Calculations of gas thermal radiation transfer in one-dimensional planar enclosure using LBL and SNB models

Thermal radiation transfer in one-dimensional enclosure between two parallel plates filled with real gases, namely CO₂, H₂O, or their mixtures, was calculated using the line-by-line approach and the statistical narrow-band model. Line-by-line calculations were carried out using the HITEMP1995, HITRAN2004, HITRAN2008, HITEMP2010, and updated CDSD-1000 databases. This study demonstrates the importance of spectral database to the accuracy of line-by-line calculations through a systematic comparison of line-by-line results using different databases. Calculations of the statistical narrow-band model were conducted using the EM2C narrow-band database. The strong dependence of line-by-line results on the spectral database was demonstrated through several gas radiation transfer problems in planar-plate enclosure containing real gases of both isothermal or non-isothermal and uniform or non-uniform concentrations at 1 atm. Fairly significant differences were found between the line-by-line results using the HITEMP2010 database and those using older databases. Very good agreement in both the wall heat flux and the radiative source term was observed between the line-by-line results using the HITEMP2010 database and the results of the statistical narrow-band model in all the cases tested, confirming the EM2C narrow-band parameters for both H₂O and CO₂ are accurate. For cases involving CO₂ the line-by-line results using the HITEMP2010 database are in excellent agreement with those using the updated CDSD-1000 databases. The line-by-line results based on the HITEMP2010 database should be used as benchmark solutions to evaluate the accuracy of other approximate models.     

Spectrally correlated radiation and laminar forced convection in the entrance region of a circular duct

The two-dimensional combined radiative and convective transfer in emitting and absorbing real gases in the entrance region of a duct with a jump of wall temperature is studied. The axial propagation of radiation is taken into account in the analysis. The flow field and the energy equations are solved simultaneously and the radiative properties of the flowing gases, CO₂ or H₂O, are modeled by using either the narrow-band correlated-k model or the global absorption distribution function (ADF) model. The results are presented in terms of temperature and radiative power fields, and of the evolution of bulk temperatures and of heat transfer coefficients. Due to the axial component of the radiative flux, the gas is preheated or precooled before the change in wall temperature and this induces a persistent difference between the results of 1-D and 2-D radiation analyses. Some differences between CO₂ and H₂O temperature and radiative power profiles, due to the different structures of their spectra, are put in evidence. The ADF model, only suitable for gray walls, is shown to be less accurate when the gas is heated than when it is cooled.     

Updated band model parameters for H2O,CO2, CH4 and CO radiation at high temperature

Statistical narrow-band (SNB) model parameters for H₂O, CO₂, CH₄ and CO, and correlated-k (CK) parameters for H₂O and CO₂ are generated from line by line calculations and recently improved spectroscopic databases in wide temperature and spectral ranges. Results from the new parameters are compared to direct line by line calculations and to results from earlier model parameters [A. Soufiani, J. Taine, High temperature gas radiative property parameters of statistical narrow-band model for H₂O, CO₂ and CO and correlated-k (ck) model for H₂O and CO₂, Int. J. Heat Mass Transfer 40 (1997) 987–991] in terms of band averaged spectral transmissivities, Planck mean absorption coefficients, and total emissivities. The comparisons show first a good agreement between updated SNB, CK and LBL results. Significant improvements on earlier parameters are observed for H₂O and CO₂, especially at very high temperatures and path lengths. Model parameters and computer programs illustrating their implementation are provided as Supplementary data.     

Fouling in a Steam Cracker Convection Section Part 2: Coupled Tube Bank Simulation using an Improved Hybrid CFD-1D Model

Abstract

Performing an adequate fouling study for the heat exchangers in the convection section of a steam cracker requires reliable data on circumferential tube wall temperature profiles. A hybrid Computational Fluid Dynamics (CFD)-1D convection section model, developed to perform coupled flue gas/process gas side simulations of convection sections, is improved by the implementation of flue gas radiation modeling and extended to include typical tube banks. A complete naphtha cracker convection section is simulated with the improved hybrid CFD-1D model. All tubes show distinct maximum heat fluxes on the tube walls due to the high flue gas velocity. Based on the calculated circumferential heat flux profiles, the maximum heat flux value is calculated to be 1.8 times the average tube heat flux value. As computational costs associated with a hybrid CFD-1D simulation are high, a convective heat flux profile reconstruction scheme is developed. Using the scheme, circumferential heat flux profiles are reconstructed, based on the heat fluxes calculated when performing a fully 1D coupled convection section simulation. The heat flux reconstruction profile scheme enables fast retrieval of circumferential heat flux profiles and, thus, tube wall temperature profiles. Optimization and/or design of a steam cracker convection section becomes less computationally demanding.     

