On the discrete ordinates method for radiative heat transfer in anisotropically scattering media

In the discrete ordinates method (DOM), the normalized condition for the numerical quadrature of some complex scattering phase functions may not be satisfied. In this paper, a revised discrete ordinates method (RDOM) is developed to overcome this problem, in which a renormalizing factor is added into the numerical quadrature of in-scattering term. The RDOM is used to solve the radiative transfer problem in one-dimensional anisotropically scattering media with complex phase function. The radiative heat fluxes obtained by the RDOM are compared with those obtained by the conventional discrete ordinates method (CDOM) and Monte Carlo method. The results show the RDOM can overcome the false scattering resulted from the numerical quadrature of in-scattering term and improve largely the accuracy of solution of the radiative transfer equation by comparison with the CDOM.     

3D modelling of radiative heat transfer in circulating fluidized bed combustors: influence of the particulate composition

A three-dimensional model is developed to predict the bed-to-wall radiative heat transfer coefficient in the upper dilute zone of circulating fluidized bed (CFB) combustors. The radiative transfer equation is solved by the discrete ordinates method and Mie scattering theory is applied to calculate the absorption and scattering efficiency factors of particles existing in CFB combustors. Empirical correlations calculate both spacial variation of solid volume fraction and temperature distribution at the wall. The model considers the influences of the particle properties (including particle size distribution, particle optical constants and solid composition) on the radiative heat transfer coefficient. Simulation results show that the particle properties have significant influences on the bed-to-wall radiative heat transfer coefficient in CFB combustors. A very good agreement of predicted results is shown with experimental data.     

Heat transfer and thermophotovoltaic power generation in oil-fired heating systems

The focus of this study is the production of electric power in an oil-fired, residential heating system using thermophotovoltaic (TPV) conversion devices. This work uses experimental, computational, and analytical methods to investigate thermal mechanisms that drive electric power production in the TPV systems. An objective of this work is to produce results that will lead to the development of systems that generate enough electricity such that the boiler is self-powering. An important design constraint employed in this investigation is the use of conventional, yellow-flame oil burners, integrated with a typical boiler. The power production target for the systems developed here is 100 W – the power requirement for a boiler that uses low-power auxiliary components. The important heat transfer coupling mechanisms that drive power production in the systems studied are discussed. The results of this work may lead to the development of systems that export power to the home electric system.     

Radiative transfer in one-dimensional hollow cylindrical geometry with anisotropic scattering and variable medium properties

The effects of spatially varying absorption and scattering coefficients on radiation transfer in absorbing, emitting, anisotropically scattering hollow cylinders with reflecting boundaries were investigated using the discrete ordinates method (DOM) by Tsai et al. [Int. J. Heat Mass Transfer 33 (1990) 2651]. Their problem solutions for hollow cylinder cases are incorrect. The cause of this inaccuracies are identified and the correct solutions obtained using DOM S₆ are provided.     

Fluid flow and mass transfer modelling in lysozyme ultrafiltration

This work addresses the mass transfer modelling of ternary solutions, water/lysozyme/sodium chloride, in the slit feed channel of a ultrafiltration (UF) cell. Permeation experiments are performed using a laboratory-made UF cellulose acetate membrane, characterised by an hydraulic permeability of 2.05 × 10⁻¹¹ m/s/Pa and a molecular weight cut-off of 30 kDa. The simulation of the UF operating conditions with recourse to computer fluid dynamics allows the prediction of the selective permeation performance in terms of permeation fluxes and concentration polarization. The predictions of the permeation fluxes based on different mass transport assumptions are compared with experimental ones and a good agreement is obtained.     

Three-dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinates method

The main purpose of this paper is to study, in a three-dimensional, differentially heated cavity, the phenomenon of radiation and natural convection in both transparent and participating media. The discrete ordinates method (DOM) is used to solve the radiative transfer equation. The Navier-Stokes equations (NSE), describing natural convection, are solved with a segregated SIMPLE-like algorithm. For non-participating media, the coupling between the radiative transfer and NSE is done via the radiative heat exchange between surfaces. For participating media, a source term is added in the energy equation. The local and mean heat flux as a function of the Rayleigh number is studied, for both transparent and participating media with different optical thicknesses. The effect of the Planck number on the heat flux is also analyzed for different values of the Rayleigh number. Also, a comparison between a purely two-dimensional case and the results obtained in the mid-plane of a long rectangular enclosure is presented.     

Heat transfer in ash deposits: A modelling tool-box

The objective of this paper is to review the present state-of-the-art knowledge on heat transfer to the surface of and inside ash deposits formed in solid fuel-fired utility boilers, and-based on the review-to propose models for calculation of heat transfer, e.g. in deposition models. Heat transfer will control the surface temperature of the deposit, thereby influencing the physical conditions at the deposit surface, e.g. if the surface is molten. The deposit surface conditions will affect the deposit build-up rate as well as the removal/shedding of deposits: molten deposit may lead to a more efficient particle capturing, but may also flow down the heat transfer surfaces.

