Numerical investigation of heat and mass transfer during the desorption process of an Mg2Ni–H2 reactor

In this paper, a numerical study of coupled heat and mass transfer during the desorption process of metal–hydrogen reactor (Mg₂Ni–H₂), is presented. Analytical expressions describing, the reaction kinetic and the equilibrium pressure of the Mg₂Ni-H₂ system have been determined and integrated into a theoretical model that describes the dynamic behavior of the reactor. This model, which takes into account radiative heat transfer, is solved by the control volume finite element method (CVFEM). The numerical simulation is used to present the time–space evolutions of the temperature and the hydride density within the reactor and to evaluate the effect of radiative heat transfer and the governing operating parameters (outlet pressure, temperature of heating fluid, heat exchange coefficient) on the dynamic behavior of the reactor. In addition, a new geometric configuration of the reactor is proposed and simulated.     

WSGG models for radiative heat transfer calculations in hydrogen and hydrogen-mixture flames at various pressures

Radiative heat transfer strongly influences pollutant emission prediction in combustion systems. In this work, the weighted sum of gray gas (WSGG) models have been developed for calculating radiative heat transfer in hydrogen and hydrogen-mixture flames. The total pressure effect on cut-off width of the Lorentz line profile is analyzed and properly considered in the line by line (LBL) calculations. Based on the LBL benchmark results, two sets of WSGG model correlations have been proposed for H₂O and its mixture with CO₂ at a molar ratio (Mr) of 3, representing the typical combustion products of the hydrogen and a hydrogen-rich mixture (e.g., 50% hydrogen and 50% methane). The WSGG models are applicable and accurate with a total pressure ranging from 1 to 60 atm. Partial pressure is explicitly applied as an independent variable in the model coefficients to account for its nonlinear effect on gas emissivity, which is particularly important for a participating gas medium with a large amount of H₂O at a total pressure below 5 atm. Detailed studies are carried out to solve radiative heat transfer in non-isothermal and non-homogeneous gas media at different conditions. Results show improvement over the existing WSGG models at the atmospheric pressure and have good agreement with LBL solutions under various conditions.     

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.     

Monte Carlo modeling of radiative transfer in a turbulent sooty flame

The calculation of radiative transfer within a sooty turbulent ethylene-air diffusion jet flame has been carried out by using a Monte Carlo method and an accurate CK model for the gases. The influence of the turbulence-radiation interaction (TRI) has been studied. In the TRI modeling, the radiative properties of the assumed homogeneous turbulent structures are randomly obtained from a multidimensional probability density function (PDF) of the reaction progress variable, of the mixture ratio and of the soot volume fraction. This joint PDF is obtained from an Eulerian-Lagrangian turbulent combustion model and the sizes of the turbulent structures are directly derived from a k-? model. In the considered flame, the TRI effect is an increase of the radiative heat loss by about 30%. The radiative heat loss becomes almost equal to one-third of the chemical heat release. Soot particles play the most important role in the global radiative heat loss but the influence of gaseous species like CO₂ and H₂O can be important in the local energy balance.     

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.     

Numerical investigation of coupled natural convection and radiation in a differentially heated cubic cavity filled with humid air. Effects of the cavity size

A numerical study of natural convection with surface and air/H₂O mixture radiation in a differentially heated cubic square cavity is presented. The coupled flow and heat transfers in the cavity are predicted by coupling a finite volume method with a spectral line weighted sum of gray gase model to describe gas radiative properties. The radiative transfer equation is solved by means of the discrete ordinate method. Simulations are performed at Ra?=?10⁶, considering different combinations of passive wall and/or gas radiation properties and different cavity length. It was found that in presence of a participative medium representative of building, cavity length has a strong influence on temperature and velocity fields which affect the global circulation and heat transfers in the cavity. For each steady-state solution, the convective and radiative contributions to the global heat transfer are discussed. More specifically, boundary layer thickness, thermal stratification parameter, and three-dimensional effects are compared to pure convective case results. The results suggest that radiative effects, often considered as negligible in view of the relatively low optical thickness, may not be neglected when trying to predict regime transitions.     

