Surface Heating Conditions Research Articles

In situ Si Wafer Surface Temperature Measurement during Flash Lamp Annealing

Automatic emissivity compensating radiation thermometry based on polaradiometry was applied to in situ wafer surface temperature measurement on a flash lamp annealing prototype system. The developed temperature measurement system consists of a dual polarization radiation thermometer and a modulating reference light source, which were mounted on two opposing ports of the process chamber. The intense background radiation from the flash lamp was successfully suppressed by introducing a water flow layer beneath the flash lamp unit and measuring at the water absorption band of 1.95 µm. Millisecond heating and cooling of the wafer was measured for various operating conditions of the flash lamp and for various silicon wafers including wafers with microstructures. The peak temperature was compared with the sheet resistance after treatment and device properties after fabrication. Good correlation was confirmed between sheet resistance and measured peak temperature for various flash lamp intensities irrespective of the surface emissivity or heating conditions. Transistor threshold voltage showed similar correlation, which verifies the applicability of the developed thermometer system to in situ measurement during production.

Inverse estimation of surface heating condition in a three-dimensional object using conjugate gradient method

Temperature and heat flux on inaccessible surfaces can be estimated by solving an inverse heat conduction problem (IHCP) based on the measured temperature and/or heat flux on accessible surfaces. In this study, the heat flux and temperature on the front (heated) surface of a three-dimensional (3D) object is recovered using the conjugate gradient method (CGM) with temperature and heat flux measured on back surface (opposite to the heated surface). The thermal properties of the 3D object are considered to be temperature-dependent. The simulated measurement data, i.e., the temperature and heat flux on the back surface, are obtained by numerically solving a direct problem where the front surface of the object is subjected to high intensity periodic laser heat flux with a Gaussian profile. The robustness of the formulated 3D IHCP algorithm is tested for two materials. The effects of the uncertainties in thermophysical properties on the inverse solutions are also examined. Efforts are made to reduce the total number of heat flux sensors on the back surface required to recover the front-surface heating condition.

SATELLITE-MEASURED SPATIAL AND TEMPORAL CHLOROPHYLL-A VARIABILITY IN THE GULF OF TOMINI, SULAWESI

Chlorophyll-a concentration, an index of phytoplankton biomass, is an important parameter for fisheries resources and marine aquaculture development. Spatial and temporal variability of surface cholophyll-a (chl-a) concentration and water condition in the Gulf of Tomini were investigated using monthly climatologies the Sea-viewing Wide Field-of-view sensor (SeaWiFS), sea surface temperature (SST), and wind data from January 2000 to December 2007. The results showed seasonal variation of chla and SST in the Gulf of Tomini. High chl-a concentrations located in the eastern part of the gulf were observed during the southeast monsoon in August. During the northwest monsoon, chl-a concentrations were relatively low (<0.2 mg m-3) and distributed uniformly throughout most of the region. Chl-a concentrations peaked in August at every year, and chl-a concentrations were observed low in November at every year from 2000 to 2007. SSTs were relatively high (> 28oC) during the northwest monsoon, but low during the southeast monsoon. High wind speed was coincided with high chl-a concentrations. Local forcing such as sea surface heating and wind condition are the mechanisms that controlled the spatial and temporal variations of chlorophyll concentrations.

Impacts of Soil Heating Condition on Precipitation Simulations in the Weather Research and Forecasting Model

