Sidewall Temperature Research Articles

Numerical Study of Natural Convection in Vertical Enclosures using a Novel Non-Boussinesq Algorithm

This article applies a novel non-Boussinesq numerical algorithm to solve the free-convection problem in a wide range of thin to thick vertical cavities subject to different side-wall temperatures. In this regard, the compressible flow equations are solved using a primitive incompressible method. No Boussinesq approximation and low Mach number consideration are included in the formulation. To implement the compressibility effect, the density field is calculated via the equation of state for gas. The temperature gradient is suitably varied to generate different low to high thermobuoyant fields, where the Boussinesq approximation may or may not be valid. Contrary to published works on the thin vertical cavity problem, the thin cavity is studied over a wide range of temperature gradients. The results are presented for different length-to-height ratios varying from 0.1 to 1.0. The present results are in full qualitative and quantitative agreement with those available in the literature. The quantitative comparisons show that the conduction mechanism is dominant at lower length-to-height ratios if and only if the Rayleigh number is sufficiently low. It is shown that the current formulations provide more reliable solutions than those of past works.

Density maximum effect on buoyancy-driven convection of water in a porous cavity with variable side wall temperatures

The buoyancy-driven convection in a square cavity filled with water-saturated porous medium is studied numerically. While the right and left side wall temperatures vary linearly from θa to θo and θo to θb, respectively with height and θo is the mean of θa and θb, the top and bottom walls of the cavity are thermally insulated. The Brinkman–Forchheimer extended Darcy model is considered to study the effects of density maximum, Grashof numbers, porosity and Darcy numbers on the buoyancy-induced flow and heat transfer. The finite volume method is used to discretize the governing equations, which are solved by Gauss–Seidel and successive over relaxation methods. The temperature distribution and flow fields are presented in the form of streamlines, isotherms and mid-height velocity profiles. It is found that the effect of density maximum is to slow down the natural convection and reduce the average heat transfer. The strength of convection and heat transfer rate become weak due to more flow restriction in the porous medium for small porosity.

Numerical study of boundary condition influence on convective flow and heat/mass transfer during concentrated alloy Bridgman crystal growth

This paper is devoted to the numerical investigation of the influence of growth conditions (external temperature regime, crucible design) on convection motion and heat-mass transfer in the melt and then on crystal composition, during InxGa1−xSb crystal growth by the Bridgman method. Thermocouple data of crystal growth experiments were used as boundary conditions for mathematical modelling. Calculations were performed for a two part crucible composed of BN and silica according to the experimental conditions. Numerical results show good agreement with the experimental data of the melt/crystal (m/c) interface and the crystal composition. The dependence of complex non-linear crystallization dynamics on boundary conditions, on rejection of heavy InSb, phase diagram and thermosolutal convection is also studied. As was shown in the mathematical modelling, crystal composition heterogeneity is caused by a stagnant flow zone close to the interface. According to the analysis of experimental thermocouple data, it was found that the side wall temperature gradient increased during time. Simulations showed that the time interval of the gradient increase concurred with the m/c interface passing through the crucible junction. As a result, mathematical modelling clarified that the improved homogeneity of the crystal grown after the crucible junction consists of the increase in the thermal gradient.

Natural Convection in a Square Cavity with Spatial Side-Wall Temperature Variation

ABSTRACT Laminar natural convection in a two-dimensional square cavity filled with a pure air (Pr = 0.71) is studied numerically in the present article with nonuniform side-wall temperature. The heated vertical wall is assumed to have spatial sinusoidal temperature variations about a constant mean value, which is higher than the cold side-wall temperature, while the top and the bottom walls are adiabatic. A finite-volume method is used to solve numerically the nondimensional governing equations in the vorticity–stream function formulation. The effects of the amplitude and the wave number of the heated side-wall temperature variation on the natural convection in the cavity are investigated. It is found that the average Nusselt number varies based on the hot-wall temperature. It increases with an increase in the amplitude, while the maximum average Nusselt number occurs at the wave number of k = 0.7 for Rayleigh number range 103 ≤ Ra ≤ 106. It is found that the values of maximum fluid circulation occur at a similar wave number, which produces maximum heat transfer for small values of Ra, while it occurs at higher values of wave number at high Ra.