The heat transfer parameters of prime interest are the convective heat transfer coefficient h, the effective thermal conductivity of the deposit k_eff, and the surface emissivity ε of the deposit. The convective heat transfer coefficient is a function of flow characteristics, and can be calculated using different correlation equations, while the other two parameters depend on the deposit properties, and can be calculated using different structure-based models.

The thermal conductivity of porous ash deposits can be modelled using different models for packed beds. These models can be divided into two major groups, depending on the way they treat the radiation heat transfer, i.e. the unit cell models and the pseudo homogeneous models. Which model will be suitable for a particular application depends primarily on the deposit structure, i.e. whether deposit is particulate, partly sintered or completely fused.

Simple calculations of heat transfer resistances for deposits have been performed, showing that major resistances are in the heat transfer to the deposit (by convection), and the heat transfer through the deposit (by conduction). Very few experimental data on the thermal conductivity of ash deposits, especially at high temperatures where radiation is important, are found in the literature. Although the structure of the deposit is essential for its thermal conductivity, most of the measurements were done on crushed samples. The results obtained using different models were compared with the experimental data published in Rezaei et al. [Rezaei, Gupta, Bryant, Hart, Liu, Bailey, et al. Thermal conductivity of coal ash and slags and models used. Fuel 2000;79:1697–1710.], measured on crushed coal ash samples. Although errors of the predictions were very high in most cases, two models were proposed as suitable for heat conductivity calculations, i.e. the Yagi and Kunii model for particulate deposits, and the Hadley model for sintered and fused deposits.

This literature study showed the need for a wide range of experimental data, which would help in evaluating and improving the existing thermal conductivity models. Also, it is necessary to formulate a more accurate model for the thermal conductivity of solid mixtures, in which potentially important sources of errors can be identified.     

Heat transfer in rectangular microchannels heat sink using nanofluids

The effect of using nanofluids on heat transfer and fluid flow characteristics in rectangular shaped microchannel heat sink (MCHS) is numerically investigated for Reynolds number range of 100–1000. In this study, the MCHS performance using alumina–water (Al₂O₃-H₂O) nanofluid with volume fraction ranged from 1% to 5% was used as a coolant is examined. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using finite volume method. The MCHS performance is evaluated in terms of temperature profile, heat transfer coefficient, pressure drop, friction factor, wall shear stress and thermal resistance. The results reveal that when the volume fraction of nanoparticles is increased under the extreme heat flux, both the heat transfer coefficient and wall shear stress are increased while the thermal resistance of the MCHS is decreased. However, nanofluid with volume fraction of 5% could not be able to enhance the heat transfer or performing almost the same result as pure water. Therefore, the presence of nanoparticles could enhance the cooling of MCHS under the extreme heat flux conditions with the optimum value of nanoparticles. Only a slight increase in the pressure drop across the MCHS is found compared with the pure water-cooled MCHS.     

Heat and mass transfer in porous media with ice inclusions near the freezing-point

Heat and mass transfer in biporous medium of regular structure near the phase transition point is studied theoretically. Large pores contain ice. Small pores are filled with pure water. The thermal and filtration problems for a separate cell of the medium are solved by the anisotropic conductivity method. Heat and mass flows depend linearly on the gradients of the temperature and the water pressure. The Onsager reciprocal relations are confirmed for systems with phase transformations. With the advent of the solid phase (ice) in porous media, the straight transport coefficients multiply several times, and the cross coefficients increase more than one order of magnitude.     

Heat transfer coefficient and latent heat of martensite in a medium-carbon steel

In this paper the method used in a recently published paper to measure the latent heat of the martensite transformation during quenching of a steel is analysed. The arrangement of the experiment made it possible to obtain reasonable values for the latent heat of transformation, but cannot be expected to produce reasonable values for the heat transfer coefficient. Improved methods are discussed, including the novel probe design of the present authors.     

Heat and mass transfer effects in a direct methanol fuel cell: A 1D model

Models are a fundamental tool for the design process of fuel cells and fuel cell systems. In this work, a steady-state, one-dimensional model accounting for coupled heat and mass transfer, along with the electrochemical reactions occurring in the DMFC, is presented. The model output is the temperature profile through the cell and the water balance and methanol crossover between the anode and the cathode. The model predicts the correct trends for the influence of current density and methanol feed concentration on both methanol and water crossover. The model estimates the net water transfer coefficient through the membrane, α, a very important parameter to describe water management in the DMFC. Suitable operating ranges can be set up for different MEA structures maintaining the crossover of methanol and water within acceptable levels. The model is rapidly implemented and is therefore suitable for inclusion in real-time system level DMFC calculations.     