Combined heat transfer of radiation and natural convection in a square cavity containing participating gases

This article deals with analyzing the effect of radiative heat transfer on natural convection heat transfer in a square cavity under normal room conditions. The governing equations of natural convection and radiative transfer are solved simultaneously to obtain the temperature, velocity and heat flux distributions inside the participating medium. The finite volume method has been adopted to solve the governing equations and the discrete ordinates method (DOM) is used to model the radiative transfer in absorbing-emitting media. The radiative–convective model is validated by comparison with test cases solutions from the literature. Then, the effects of Rayleigh number from 10² to 10⁶ and optical thickness in a broad range from 0 to 100 on temperature and velocity distributions and Nusselt numbers are investigated. The results show that even under normal room conditions with a low temperature difference, the radiation plays a significant role on temperature distribution and flow pattern in the cavity. Also, several interesting effects of radiation are observed such as a sweep behavior on the isotherms, streamlines and velocity distributions of the cavity along the optical thickness and a reverse behavior on maximum stream function and convective Nusselt number at different Rayleigh numbers.     

Numerical prediction of effective thermal conductivity of ceramic fiber board using lattice Boltzmann method

Abstract

Application of the lattice Boltzmann method has been extended for the analysis of combined transient conduction and radiation heat transfer through highly porous fibrous insulation media. Firstly, LBM has been employed for the analysis of combined mode of transient conduction radiation heat transfer in a 2?D rectangular enclosure containing an absorbing, emitting and scattering medium and results are compared with already published ones. The results have been found in good accord for different values of radiation-conduction parameter, scattering albedo and south (hot) wall emissivity. Furthermore, the proposed LBM for the calculation of effective thermal conductivity of ceramic fiber board has been employed. A random-generation growth method for generating micro morphology of natural ceramic fiber board has been selected. The conductive, radiative and effective thermal conductivity has been numerically estimated using the present LBM. It is found that the predicted effective thermal conductivity for different values of fibrous bulk density is in good agreement with the experimental data.     

Combustion of suspended fine solid fuel in air inside inert porous medium: A heat transfer analysis

Present work is a numerical analysis of combustion of submicron carbon particles inside an inert porous medium where the particles in form of suspension in air enter the porous medium. A one-dimensional heat transfer model has been developed using the two-flux gray radiation approximation for radiative heat flux equations. The effects of absorption coefficient, emissivity of medium, flame position and reaction enthalpy flux on radiative energy output efficiency have been presented. It is revealed that in porous medium the combustion of suspended carbon particles is similar to premixed single phase gaseous fuel combustion except the former has shorter preheating temperature zone length. Use of porous ceramic having high porosity and made of Al₂O₃ or ZrO₂ with stabilized flame position operated nearer to downstream end will ensure radiative output maximum and minimum at downstream and upstream end, respectively.     

RADIATION MODELING OF STATIONARY FUSED SILICA RODS AND FIBERS HEATED BY CO2 LASER IRRADIATION

This study presents a heat transfer model for a stationary fused silica rod heated by a CO₂ laser. During laser heating, the effect of fused silica being modeled to be opaque or semitransparent to laser irradiation is studied. The radiative heat transfer caused by the emission of fused silica is modeled using the zonal method, and compared to the Rosseland diffusion approximation. The spectral dependence of the fused silica absorption coefficient in semitransparent wavelengths is approximated by a two-band model. The weighted-sum-of-gray-gas (WSGG) method is used to calculate the radiative source term. The governing equation with conduction and radiation heat transfer is solved by the finite-volume method. The importance of modeling the effects of laser energy penetration below the fused silica surface during heating, especially for small diameter fibers, is discussed. The importance of radiative heat transfer in fused silica is also discussed. Around 25 K in temperature difference is observed when the diffusion approximation is used in place of the zonal method to model the radiative transfer in fused silica.     

Wind heat transfer coefficient in solar collectors in outdoor conditions

Knowledge of wind heat transfer coefficient, h_w, is required for estimation of upward losses from the outer surface of flat plate solar collectors/solar cookers. In present study, an attempt has been made to estimate the wind induced convective heat transfer coefficient by employing unglazed test plate (of size about 0.9 m square) in outdoor conditions. Experiments, for measurement of h_w, have been conducted on rooftop of a building in the Institute campus in summer season for 2 years. The estimated wind heat transfer coefficient has been correlated against wind speed by linear regression and power regression. Experimental values of wind heat transfer coefficient estimated in present work have been compared with studies of other researchers after normalizing for plate length.     