Soil temperature is a major variable in land surface models, representing soil energy status, storage, and transfer. It serves as an important factor indicating the underlying surface heating condition for weather and climate forecasts. This study utilizes the Weather Research and Forecasting (WRF) model to study the impacts of changes to the surface heating condition, derived from soil temperature observations, on regional weather simulations. Large cold biases are found in the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis project (ERA-40) soil temperatures as compared to observations. At the same time, a warm bias is found in the lower boundary assumption adopted by the Noah land surface model. In six heavy rain cases studied herein, observed soil temperatures are used to initialize the land surface model and to provide a lower boundary condition at the bottom of the model soil layer. By analyzing the impacts from the incorporation of observed soil temperatures, the following major conclusions are drawn: 1) A consistent increase in the ground heat flux is found during the day, when the observed soil temperatures are used to correct the cold bias present in ERA-40. Soil temperature changes introduced at the initial time maintain positive values but gradually decrease in magnitude with time. Sensible and latent heat fluxes and the moisture flux experience an increase during the first 6 h. 2) An increase in soil temperature impacts the air temperature through surface exchange, and near-surface moisture through evaporation. During the first two days, an increase in air temperature is seen across the region from the surface up to about 800 hPa (∼1450 m). The maximum near-surface air temperature increase is found to be, averaged over all cases, 0.5 K on the first day and 0.3 K on the second day. 3) The strength of the low-level jet is affected by the changes described above and also by the consequent changes in horizontal gradients of pressure and thermal fields. Thus, the three-dimensional circulation is affected, in addition to changes seen in the humidity and thermal fields and the locations and intensities of precipitating systems. 4) Overall results indicate that the incorporation of observed soil temperatures introduces a persistent soil heating condition that is favorable to convective development and, consequently, improves the simulation of precipitation.

The Influence of the Wall Surface Heating Conditions on Velocity Profiles of the Natural Convection in a Vertical Channel of Electronic Equipment

The Influence of the Wall Surface Heating Conditions on Velocity Profiles of the Natural Convection in a Vertical Channel of Electronic Equipment

Numerical Computation of Radiative Heating Environment for Huygens Probe Entry Flight

A trajectory-based analysis for obtaining aerodynamic heating environment for the Huygens probe is carried out using the thermochemical nonequilibrium computational fluid dynamics code. Radiative heat transfer is accounted for in computational fluid dynamics calculations where a modern multiband radiation model is employed. In this study, we first compare the radiative heat flux obtained by the ray-tracing approach in three-dimensional space with that given by the tangent-slab approximation, to determine how the difference in obtaining radiative heat flux can alter the overall aerodynamic heating environment. We then explore the radiative cooling effect on surface heat flux through radiation coupled computational fluid dynamics calculations. It is shown that the radiative heat flux value at the stagnation point obtained by the ray-tracing approach becomes about 17-19% smaller than that given by the tangent-slab approximation due to body curvature at all the chosen trajectory points. Furthermore, it is also shown that the radiative cooling effect can reduce the surface radiative heat flux by almost the same amount at the stagnation point when computational fluid dynamics calculation coupled with radiation is conducted. It is therefore confirmed that, even for the relatively lower radiative heating rate such as for the Huygens entry flight, we need to employ the ray-tracing approach instead of the tangent-slab approximation, and also need to account for radiative cooling effect through radiation coupled computational fluid dynamics calculation, to evaluate the surface heating condition accurately.

사각 채널에서 테이프에 의한 스월유동이 열전달과 마찰계수에 미치는 효과

Regionally averaged heat transfer distributions and friction factors in square channels with twisted tape inserts and with twisted tape inserts plus interrupted ribs are experimentally investigated. The effects of surface heating condition on heat transfer enhancement are also investigated. Each wall of the square channel is composed of isolated aluminum plates. The interrupted square ribs are arranged along the axial flow direction on the bottom wall only. Experimental tests are performed for Reynolds numbers ranging from 8,900 to 29,000. The results are compared with those of previous investigations for circular tube with axial interrupted ribs and twisted tape inserts.

Effect of Unheated Starting Lengths on Film Cooling Experiments

The effect of an unheated starting length upstream of a row of film cooling holes was studied experimentally to determine its effect on heat transfer coefficients downstream of the holes. Cases with a single row of cylindrical film cooling holes inclined at 35deg to the surface of a flat plate were considered at blowing ratios of 0.25, 0.5, 1.0, and 1.5. For each case, experiments were conducted to determine the film-cooling effectiveness and the Stanton number distributions in cases with the surface upstream of the holes heated and unheated. Measurements were made using an infrared camera, thermocouples, and hot and cold-wire anemometry. Ratios were computed of the Stanton number with film cooling (Stf) to corresponding Stanton numbers in cases without film cooling (Sto), but the same surface heating conditions. Contours of these ratios were qualitatively the same regardless of the upstream heating conditions, but the ratios were larger for the cases with a heating starting length. Differences were most pronounced just downstream of the holes and for the lower blowing rate cases. Even 12 diameters downstream of the holes, the Stanton number ratios were 10–15% higher with a heated starting length. At higher blowing rates the differences between the heated and unheated starting length cases were not significant. The differences in Stanton number distributions are related to jet flow structures, which vary with blowing rate.