Radiative heat transfer from potassium seeded water gas combustion plasma

Radiative heat transfer calculations from a potassium seeded water gas combustion plasma have been made to estimate the radiative heat losses through the walls of a MHD channel. Both molecular combustion products and seed contribute significantly to the total radiation loss from a plasma. The spectral emission properties of CO₂, H₂O, CO and potassium have been taken into account. It has been shown that the contribution of CO to heat flux is very small and, thus, can be neglected. CO₂ and H₂O are the primary contributors to the radiation from the combustion products. At MHD temperatures, 55–80% of the contribution to heat flux from the combustion products comes from bands lying up to 2.7 μm in the near infrared. It has been shown that accurate knowledge of absorption cross-section data is essential to predict the radiative heat transfer from potassium. It has been estimated that 25–30% of the total radiative heat flux is from the potassium seed.     

Radiation-convection interaction in the boundary layer regime of an enclosure

The interaction of thermal radiation and free convection in the boundary layer regime of a vertical enclosure is analytically and experimentally examined. The local heat flux from the highlyreflecting heated wall in the enclosure is obtained interferometrically; the second wall is a nearly-black cooled plate. The experimental data are compared to a boundary layer type analysis based on the exponential wide-band model. Experiments are presented for pure NH₃, pureN₂, and N₂-NH₃ mixtures for pressures up to 2 bar at a temperature level near 300 K.     

Effect of gas radiation on radiative heat transfer in urban street canyon model

In this paper, we describe the results of numerical simulation of radiative heat transfer between the human body and an urban street canyon (building walls, pavement, and the sky) in the presence of participating non‐gray gas mixtures consisting of H₂O and CO₂. The ambient temperature in typical summer conditions and the concentration of gas mixtures during summer in Tokyo were assumed. Further, the parallel infinite plane model and simple urban street canyon model were used. The results show that the participating gas significantly affects the infrared radiation field in an urban street canyon. The radiation flux emitted by the participating gas is approximately 35% of the total radiation flux incident on the human body surface. This causes a homogenization of the infrared radiation field surrounding the human body. Gas radiation plays an important role in the heat transfer between the human body and the environment under hot and humid summer conditions. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20258     

Natural convection in a partially open square cavity with internal heat source: An analysis of the opening mass flow

A steady buoyancy-driven flow of air in a partially open square 2D cavity with internal heat source, adiabatic bottom and top walls, and vertical walls maintained at different constant temperatures is investigated numerically in this work. A heat source with 1% of the cavity volume is present in the center of the bottom wall. The cold right wall contains a partial opening occupying 25%, 50% or 75% of the wall. The influence of the temperature gradient between the verticals walls was analyzed for Ra_e = 10³–10⁵, while the influence of the heat source was evaluated through the relation R = Ra_i/Ra_e, investigated at between 400 and 2000. Interesting results were obtained. For a low Rayleigh number, it is found that the isotherm plots are smooth and follow a parabolic shape indicating the dominance of the heat source. But as the Ra_e increases, the flow slowly becomes dominated by the temperature difference between the walls. It is also observed that multiple strong secondary circulations are formed for fluids with a small Ra_e whereas these features are absent at higher Ra_e. The comprehensive analysis is concluded with horizontal air velocity and temperature plots for the opening. The numerical results show a significant influence of the opening on the heat transfer in the cavity.     