Pool Boiling Heat Transfer to Phosphoric Acid Solutions

Phosphoric acid is a weak electrolyte with complex physical properties. This complexity combined with its industrial importance has necessitated intensive studies into its heat transfer behavior. In this investigation, pool boiling heat transfer coefficients of phosphoric acid solutions have been measured over a wide range of acid concentrations. The effects of various operating parameters such as heat flux, temperature, and acid concentration have been investigated. Also, the bubble departure diameter and the number of active nucleation sites for phosphoric acid solutions are compared with those for pure water under identical conditions. A model was developed for pool boiling heat transfer of phosphoric acid solutions, which can easily be adapted for other weak electrolyte solutions. In this model, the correct boiling temperature at the vapor/liquid interface is determined rather than applying an arbitrary correction to the boiling heat transfer coefficient. The proposed model is confirmed by comparison between calculated and experimental data.     

Anisotropy Effects on Heat and Fluid Flow by Unsteady Natural Convection and Radiation in Saturated Porous Media

ABSTRACT

This article deals with a numerical study of fluid flow and heat transfer by unsteady natural convection and thermal radiation in a vertical channel opened at both ends and filled with anisotropic, in both thermal conductivity and permeability, fluid-saturated porous medium. The bounding walls of the channel are gray and kept at a constant hot temperature.

In the present study we suppose the validity of the Darcy law for motion and of the local thermal equilibrium assumption. The radiative transfer equation (RTE) is solved by the finite-volume method (FVM). The numerical results allow us to represent the time–space variations of the different state variables. The sensitivity of the fluid flow and the heat transfer to different controlling parameters, namely, the single scattering albedo ω, the temperature ratio R, the anisotropic thermal conductivity ratio R_c, and the anisotropic permeability ratio R_k, are addressed. Numerical results indicate that the controlling parameters of the problem, namely, ω, R, R_c, and R_k, have significant effects on the flow and thermal field behavior and also on the transient process of heating or cooling of the medium. Effects of such parameters on time variations of the volumetric flow rate q_v and the convected heat flux Q at the channel's outlet are also studied.     

Effect of Radiation on Mixed Convection Inside a Lid-Driven Square Cavity With Various Optical Thicknesses and Richardson Numbers

This work studies numerically the effect of the radiative heat transfer on the flow and thermal behaviors of the mixed convection in a lid-driven square cavity in the presence of radiatively emitting, absorbing, and isotropically scattering gray medium. The Boussinesq approximation has been used in modeling the governing equations, and the SIMPLE (semi-implicit method for pressure-linked equations) algorithm is used in coupling the velocity and pressure fields. The radiative transfer equation and the governing equations have been solved respectively by the discrete ordinates method and the finite-volume method in order to obtain the temperature, velocity, and heat flux distributions in the participating medium. The present numerical simulations are validated by comparison with several earlier studies. Then, the temperature and velocity distributions and Nusselt numbers have been analyzed in a broad range of optical thicknesses from 0 to 100 and Richardson numbers from 0.01 to 100. The results show that the radiation has a significant role on the flow and thermal behaviors in the lid-driven square cavity. As an example, we can refer to a sweep behavior that is detected in the velocity distributions of the lid-driven cavity.     

RAD-NNET,a neural network based correlation developed for a realistic simulation of the non-gray radiative heat transfer effect in three-dimensional gas-particle mixtures

A neural network correlation, RAD-NNET, is developed to simulate the realistic effect of non-gray radiative absorption by a homogeneous mixture of combustion gases (CO₂ and H₂O) and soot using numerical data generated by RADCAL. RAD-NNET is then applied to assess the accuracy of some commonly accepted approximate approaches to evaluate radiative heat transfer in three-dimensional non-gray media. Results show that there are significant errors associated with the current approximate approaches. RAD-NNET can be readily implemented in commercial CFD codes to greatly enhance the accuracy of simulation of radiative heat transfer in practical engineering systems.     

Enhancement of Heat Transfer with Porous/Solid Insert for Laminar Flow of a Participating Gas in a 3-D Square Duct

In recent years, porous or solid insert has been used in a duct for enhancing heat transfer in high temperature thermal equipment, where both convective and radiative heat transfer play a major role. In the present work, the study of heat transfer enhancement is carried out for flow through a square duct with a porous or a solid insert. Most of the analyses are carried out for a porous insert. The hydrodynamically developing flow field is solved using the Navier–Stokes equation and the Darcy–Brinkman model is considered for solving the flow in the porous region. The radiative heat transfer is included in the analysis by coupling the radiative transfer equation to the energy equation. The fluid considered is CO₂ with temperature dependent thermophysical properties. Both the fluid and the porous medium are considered as gray participating medium. The increase in heat transfer is analyzed by comparing the bulk mean temperature, Nusselt number, and radiative heat flux for different porous size and orientation, Reyonlds number, and Darcy number.     