Convective Structures in a Cold Air Outbreak over Lake Michigan during Lake-ICE

Abstract The Lake-Induced Convection Experiment provided special field data during a westerly flow cold air outbreak (CAO) on 13 January 1998, which has afforded the opportunity to examine in detail an evolving convective boundary layer. Vertical cross sections prepared from these data, extending from upstream over Wisconsin out across Lake Michigan, show the modifying effects of land–water contrast on boundary layer mixing, entrainment, heating, and moisture flux. Through this analysis, an interesting case of lake-effect airmass modification was discovered. The data show atypical differing heights in vertical mixing of heat and moisture, as well as offshore downwelling and subsidence effects in the atmosphere. Analysis shows evidence of a new observational feature, the moisture internal boundary layer (MIBL) that accords well with the often recognized thermal internal boundary layer (TIBL). The “interfacial” layer over the lake is also found to be unusually thick and moist, due in part to the upstream conditions over Wisconsin as well as the effectiveness of vertical mixing of moist plumes over the lake (also seen in the aircraft datasets presented). Results show that the atmosphere can be much more effective in the vertical mixing of moisture than heat or momentum (which mixed the same), and thus represents a significant departure from the classical bottom-up and top-down mixing formulation. Four scales of coherent structures (CSs) with differing spatial and temporal dimensions have been identified. The CSs grow in a building block fashion with buoyancy as the dominating physical mechanism for organizing the convection (even in the presence of substantial wind shear). Characteristic turbulence statistics from aircraft measurements show evidence of these multiple scales of CSs, ranging from the smallest (microscale) in the cloud-free path region near the Wisconsin shore, to the largest (mesoscale) in the snow-filled boundary layer near the Michigan shore. A large eddy simulation (LES) model has also been employed to study the effects of buoyancy and shear on the convective structures in lake-effect boundary layers. The model simulation results have been divided into two parts: 1) the general relationship of surface heat flux versus wind shear, which shows the interplay and dominance of these two competing forcing mechanisms for establishing convection patterns and geometry (i.e., rolls versus cells), and 2) a case study simulation of convection analogous to the CSs seen in the CFP region for the 13 January 1998 CAO event. Model simulations also show, under proper conditions of surface heating and wind shear, the simultaneous occurrence of differing scales of CSs and at different heights, including both cells and rolls and their coexisting patterns (based on the interplay between the effects of buoyancy and shear).

A modified sequential function specification finite element-based method for parabolic inverse heat conduction problems

A method for enhancing the stability of parabolic inverse heat conduction problems (IHCP) is presented. The investigation extends recent work on non-iterative finite element-based IHCP algorithms which, following Beck’s two-step approach, first derives a discretized standard form equation relating the instantaneous global temperature and surface heat flux vectors, and then formulates a least squares-based linear matrix normal equation in the unknown flux. In the present study, the non-iterative IHCP algorithm is stabilized using a modified form of Beck’s sequential function specification scheme in which: (i) inverse solution time steps, Δt, are set larger than the data sample rate, Δτ, and (ii) future temperatures are obtained at intervals equal to Δτ. These modifications, contrasting with the standard approach in which the computational, experimental, and future time intervals are all set equal, are designed respectively to allow for diffusive time lag (under the typical circumstance where Δτ is smaller than, or on the order of the characteristic thermal diffusion time scale), and to improve the temporal resolution and accuracy of the inverse solution. Based on validation tests using three benchmark problems, the principle findings of the study are as follows: (i) under dynamic surface heating conditions, the modified and standard methods provide comparable levels of early-time resolution; however, the modified technique is not subject to over-damped estimation (as characteristic of the standard scheme) and provides improved error suppression rates, (ii) the present method provides superior performance relative to the standard approach when subjected to data truncation and thermal measurement error, and (iii) in the nonlinear test problem considered, both approaches provide comparable levels of performance. Following validation, the technique is applied to a quenching experiment and estimated heat flux histories are compared against available analytical and experimental results.