Estimation of heat transfer coefficients in oscillating flows: The thermoacoustic case

The classical linear thermoacoustic theory is integrated through a numerical calculus with a simple energy conservation model to allow estimates of the optimal length of thermoacoustic heat exchangers and of the magnitude of the related heat transfer coefficients between gas and solid walls. This information results from the analysis of the temperature and heat flux density distributions inside a thermally isolated thermoacoustic stack. The effects of acoustic amplitude, plate spacing, plate thickness and Reynolds number on the heat transfer characteristics are examined. The results indicate that a net heat exchange between the acoustically oscillating gas and the solid boundary takes place only within a limited distance from the stack edges. This distance is found to be an increasing function of the plate spacing in the range (0 ⩽ y₀/δ_κ ⩽ 2), becoming constant for y₀/δ_κ ⩾ 2. The calculated dimensionless convective heat transfer coefficients, the Nusselt numbers, between gas and solid wall are comparable to those evaluated from classical correlations for steady laminar flow revised under the “Time-Average Steady-Flow Equivalent” (TASFE) and “root-mean-square Reynolds number” (RMSRe) models. Numerical results agree with measurements of the heat transfer coefficient found in literature to within 20%.     

Account for variations in the H2O to CO2 molar ratio when modelling gaseous radiative heat transfer with the weighted-sum-of-grey-gases model

This work focuses on models suitable for taking into account the spectral properties of combustion gases in computationally demanding applications, such as computational fluid dynamics. One such model, which is often applied in combustion modelling, is the weighted-sum-of-grey-gases (WSGG) model. The standard formulation of this model uses parameters fitted to a wide range of temperatures, but only for specific ratios of H₂O to CO₂. Then, the model is limited to gases from fuels with a given composition of hydrogen and carbon, unless several sets of fitted parameters are used. Here, the WSGG model is modified to account for various ratios of H₂O to CO₂ concentrations. The range of molar ratios covers both oxy-fuel combustion of coal, with dry- or wet flue gas recycling, as well as combustion of natural gas. The non-grey formulation of the modified WSGG model is tested by comparing predictions of the radiative source term and wall fluxes in a gaseous domain between two infinite plates with predictions by a statistical narrow-band model. Two grey approximations are also included in the comparison, since such models are frequently used for calculation of gas radiation in comprehensive combustion computations. It is shown that the modified WSGG model significantly improves the estimation of the radiative source term compared to the grey models, while the accuracy of wall fluxes is similar to that of the grey models or better.     

Convective boiling heat transfer characteristics of CO2 in microchannels

Convective boiling heat transfer coefficients and dryout phenomena of CO₂ are investigated in rectangular microchannels whose hydraulic diameters range from 1.08 to 1.54 mm. The tests are conducted by varying the mass flux of CO₂ from 200 to 400 kg/m² s, heat flux from 10 to 20 kW/m², while maintaining saturation temperature at 0, 5 and 10 °C. Test results show that the average heat transfer coefficient of CO₂ is 53% higher than that of R134a. The effects of heat flux on the heat transfer coefficient are much significant than those of mass flux. As the mass flux increases, dryout becomes more pronounced. As the hydraulic diameter decreases from 1.54 to 1.27 mm and from 1.27 to 1.08 mm at a heat flux of 15 kW/m² and a mass flux of 300 kg/m² s, the heat transfer coefficients increase by 5% and 31%, respectively. Based on the comparison of the data from the existing models with the present data, the Cooper model and the Gorenflo model yield relatively good predictions of the measured data with mean deviations between predicted and measured data of 21.7% and 21.2%, respectively.     

NUMERICAL SIMULATION OF CHEMICAL VAPOR DEPOSITION PROCESSES UNDER VARIABLE AND CONSTANT PROPERTY APPROXIMATIONS

The chemical vapor deposition (CVD) process for silicon, using silane (SiH₄) with hydrogen (H₂) as the carrier gas, is modeled numerically using constant properties evaluated at various reference temperatures T _{r e f}. Results are compared with those from a numerical model based on variable transport properties. When the susceptor is isothermally heated, deposition rates predicted by the simplified model agree very well (5% error) with the variable property solution. A susceptor heated by means of a uniform heat flux input has a large temperature variation across the susceptor surface, yielding considerable error from the constant property model. However, a carefully chosen T _{r e f} for cases with large heat flux input, which gives rise to diffusion-controlled deposition (surface Damkohler number Da^s >> 1), is able to capture property variation effects and predict the deposition rate with reasonable accuracy. A variable property model is necessary at low heating rates, since reaction-controlled deposition (Da^s << 1) has a strong dependence arising from exponential temperature dependence of the chemical reactions and the properties. The study shows that the constant property model may be used to obtain solutions with satisfactory accuracy for a variety of operating conditions. The results and observations may be used as guidelines for future CVD reactor design and choice of appropriate operating conditions.     

