfer have been measured on a single face of the condensing plate suspended in a cylindrical test section as steam and mixtures of steam and air flowed over it. The rate of heat transfer decreased as the angle of the plate to the horizontal was reduced and as the concentration of air was increased. A notable observation was that comparison of results for the upward and downward facing cases showed that the heat transfer rates with pure steam are higher for an upward facing plate than for a downward facing one. However, with air present in the steam, this trend is reversed. The effects of plate orientation, mixture flows and buoyancy are discussed.

Free convection-radiation interaction from an isothermal plate inclined at a small angle to the horizontal

The interaction of free convection with thermal radiation in boundary layer flow from an inclined isothermal plate is studied numerically. Introducing appropriate transformations the equations governing the flow are expressed in the form of local nonsimilarity equations valid near the leading edge as well as in the downstream region. A group of transformations is also introduced such that the flow near the leading edge and far downstream can be described. Heated upward facing plates with positive and negative inclination angles are investigated. When the inclination is negative the boundary layer separates from the surface and the numerical solutions can be extended downstream past the point of separation. From the present investigation it may be concluded that the position of the separation point moves away from the leading edge with the increase of either of the thermal radiation parameter or the surface temperature parameter of the heated surface.

Enhancement of Steam Absorption into a Film of LiBr Aqueous Solution Falling over a Downward Facing Plate.

An experimental study was performed on the enhancement of steam absorption into a LiBr aqueous solution. The enhancement method proposed here is to set an absorption heat transfer plate facing downward to generate free convection within a liquid film falling over the plate. The experiment was conducted varying the tilt angle of the heat transfer plate in a range of 40 to 90 degrees, and the heat transfer coefficients were compared for both cases of the heat transfer plate facing upward and downward. It was found from the experimental results that the downward facing plate has higher heat transfer coefficient than the upward facing plate, which confirmed that free convection and mixing occur in the liquid film and enhance the absorption heat transfer in case of downward facing plate. The enhancement effect becomes remarkable as the tilt angle approaches horizontal, though the liquid film becomes thick and its thermal resistance increases.

A Numerical Study of Local and Average Natural Convection Nusselt Numbers for Simultaneous Convection Above and Below a Uniformly Heated Horizontal Thin Plate

Numerical simulations were conducted to determine local and average natural convection Nusselt numbers for uniformly heated horizontal plates with convection occurring simultaneously from upper and lower surfaces. Plate width and heating rate were used to vary the modified Rayleigh number over the range of 86 to 1.9 × 108. Upper surface Nusselt numbers were found to be smaller than corresponding lower surface Nusselt numbers. The local Nusselt number was largest at the plate edge and decreased towards the plate center for both surfaces. This variation followed approximately a minus 1/3-power law variation with the non-dimensionalized x coordinate on the upper surface for modified Rayleigh numbers greater than 104, and a minus 1/9-power law variation on the lower surface for all modified Rayleigh numbers. Comparative simulations were also performed for upward and downward facing uniformly heated plates (single sided convection). For these cases, Nusselt numbers on the upward facing plates were larger than for downward facing plates.

Film condensation on an upward facing plate with free edges

Film condensation on an upward facing plate with free edges

Free convection heat transfer from an isothermal plate with arbitrary inclination

This paper presents a new formulation for the laminar free convection from an arbitrarily inclined isothermal plate to fluids of any Prandtl number between 0.001 and infinity. A novel inclination parameterξ is proposed such that all cases of the horizontal, inclined and vertical plates can be described by a single set of transformed equations. Moreover, the self-similar equations for the limiting cases of the horizontal and vertical plates are recovered from the transformed equations by settingξ=0 andξ=1, respectively. Heated upward-facing plates with positive and negative inclination angles are investigated. A very accurate correlation equation of the local Nusselt number is developed for arbitrary inclination angle and for 0.001 ≦Pr ≦∞.

Natural convection mass transfer adjacent to horizontal plates

Experiments on natural convection adjacent to horizontal plane surfaces were performed using the naphthalene sublimation technique. By analogy, the present mass transfer experiments correspond to heat transfer at a heated isothermal upward-facing plate or at a cooled downward-facing plate. Circular, square and 7:1 rectangular planforms were employed in the tests. Overall mass transfer coefficients and Sherwood numbers were determined and correlated as a function of the Rayleigh number. A common correlation for all three planforms was attained by using characteristic lengths equal to the ratio of the surface area to the perimeter. The transfer coefficients predicted by laminar boundary layer theory fell well below the experimental data and exhibited a different dependence on the Rayleigh number. The oft-quoted empirical correlation of Fishenden and Saunders was found to be a less satisfactory representation of the present data than that of Mikheyev. In the range of lower Rayleigh numbers, the results given by a numerical finite-difference solution were very much lower than the experimental data.