Convection cooling of a continuously moving surface in manufacturing processes

An analysis of flow and heat transfer from a heated flat surface continuously moving in a parallel free stream of non-Newtonian fluid has been performed. This kind of problem is of practical interest in materials processing. The surface temperature is assumed to have a power-law variation. Three surface heating conditions of uniform wall temperature (UWT), variable wall temperature (VWT), and uniform surface heat flux (UHF) are considered in this study. Numerical solutions for the momentum and thermal transport between the continuous surface and the flowing non-Newtonian fluid are generated by using a finite-difference method. Velocity and temperature profiles are presented at selected values of free stream velocity using the power-law viscosity index. The friction factor and Nusselt number are illustrated for a wide range of governing parameters. For the same normalized velocity difference, the Nusselt number is increased for a shear thinning fluid but decreased for a shear thickening fluid, as compared to the Newtonian fluid. An increase in the ratio of the free stream velocity U ∞ to the wall velocity U w results in an increase in the heat transfer rate, but a decrease in the friction factor. For the same values of power-law viscosity index and the normalized velocity difference, higher values of friction factor and Nusselt number are obtained from U w> U ∞ than from U w< U ∞. Furthermore, the heat transfer rate increases with increasing the values of wall temperature exponent and the generalized Prandtl number but decreases with increasing normalized velocity difference.

The response of CAPE and CIN to tropospheric thermal variations

AbstractIn the absence of moist convection, convective available potential energy (CAPE) and convective inhibition (CIN) both respond to changes in the thermal and humidity profiles of the atmosphere. It is shown that these changes can be understood in terms of a direct effect, involving changes in the profile in the absence of parcel changes, and an indirect effect involving changes in air‐parcel evolution in a developing convective boundary layer. Succinctly, low‐wave‐number (deep) changes in the thermal profile maximize the direct influence on CAPE while higher‐wave‐number (shallower, near‐surface) thermal changes maximize the direct influence on CIN. A simple estimate of the direct influence on CAPE, which is independent of the assumptions relating to choice of parcel ascent, is shown to give accurate results.The indirect influence comes about as a result of changes in the stability of the profile just above the inversion: the stability acts as a control on the entrainment of dry air into the boundary layer under conditions of surface heating, so that a boundary layer growing into a stable lower troposphere is more humid than one growing into a less stable profile, with significantly higher equivalent potential temperature. Thus, a profile of relatively high stability just above the inversion, typically exhibiting high CIN, will also tend to allow CAPE to build up in the boundary layer quite rapidly, through a suppression of the entrainment under conditions of surface heating and boundary‐layer growth. Thus it may be said that high CIN tends to lead to the accumulation of high CAPE even in the absence of convective downdraught feedbacks. Copyright © 2002 Royal Meteorological Society.

Mixed convection cooling of a heated, continuously stretching surface

An numerical study of the flow and heat transfer characteristics associated with a heated, continuously stretching surface being cooled by a mixed convection flow has been carried out. The relevant heat transfer mechanisms are of interest in a wide variety of practical applications, such as hot rolling, continuous casting, extrusion, and drawing. The surface velocity of the continuously stretching sheet was assumed to vary according to a power-law form, that is, u w (x)=Cx p . Two conditions of surface heating were considered, a variable wall temperature (VWT) in the form T w (x)−T ∞=Ax n and a variable surface heat flux (VHF) in the form q w (x)=Bx m . The governing differential equations are transformed by introducing proper nonsimilarity variables and solved numerically using a procedure based on finite difference approximations. Results for the local Nusselt number and the local friction coefficient are obtained for a wide range of governing parameters, such as the surface velocity parameter p, the wall temperature exponent n, the surface heat flux exponent m, the buoyancy force parameters (ξ for the VWT case and χ for the VHF case), and Prandtl number of the fluid. It is found that the local Nusselt number is increased with increasing the velocity exponent parameter p for the VWT case, while the opposite trend is observed for the VHF case. The local friction coefficient is increased for a decelerated stretching surface, while it is decreased for an accelerated stretching surface. Also, appreciable effects of the buoyancy force on the local Nusselt number and the local friction coefficient are observed for both VWT and VHF cases, as expected.