Direct simulation of turbulent heat transfer in swept flow over a wire in a channel

We investigate heat transfer characteristics of a turbulent swept flow in a channel with a wire placed over one of its walls using direct numerical simulation. This geometry is a model of the flow through the wire-wrapped fuel pins, the heat exchanger, typical of many civil nuclear reactor designs. The swept flow configuration generates a recirculation bubble with net mean axial flow. A constant inward heat flux from the walls of the channel is applied. A key aspect of this flow is the presence of a high temperature region at the contact line between the wire and the channel wall, due to thermal confinement (stagnation). We analyze the variation of the temperature in the recirculation bubble at Reynolds number based on the bulk velocity along the wire-axis direction and the channel half height of 5400. Four cases are simulated with different flowrates transverse to the wire-axis direction. This configuration is topologically similar to backward-facing steps or slots with swept flow, except that the dominant flow is along the obstacle axis in the present study and the crossflow is smaller than the axial flow, i.e., the sweep angle is large. The temperature field is simulated at three different Prandtl numbers: 10^?2, 10^?1 and 1. The lower value of Prandtl number is characteristic of experimental high-temperature reactors that use a molten salt as coolant while the high value is typical of gas (or water vapor) heat exchangers. In addition, mean temperature, turbulence statistics, instantaneous wall temperature distribution and Nusselt number variation are investigated. The peak Nusselt number occurs close to the reattachment location, on the lee side of the wire, and is about 50–60% higher compared to the case without crossflow. The high temperature region follows the growth of the recirculation bubble which increases by about 65% from the lowest to highest amount of crossflow. Particular attention is devoted to the temperature distribution on the walls of the channel and the surface of the wire. The behavior of the heat-flux across the mean dividing streamline of the recirculation bubble is investigated to quantify the local heat transfer rates occurring in this region.     

Thermal protection with liquid film in turbulent mixed convection channel flows

In this numerical study, a channel flow of turbulent mixed convection of heat and mass transfer with film evaporation has been conducted. The turbulent hot air flows downward of the vertical channel and is cooled by the laminar liquid film on both sides of the channel with thermally insulated walls. The effect of gas–liquid phase coupling, variable thermophysical properties and film vaporization are considered in the analysis. In the air stream, the k–ε turbulent model has been utilized to formulate the turbulent flow. Parameters used in this study are the mass flow rate of the liquid film B, Reynolds number Re, and the free stream temperature of the hot air T_o. Results show that the heat flux was dramatically increases due to the evaporation of liquid water film. The heat transfer increases as the mass flow rate of the liquid film decreases, while the Reynolds number and inlet temperature increase, and the influences of the Re and T_o are more significant than that of the liquid flow rate. It is also found that liquid film helps lowering the heat and mass transfer rate from the hot gas in the turbulent channel, especially at the downstream.     

Determination of emittance of selective absorbing surfaces

The hemispherical emittance of the selective absorbing coating on the outside of the inner glass tube of an all-glass evacuated collector tube has been determined, using calorimetry at steady state in the temperature range 50–300°C and gas pressure range 1.0×10⁻³–1.6 Pa at the jacket between cover and inner glass tubes. Calculated gas heat flux q_c and equivalent emittance _g based on the theory of gas conduction at medium and low pressures have been determined. The calculations agree well with experiments. The experimental results indicate that heat losses of all-glass evacuated collector tubes due to gas convection and conduction are negligible when the gas pressure in the tube is less than 5×10⁻² Pa.     