Identification of reheat furnace temperature models from closed‐loop data—an industrial case study

AbstractThis work deals with the application of prediction error (PE) method to identify the furnace temperature models from a set of closed‐loop data. In this study, we gather a set of measurement data of the set points of the furnace zone temperatures as inputs and the furnace sidewall temperatures as outputs under a dynamic change of the slab pace rate. Owing to the complexity of its process dynamics, we assume no knowledge about the nature of the feedback mechanism. By treating the slab pace rate as an additive external signal, we show that the closed‐loop data is informative for applying a direct approach to the closed‐loop identification using the PE method, but only for a particular class of model structures. Model validation results support this analysis, in which the identified ARX, Box–Jenkins, and state‐space models are reasonably better than the identified FIR models, according to the Akaike's index and the one‐step‐ahead prediction criteria. The residual analysis reveals that the identified ARX, Box–Jenkins, and state‐space models do satisfy a 99% confidence region of its auto‐ and cross‐correlation functions. Moreover, we find out that, for the collected data, there is no significant difference in the model predictive quality when applying the MISO and MIMO PE methods using the state‐space model structure. © 2006 Curtin University of Technology and John Wiley & Sons, Ltd.

The search for slow transients, and the effect of imperfect vertical alignment, in turbulent Rayleigh–Bénard convection

We report experimental results for the influence of a tilt angle beta relative to gravity on turbulent Rayleigh-Benard convection of cylindrical samples. The measurements were made at Rayleigh numbers R up to 10^11 with two samples of height L equal to the diameter D (aspect ratio Gamma = D/L = 1). The fluid was water with a Prandtl number sigma = 4.38. In contrast to the experiences reported by Chilla et. al. (2004) for a similar sample but with Gamma = 0.5 (D = 0.5 and L = 1.0 m), we found no long relaxation times. For R = 9.4 times 10^10 we measured the Nusselt number N as a function of tilt angle beta and obtained a small beta dependence about a factor of 50 smaller than the result found by Chilla et. al. (2004) for their Gamma = 0.5 sample. We measured side-wall temperatures at eight equally spaced azimuthal locations on the horizontal mid-plane of the sample and used their cross-correlation functions to find the turn-over time of the large-scale circulation (LSC). The resulting Reynolds numbers R_e^cc were found to increase with beta. An important conclusion is that the increase of R_e^cc with beta of the LSC does not significantly influence the heat transport. Over the range 10^9 < R < 10^11 the enhancement of R_e^cc at constant beta due to the tilt could be described by a power law of R with an exponent of -1/6, consistent with a simple model that balances the additional buoyancy due to the tilt angle by the shear stress across the boundary layers. Even a small tilt angle dramatically suppressed the azimuthal meandering and the sudden reorientations characteristic of the LSC in a sample with beta = 0. The azimuthal mean of the temperature at the horizontal mid-plane within our resolution was independent of beta.

Experimental and numerical study of melting in a cylinder

Well-controlled and well-characterized experimental measurements are obtained during the melting of a moderate-Prandtl-number material ( n-eicosane) in a cylindrical enclosure heated from the side. The study aims to provide benchmark experimental measurements for validation of numerical codes. Experimental results in terms of measured temperatures and melt front locations are reported in both graphical and tabular forms. The melt front was captured photographically and its location ascertained using digital image processing techniques. To facilitate numerical validation exercises, a complete set of experimental results have been made available on a website for public access. An illustrative numerical comparison exercise was also undertaken using a multiblock finite volume method and the enthalpy method for a range of Stefan numbers. The experimental boundary conditions can be adequately represented with a constant and uniform side wall temperature, a constant and uniform lower surface temperature, and an adiabatic top wall. Very good agreement was obtained between the predictions and the experiment for Stefan numbers of up to 0.1807. The experimental results for a Stefan number of 0.0836 are recommended as being the most suitable for numerical benchmarking, since the boundary conditions are best controlled in this set of experiments.

Natural convection in a porous cavity with spatial sidewall temperature variation

PurposeTo study the natural convention in a square porous cavity induced by heating one of the sidewalls and the other sidewall is cooled, while the horizontal walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variations about a constant mean value.Design/methodology/approachThe Darcy model is used in the mathematical modeling of the natural convection in porous cavity. A finite volume method based on QUICK scheme is used to solve numerically the non‐dimensional governing equations.FindingsIt is found that the average Nusselt number varies based on the hot wall temperature. It increases with an increase in the amplitude, while the maximum average Nusselt number occurs at the wave number of k=0.75 for Rayleigh number based on the permeability of the medium of 500 and 1000 and at k=0.70 for a Rayleigh number of 10‐200.Research limitations/implicationsThe effects of the amplitude (0‐1.0) and the wave number (0‐5) of the heated sidewall temperature variation on the natural convection in the cavity are investigated for Raleigh number 10‐1000.Practical implicationsThe spatial sinusoidal temperature variation occurs in the applications when a cylindrical heater or a periodic array of heaters placed on a flat wall.Originality/valueThis paper is providing the details of the heat transfer inside the cavity which can be used in thermal design.