Turbulent Heat Transfer Enhancement and Surface Heating Effect in Square Channels with Wavy, and Twisted Tape Inserts with Interrupted Ribs

Regionally averaged heat transfer distributions and friction factors in square channels with hemi-circular wavy tape, hemi-triangular wavy tape, twisted tape inserts, and twisted tape inserts plus interrupted ribs are investigated. The effect of surface heating condition on heat transfer enhancement is also investigated. Each wall of the square channel is composed of isolated copper sections. Regionally averaged Nusselt number ratio, channel averaged Nusselt number ratio, and friction factor ratio in turbulent air flows are presented for Reynolds numbers from 10,000 to 70,000. The results show that uneven surface heating enhances the heat transfer coefficient over uniform heating condition. Square channels with hemi-circular wavy tape (δ/D = 0.1) inserts produce a heat transfer coefficient three times higher than twisted tape inserts (H/D = 6) with almost 25 times the pressure drop penalty. Square channels with hemi-triangular or hemi-circular wavy tape (δ/D = 0.25) inserts produce almost a 2.5 times higher heat transfer coefficient than twisted tape inserts with 5 to 6 times pressure drop penalty. Square channels with twisted tape inserts plus interrupted ribs (e/D = 0.33) produce two times the heat transfer augmentation with four times pressure drop penalty over twisted tape inserts only. Square channels with twisted tape inserts plus interrupted ribs (e/D = 0.33) show the best overall heat transfer performance over other configurations.

An asymptotic model of work roll heat transfer in strip rolling

An asymptotic model of work roll heat transfer is developed using a multiple time scale approach. The model is appropriate under typical high Peclet number rolling conditions and provides a unified framework for relating previous roll heat transfer models. The solution consists of a fast time scale thermal boundary layer near the roll surface, along with a slow time scale core heat transfer problem. Several features of the model are illustrated. First, boundary layer behavior is examined under steady and dynamic conditions. Here, the decay rate for boundary layer transients is determined and theoretical steady-state temperature distributions are compared against previously reported experimental data. Heat transfer within the core is then considered under relatively general surface heating conditions. In the special case where the surface heat flux is constant, core temperatures are shown to increase linearly with time. In the last illustration, the model is used to obtain inverse estimates of circumferentially varying roll surface heat flux and temperature distributions. In this case, comparisons are made with the finite difference-based inverse estimates recently reported by Huang et al., International Journal of Heat and Mass Transfer, 1995, 38, 1019–1031.

Transient free convection past a semi‐infinite vertical plate with variable surface temperature

Presents a finite‐difference solution to transient free convection flow past a semi‐infinite vertical plate in which the plate temperature T¢w(x) varies as the power of the axial co‐ordinate in the form T¢• + axn. Gives numerical results for fluids with Prandtl numbers Pr = 0.7 (air) and Pr = 7 (water) for three representative exponent values under non‐uniform surface heating conditions. Finds that the time to reach the steady‐state increases as the value of n or Pr increases. The steady‐state local skin‐friction falls by increasing the exponent n and Pr; however, the steady‐state local Nusselt number increases with n at a distance along the plate far away from the leading edge but decreases with increasing n near the leading edge of the plate. Also, the average Nusselt number increases and the average skin‐friction decreases as n increases because of enhanced heating of the plate.

An ocean large‐eddy simulation of Langmuir circulations and convection in the surface mixed layer

Numerical experiments were performed using a three‐dimensional large‐eddy simulation model of the ocean surface mixed layer that includes the Craik‐Leibovich vortex force [Craik 1977; Leibovich 1977] to parameterize the interaction of surface waves with mean currents. Results from the experiments show that the vortex force generates Langmuir circulations that can dominate vertical mixing. The simulated vertical velocity fields show linear, small‐scale, coherent structures near the surface that extend downwind across the model domain. In the interior of the mixed layer, scales of motion increase to eddy sizes that are roughly equivalent to the mixed‐layer depth. Cases with the vortex force have stronger circulations near the surface in contrast to cases with only heat flux and wind stress, particularly when the heat flux is positive. Calculations of the velocity variance and turbulence dissipation rates for cases with and without the vortex force, surface cooling, and wind stress indicate that wave‐current interactions are a dominant mixing process in the upper mixed layer. Heat flux calculations show that the entrainment rate at the mixed‐layer base can be up to two times greater when the vortex force is included. In a case with reduced wind stress, turbulence dissipation rates remained high near the surface because of the vortex force interaction with preexisting inertial currents. In deep mixed layers (∼250 m) the simulations show that Langmuir circulations can vertically transport water 145 m during conditions of surface heating. Observations of turbulence dissipation rates and the vertical temperature structure support the model results.