Design and fabrication of thermoelectric waste heat reutilization system—possible industrial application

The current article discussed the detail design and development of an experimental test rig to derive usable energy by utilizing the waste heat energy through a heat exchanger made of Bi₂Te₃ material. The accuracy including the efficiency of the fabricated device is demonstrated further by verifying the associated parameter through a simulation model (commercial finite element package, ANSYS 15.0). To imitate the waste hot air from the industry is achieved via a heat gun and fed to the test rig for the generation of thermoelectric power. The simulation model accuracy has been demonstrated by juxtaposing the associated experimental data and computational readings. Subsequently, the feasibility and optimum range of design parameters are established by comparing the experimental and the simulation data (triggered temperature difference, voltage output, and heat flux) generated at the interface of the thermoelectric power generators. In addition, the coefficient of determination (R²) value has been evaluated statistically and verified with the current experimental results for the demonstration of the relevancy. The statistical study shows the existence of the correlation between the current experimental and the simulation model. Also, the experimental result indicates the possible implementation of the newly developed system for the recovery from the waste heat either the automobile exhaust or any other kind of dissipated heat from the industries.     

Uni-directional heat flux through the horizontal fluid layer with sinusoidal wall temperature at the top or bottom boundaries

Infinite horizontal fluid layer is considered between the top and bottom walls. Either top or bottom wall temperature is sinusoidally oscillated in terms of the constant average temperature in an opposing horizontal wall. This is the system with no temperature difference between the top and bottom walls in time-averaged sense, as studied by Kalabin et al. for a square channel. The fluid is Newtonian and Boussinesq approximation is made. The fluid layer of height 1 versus the horizontal width 1 or 4 is adopted and numerical computations are carried out for Pr = 1. The time-averaged Nusselt numbers computed both at top and bottom walls give the upward time-averaged heat flux without depending on the temperature oscillation either at the upper or lower walls. This is because the time-dependent convection plumes occur at the almost largest temperature of the bottom wall in comparison to the top wall. The time-averaged heat flux is always positive, i.e., upward, even if the time-averaged temperature difference is zero between the top and bottom walls.     

Experimental study and analysis on heat transfer coefficient of radial heat pipe

The experimental study was performed on five eccentric radial heat pipes with two outer-tube diameters.The test range can be given as follows,working fluid filling ratio Ω=44%～83%,heat flux q=10000W/m2～32000W/m2,and working temperature tv=50 ℃～120 ℃.The correlations between radial heat pipe heat transfer performance and filling ratio,heat flux,working temperature were studied in the experiment.Based on linear regression of experimental data,the relationship between heat pipe equivalent heat resistance R and working temperature tv,heat flux q and filling ratio Ω was obtained.     

Experimental study on multi-layered type of gas-to-gas heat exchanger using porous media

Based on an effective energy conversion method between flowing gas enthalpy and thermal radiation, a multi-layered type of gas-to-gas heat exchanger using porous media has been proposed. A series of experiments have been conducted for the inlet temperature of high temperature gas 300-700 °C, the optical thickness of porous media 0-15.4, the number of layers 2-5 and two types of walls (bare or finned) placed in the system. As a result, a heat recovery section is shown to play an important role in lowering an outer wall temperature of the system and at the same time in increasing the total heat recovery rate H_tot,N. In addition, it is clarified that the optical thickness of about 8 is enough to obtain sufficient H_tot,N, and the finned walls are quite effective to promote H_tot,N under the present experimental conditions.     

Numerical study on unsteady heat transfer and fluid flow in a closed cylinder of reciprocating liquid hydrogen pumps

Modeling and optimization of liquid hydrogen (LH₂) pumps require accurate in-cylinder heat transfer correlations. However, the applicability of existing correlations based on gas mediums to LH₂ remains to be verified. In this paper, the unsteady heat transfer and fluid flow in a closed LH₂ pump cylinder are numerically studied by adopting the gas spring model. The phase shifts and temperature distribution in the closed pump cylinder are investigated. LH₂ is less affected by in-cylinder heat transfer and has a more uniform temperature distribution compared to nitrogen gas, while a low-temperature zone appears near the piston face at 120 rpm. Finally, the validity of Lekic's correlation in predicting the heat flux of the LH₂ compression process in the closed pump cylinder is verified, and the efficiency decrement versus rotational speed is analyzed based on the correlation. This work would be useful for selecting a proper in-cylinder heat transfer model for predicting the thermodynamic process in reciprocating LH₂ pumps.