Thermophoretic measurements in presence of thermal stress convection in aerosols in microgravity conditions of drop tower

The aim of the work is getting reference data on thermophoretic motion eliminating gravity-induced perturbation, developing new instrumentation and procedures. A series of experiments on measuring phoretic velocities was performed in the Bremen drop tower providing 4.7 s of high quality microgravity conditions, which allowed making negligible particle sedimentation and buoyancy driven convection. Motion of aerosol particles was observed simultaneously at low resolution to control nongravity convective motion in the cell and at high resolution by the digital holographic velocimeter in order to register particle three-dimensional trajectories. By choosing appropriate cell size and experimental procedures the heat and mass transfer relaxation processes were reduced to less than 0.3 s thus allowing measurements of particle velocities during more than 4 s. Side-wall temperature creep created convective motion in the cell. Its influence was suppressed by choosing sufficiently flat cell geometry. The values of the measured thermophoretic velocities for Knudsen number in the range 0.047–0.89 were found to be between predictions of the classical models of Talbot et al [1] on one hand and Yamamoto and Ishiara [2] on the other hand. Particles of different thermal conductivities (paraffin and NaCl) had about the same velocities. No negative thermophoresis was observed at these conditions for NaCl.

Transient buoyant convection of air in an enclosure under strong magnetic effect

A numerical study is made of transient convective cool-down of air in a cylindrical container when both gravity and magnetizing force act. The magnetizing force is generated in an inhomogeneous magnetic field for an electrically non-conducting fluid with high magnetic susceptibility. Cooling of air is accomplished by abruptly lowering the temperature of the cylindrical sidewall under a strong vertical magnetic field. Comprehensive numerical computations are obtained for ranges of pertinent external parameters. The behavior of flow and temperature fields are delineated as the radius and axial position of the electrical coil are varied. When the magnetizing force is parallel to gravity, the flow is invigorated and cool-down process is facilitated. When the magnetizing force opposes the gravity, the overall cool-down process is least effective when the strength of magnetizing force is comparable to gravity.

Natural convection in a tank of oil: experimental validation of a numerical code with prescribed boundary condition

This work presents a numerical and experimental analysis of the thermal stratification inside a tank containing thermal oil. Starting from an initial condition of uniform temperature, the tank is submitted to a cooling regime in the natural convection provoked by the thermal losses to the environment. The numerical analysis is accomplished with a two-dimensional model in cylindrical coordinates with the Finite Volumes method. The program is fed with polynomials originated from experimental tests, in function of the tank height and time, prescribing the tank sidewall temperature. The bottom and the top of the tank were thermally insulated. The temperatures of the tank sidewall and centerline were measured with copper-constantan thermocouples. Results of the temperature variation at the centerline, along the time and for several tank heights, are presented. A dynamic analysis of the problem is presented through velocity fields. The numerical results show a good agreement with the experimental results.

Comparison of Vertical Soundings and Sidewall Air Temperature Measurements in a Small Alpine Basin

AbstractTethered balloon soundings from two sites on the floor of a 1-km-diameter limestone sinkhole in the eastern Alps are compared with pseudovertical temperature “soundings” from three lines of temperature dataloggers on the basin's northwest, southwest, and southeast sidewalls. Under stable nighttime conditions with low background winds, the pseudovertical profiles from all three lines were good proxies for free air temperature soundings over the basin center, with a mean nighttime cold temperature bias of about 0.4°C and a standard deviation of 0.4°C. Cold biases were highest in the upper basin where relatively warm air subsides to replace air that spills out of the basin through the lowest-altitude saddle. On a windy night, standard deviations increased to 1°–2°C. After sunrise, the varying exposures of the dataloggers to sunlight made the pseudovertical profiles less useful as proxies for free air soundings. The good correspondence between sidewall and free air temperatures during high-static-stability conditions suggests that sidewall soundings can be used to monitor temperatures, temperature gradients, and temperature inversion evolution in the sinkhole. Sidewall soundings can produce more frequent profiles at lower cost than can tethersondes or rawinsondes, and extension of these findings to other enclosed or semienclosed topographies may enhance future basic meteorological research or support applications studies in agriculture, forestry, air pollution, and land use planning.