Numerical investigation of high temperature metal hydride water pumping system

I n the present work, a high temperature Metal Hydride Water Pumping System (MHWPS) equipped with a latent heat exchanger was investigated numerically. The operating concept of the pump was presented and the mathematical model of heat and mass transfer within the pump was established. We simulated the pump under different operating conditions using the alloy Mg₂Ni as a metal hydride and the KNO₃ as a Phase Change Material (PCM). The obtained results have shown that i) the developed numerical model is flexible and accurate in predicting the dynamic behavior of the pump ii) the numerical model without radiative heat transfer gives results with errors that can reach 38%, particularly for pumping time iii) the integration of the PCM provides a reduction in the pumping time of about 90% and an increase of the efficiency of the pump of about 7.6 times compared to the case without PCM which represents an improvement of 86% and iv) the Mg₂Ni alloy requires high temperature and a mass of PCM about 9 times larger than the case of LaNi₅ alloy to pump a volume 6.5 times greater than that pumped with LaNi₅.     

Chebyshev collocation spectral domain decomposition method for coupled conductive and radiative heat transfer in a 3D L-shaped enclosure

ABSTRACT

This paper presents a Chebyshev collocation spectral domain decomposition method (CSDDM) to study the coupled conductive and radiative heat transfer in a 3D L-shaped enclosure. The partitioned 3D L-shaped enclosure is subdivided into rectangular subdomains based on the concept of domain decomposition. The radiative transfer equation is angularly discretized by the discrete ordinate method with the SRAP_N quadrature scheme and then solved by the CSDDM using the same grid system as in solving the conduction. The effects of the conduction–radiation parameter, the optical thickness, the scattering albedo, and the aspect ratio on thermal behavior of the system are investigated. The results indicate that the 3D CSDDM has a good accuracy and can be considered as a good alternative approach for the solution of the coupled conduction and radiation problems in 3D partitioned domains.     

Transient coupled heat transfer in multilayer composite with one specular boundary coated

By the ray tracing?node method, the transient coupled radiative and conductive heat transfer in absorbing, scattering multilayer composite is investigated with one surface of the composite being opaque and specular, and the others being semitransparent and specular. The effect of Fresnel’s reflective law and Snell’s refractive law on coupled heat transfer are analyzed. By using ray tracing method in combination with Hottel and Sarofim’s zonal method and spectral band model, the radiative intensity transfer model have been put forward. The difficulty for integration to solve radiative transfer coefficients (RTCs) is overcame by arranging critical angles according to their magnitudes. The RTCs are used to calculated radiative heat source term, and the transient energy equation is discretized by control volume method. The study shows that, for intensive scattering medium, if the refractive indexes are arranged decreasingly from the inner part of the composite to both side directions respectively, then, the total reflection phenomenon in the composite is advantageous for the scattered energy to be absorbed by the layer with the biggest refractive index, so at transient beginning a maximum temperature peak may appear in the layer with the biggest refractive index.     

Theoretical approach of a flat plate solar collector with clear and low-iron glass covers taking into account the spectral absorption and emission within glass covers layer

Accurate modeling of solar collector system using a rigorous radiative model is applied for the glass cover which represents the most important component of the system and greatly affects the thermal performance. The glass material is analyzed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in one dimensional case using the radiation element method by ray emission model (REM²). The optical constants of a clear and low-iron glass materials proposed by Rubin have been used. These optical constants, 160 values of real part n and imaginary part k of the complex refractive index of such materials, cover the range of interest for calculating the solar and thermal radiative transfer through the glass cover. The computational times for predicting the thermal behavior of solar collector were found to be prohibitively long for the non-gray calculation using 160 values of n and k for both glasses. Therefore, suitable semi-gray models have been proposed for rapid calculation. The temperature distribution within the glass cover shows a good agreement with that obtained with iterative method in case of clear glass. It has been shown that the effect of the non-linearity of the radiative heat exchange between the black plate absorber and the surroundings on the shape of the efficiency curve is important. Indeed, the thermal loss coefficient is not constant but is a function of temperature, due primarily to the radiative transfer effects. Therefore, when the heat exchange by radiation is dominant compared with the convective mode, the profile of the efficiency curve is not linear. It has been also shown that the instantaneous efficiency of the solar collector is higher in case of low-iron glass cover.