MIXED CONVECTION OVER NONISOTHERMAL HORIZONTAL SURFACES IN A POROUS MEDIUM: THE ENTIRE REGIME”“

ABSTRACT Flow and heat transfer characteristics of mixed convection from horizontal surfaces in a saturated porous medium are investigated. Two conditions of surface heating were considered, a variable wall temperature (VWT) in the form Tw(x) — T∞ = axn and a variable surface heat flux (VHF) in the form qw(x) = bxm. Two different nonsimilarity parameters for VWT and VHF cases, respectively, due to the nonuniform heating conditions, are found by nondimensionalizing the governing equations. The nonsimilarity parameters cover the entire regime of mixed convection from the pure forced convection limit at X = 1 (or X* = 1) to the pure free convection limit at X = 0 (or X* = 0). The resulting transformed governing equations are solved by a finite difference scheme. Numerical results for both VWT and VHT boundary conditions, including velocity and temperature profiles and local Nusselt numbers, are presented for selected values of the exponents n and m. Simple and accurate correlation equations valid for the entire mixed convection regime are also presented for the local and average Nusselt numbers.

Influence of Surface Heating Condition on Local Heat Transfer in a Rotating Square Channel With Smooth Walls and Radial Outward Flow

The effect of a surface heating condition on the local heat transfer coefficient in a rotating square channel with smooth walls and radial outward flow was investigated for Reynolds numbers from 2500 to 25,000 and rotation numbers from 0 to 0.352. The square channel, composed of six isolated copper sections, has a length-to-hydraulic diameter ratio of 12. The mean rotating radius to the channel hydraulic diameter ratio is kept at a constant value of 30. Four surface heating conditions were tested: (1) four walls at uniform temperature, (2) temperature ratio of leading surface to side wall and trailing surface to side wall is 1.05 and 1.10, respectively, (3) trailing surface hot and remaining three walls cold, and (4) leading surface hot and remaining three walls cold. The results show that the heat transfer coefficients on the leading surface are much lower than that of the trailing surface due to rotation. For case (1) of four walls at uniform temperature, the leading surface heat transfer coefficient decreases and then increases with increasing rotation numbers, and the trailing surface heat transfer coefficient increases monotonically with rotation numbers. However, the trailing surface heat transfer coefficients for cases (2) and (3) are slightly lower than case (1), and the leading surface heat transfer coefficients for cases (2) and (4) are significantly higher than for case (1). The results suggest that the local wall heating condition creates the local buoyancy forces, which reduce the effects of the bulk buoyancy and Coriolis forces. Therefore, the local heat transfer coefficients on the leading and trailing surfaces are altered by the surface local heating condition.

Distribution of the brightness temperature of land surfaces determined from AVHRR data

Abstract The surface temperature of the Earth is a very important climate parameter. With remote sensing techniques its global distribution can be derived with good temporal and spatial resolution. The 10·7 μm and ll·9 μm channels of the Advanced Very High Resolution Radiometer (AVHRR) aboard the NOAA satellites provide information for monitoring the surface temperature. In principle, the sea surface temperature (SST) can be obtained twice a day with the split window algorithm. An algorithm has been developed to determine the brightness temperature of arbitrary surfaces from the data of one AVHRR channel. It takes into account the dominant effects as scan angle dependency, surface heating and different atmospheric conditions. Neglecting one of these effects causes errors that are bigger than those due to unknown emissivity of natural surfaces of the Earth, Atmospheric parameters are taken from actual radiosonde data. Land surface temperatures can be determined at least four times a day, in high latitude r...