The study on approximating the open boundary of two-dimension medium as one black wall

By means of Monte-Carlo model, the equivalent treatment of open boundary in two-dimensional rectangle furnace is introduced. Radiative equilibrium and non-radiative equilibrium problems are studied respectively. Both results indicate that if the interest zone is located in the high temperature region, the temperature of side-wall, instead of mean medium temperature over the open boundary cross-section, should be treated as the temperature of the imaginary black wall at open boundary. However, if the interest zone is located in the low temperature region, the imaginary black wall assumption will introduce some errors.

Analysis of thermal convection in a fluid-saturated porous cavity with internal heat generation

In this paper, the thermal convection flow in a fluid-saturated porous cavity with external sidewall heating and internal heat generation is studied by a semi-implicit projection finite element method. Concerned physical phenomena are constructed by impulsively switching on a uniform internal heat generation at t = 0 in a steady state flow field established by two different sidewall temperatures. Flows in the range 103 ≤ Ra I ≤ 108 and Ra E = 105 are mainly investigated for porous media ɛ = 0.4 and 10–10 < Da < 10–1. The results include the steady state flow field and heat transfer phenomena, as well as the evolution of heat transfer. According to the results, porosity demonstrates obvious influence in heat transfer as Da ≥ 10–2, and permeability significantly affects the flow field and heat transfer rate for Da < 10–2. The decrease in permeability diminishes the strength of external heating driven circulation and provides a chance for the cell driven by internal heat generation to develop. In addition, the flow in a porous medium with smaller flow restriction more quickly reaches the steady state from the instantaneously started internal heat generation.

Preparation of poly-Si films by Cat-CVD for thin film transistor

Polycrystalline silicon (poly-Si) films have been deposited on low-temperature substrates using a hot-wall type catalytic chemical vapor deposition apparatus. Average grain size of the deposited poly-Si films was 10–20 nm. Hall mobility of 2–5 cm 2 V −1 s −1 was obtained even for a sample left at ambient conditions for a month. The influence of the sidewall temperature on poly-Si film properties has been investigated. The poly-Si films have been prepared under the hot/cold-wall conditions. Comparing crystalline fractions of both films measured by Raman spectroscopy, the difference was small. The crystalline fractions of 89 and 85% were obtained for the hot- and cold-wall conditions, respectively. As for the results of attenuated total reflection Fourier-transform infrared spectroscopy, a distinct difference between the two films was found, H and O atoms were more incorporated in the films deposited under the cold-wall conditions than in the films under the hot-wall conditions.

Investigation of Blast-furnace Hearth Sidewall Erosion by Core Sample Analysis and Consideration of Campaign Operation.

The sidewall core boring of the Tobata No. 1 BF, which had been blown out in 1998, was carried out. Bricks and residue in the hearth were sampled and investigated in order to estimate the erosion and protection mechanism of the hearth sidewall. Sampled carbon bricks were observed. [1] A metal-rich layer, [2] a layer which a large amount of metal penetrated, [3] a solid layer which a small amount of metal penetrated, and [4] a weakened layer in which the block has become brittle although metal did not penetrate, [51 a sound layer were observed in this order from the furnace inside side. Na and K are widely distributed from the hot face side to the cold face side, while zinc is accumulated in a high concentration in the brittle layer. As a result of investigation of the residue in the hearth near sidewall bricks, it became apparent that the residue in the hearth is a layer mainly composed of iron with high carbon concentration. It was estimated that the solidification structure is molten iron which solidified gradually while entraining carbon sources. TiN was observed in some samples by microscopic observation. From the consideration of period and spatial distribution of temperature rise, it was estimated that flows of molten iron which move in the hearth toward tapholes are the cause of the sidewall temperature rise. The mechanism of sidewall erosion by the shrinkage of the viscous layer and solidified layer near bricks was estimated.

Effects of Sidewall Temperature on the Flow Pattern and the Bifurcation to Chaos of Rayleigh-Benard Cells in an Enclosure (Aspect Ratio of Enclosure: 6:4:1)

Experimental and numerical studies relating to the effects of sidewall temperatures on the flow pattern and the bifurcation to chaos of Rayleigh-Benard cells in a rectangular enclosure with a length: width: height aspect ratio of 6: 4: 1 are presented. Experiments were carried out using air with several Rayleigh numbers (Ra) of up to 32000. At Ra=8000 there appear three steady flow patterns consisting of the following: four transversal rolls with axes parallel to the short sidewalls, two cells, and two longitudinal rolls with axes parallel to the long sidewalls. At Ra=8200, the pattern consisting of two longitudinal rolls begins firstly to exhibit time-dependent sinuous oscillatory flow among three steady flow patterns. The resulting sinuous oscillation takes the form of a standing wave. Further increase of Ra results in a series of successive subharmonic bifurcations and eventually chaos. Furthermore, it was found that the dependence on Ra of the peak oscillation frequency f1 changes at Ra=20000 due to a change of the dynamical mode in the two oscillatory rolls. Both the two-cell pattern and the two-longitudinal-roll pattern undergo a series of successive subharmonic bifurcations, but the changes in the spatial structure exhibited by each through these bifurcations are quite different.

SUMMARY OF BENCHMARK NUMERICAL STUDIES FOR 3-D NATURAL CONVECTION IN AN AIR-FILLED ENCLOSURE

A numerical benchmark study dealing with 3-D natural convection in an air-filled cavity oriented at three different angles was held at the International Center for Heat and Mass Transfer (ICHMT) 2nd International Symposium on Advances in Computational Heat Transfer (CHT'01), May 20 - 25, 2001, in Palm Cove, Australia. The benchmark problem derives from an experimental study conducted by Leong, Hollands, and Brung involving natural convection within a differentially heated cubical cavity oriented at three different angles (φ) and subjected to four different Rayleigh numbers ( Ra ), all in the range 10 5 h Ra h 10 8 . The cube sidewall temperature varied linearly with distance from the hot face. In view of the number of test cases reported and the relatively low experimental uncertainty (about 1% of measurement), the problem appeared to be well suited as a benchmark for numerical validation. Ten teams (sets of participants) submitted papers using various mesh sizes and computational techniques. Most teams reported the existence of oscillatory solutions for cases at high Ra where the heating was primarily from below. Computed Nusselt numbers agreed with measurements at Ra and at inclinations where the heating was at least partly from the side. However, no one set of participants produced Nusselt numbers that agreed with the experimental results for all test cases.

Enclosed Buoyant Convection With Internal Heat Generation Under Oscillating Sidewall Temperature

A numerical study is made of buoyant convection in a square cavity with uniform internal heat generation q 0 '. Unsteady motions are generated by the imposition of time-periodic temperature at the right vertical sidewall, Θ = esin(ωτ). The temperature at the left sidewall is constant (Θ = 0). The Rayleigh number based on q 0 ' is large (10?≤Ra l ≤10 10 ), and the Prandtl number is 7.0 and e is moderate. Numerical solutions to the governing balance equations are abtained. The amplitude of the Nusselt number at the interior vertical lines, A(Nu*), shows two sharp peaks at the primary (ω r1 ) and secondary (ω r2 ) resonance frequencies. The numerical data for resonance frequencies are in close agreement with the theoretical predictions based on internal gravity oscillations. Details of flow- and temperature-field evolutions are depicted, and distinguishing features between the cases of ω r1 and ω r2 are scrutinized. Descriptions are given of the intensification/decaying processes of the prevailing cell structures. The extensive numerical exercises reinforce the assertion that resonance is expected when the external forcing frequency matches the modes of internal gravity oscillations. Physical rationalizations are offered in the present context.

THREE-DIMENSIONAL FLOW AND HEAT TRANSFER IN SLAG

Three-dimensional, turbulent flow and heat transfer in the slag are numerically investigated. Constant electrode heat flux is used to simulate the electrode heating as a simplified approach to flows in a slag cleaning furnace. Effects of the electrode heat flux, sidewall temperature and the heat loss rate from the slag surface on the slag flow and heat transfer are examined. Results are presented in the form of velocity vectors, temperature field, heat loss rate from the slag surface, and mean slag temperature change. Predictions reveal that the slag flow is three-dimensional, especially in the central region, and the slag is thermally stratified in most of flow domain. The predicted slag temperature is in good agreement with the plant operational temperature in the range of the electrode power input. Results show that it may be reasonable to assume a constant electrode heat flux to simulate the slag flows in the cleaning furnace.