Heat transfer enhancement in annular fins using functionally graded material

This study presents a new approach on the heat transfer enhancement of annular fins with constant thickness using functionally graded materials. The thermal conductivity of the annular fin is assumed to be graded along the fin radius as a power‐law function. The resulting fin equation is solved by an approximate analytical method using the mean value theorem. The variable coefficients of second and third terms in the second‐order differential equation of the fin are replaced with their mean values along the fin radius. Several different graphs regarding the computed temperature profile, fin tip temperature, and fin efficiency are plotted with respect to the radii ratio thermo‐geometric parameter, and inhomogeneity parameter. It is demonstrated that the inhomogeneity parameter plays an important role on the heat transfer enhancement of the annular fin. However, for large radii ratios the effect of the inhomogeneity parameter decreases. Finally, it is stated that application of the functionally graded material in the annular fins, enhances the heat transfer rate between the fin and surrounding fluid resulting from the higher fin efficiency in comparison to the homogeneous annular fin. It is hoped that the results obtained from this study arouse interest among thermal designers and heat exchanger industries. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 603–617, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21053     

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.     

Heat transfer augmentation in a wedge-ribbed channel using winglet vortex generators

Experimental investigations have been carried out to study the effect of combined wedge ribs and winglet type vortex generators (WVGs) on heat transfer and friction loss behaviors for turbulent airflow through a constant heat flux channel. To create a reverse flow in the channel, two types of wedge (right-triangle) ribs are introduced: wedge ribs pointing downstream and pointing upstream. The arrangements of both rib types placed inside the opposite channel walls are in-line and staggered arrays. To generate longitudinal vortex flows through the tested section, two pairs of the WVGs with the attack angle of 60° are mounted on the test channel entrance. The test channel has an aspect ratio, AR = 10 and height, H = 30 mm with a rib height, e/H = 0.2 and rib pitch, P/H = 1.33. The flow rate in terms of Reynolds numbers is based on the inlet hydraulic diameter of the channel ranging from 5000 to 22,000. The presence of the combined ribs and the WVGs shows the significant increase in heat transfer rate and friction loss over the smooth channel. The Nusselt number and friction factor values obtained from combined the ribs and the WVGs are found to be much higher than those from the ribs/WVGs alone. In conjunction with the WVGs, the in-line wedge pointing downstream provides the highest increase in both the heat transfer rate and the friction factor while the staggered wedge pointing upstream yields the best thermal performance.     

Heat transfer regulation in a rectangular enclosure using a rotating plate

The effects of an inner rotating plate with horizontal axis on the heat transfer in a differentially heated vertical enclosure were investigated experimentally. The aspect ratio of the enclosure height/width was 1 throughout the experiments. An acrylic plate with a small thermal conductivity was installed horizontally at the center of the square enclosure, and was rotated at various speeds for normal and reverse rotations by using the motor attached outside of the enclosure. Purified water was used as the working fluid. The flow pattern was sketched by a visualization experiment using aluminum powder. The heat transfer results were also compared with those from a previous paper on a rotating cylinder. It is clarified here that the heat transfer rate of the enclosure depends largely on the parameter Gr_w/Re_ω², and is characterized by three regions. The heat transfer rate of the enclosure with a rotating plate is somewhat larger than that of a rotating cylinder in the forced convection region. The rotating plate used here will be useful for regulation of wide‐ranging heat transfer. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 342–353, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10099     

Heat transfer enhancement using hybrid nanofluids in spiral plate heat exchangers

A possible way to enhance the rate of heat transfer in the spiral plate heat exchanger (SPHE) is by employing hybrid nanofluids as its working medium. Hence, in the present work, effects of hybrid nanofluids on the thermal performance of SPHE has been investigated numerically. First, a countercurrent SPHE is designed and modeled. Later, simulation of SPHE has been carried out by employing conventional fluid , nanofluids , and hybrid nanofluids to investigate the heat transfer rates. Finally, the performance of SPHE using hybrid nanofluid is compared with that of using water and nanofluids. The heat transfer augmentation of approximately 16%‐27% with hybrid nanofluids of overall 4% nanoparticles volume concentration and 10%‐16% with 2% nanoparticles volume concentration is observed when compared with that of pure water. Therefore, it can be inferred that the application of hybrid nanofluids in SPHE seems to be one of the promising solutions for augmentation of its thermal performance.     

Heat transfer enhancement in medium temperature thermal energy storage system using a multitube heat transfer array

An experimental energy storage system has been designed using an horizontal shell and tube heat exchanger incorporating a medium temperature phase change material (PCM) with a melting point of 117.7 °C. Two experimental configurations consisting of a control unit with one heat transfer tube and a multitube unit with four heat transfer tubes were studied. The thermal characteristics in the systems have been analysed using isothermal contour plots and temperature time curves. Temperature gradients along the three directions of the shell and tube systems; axial, radial and angular directions have been analysed and compared. The phase change in the multitube system was dominated by the effect of convective heat transfer compared to conductive heat transfer in the control system. The temperature gradient in the PCM during phase change was greatest in the radial direction for both the control and multitube systems. The temperature gradients recorded in the axial direction for the control and multitube systems during the change of phase were respectively 2.5 and 3.5% that of the radial direction, indicating essentially a two-dimensional heat transfer in the PCM. The onset of natural convection through the formation of multiple convective cells in the multitube system significantly altered the shape of the solid liquid interface fluid flow and indicates the requirement for an in-depth study of multitube arrangements.     

Computational modelling of unsaturated flow of liquid in heap leaching—using the results of column tests to calibrate the model

Unsaturated flow of liquid in a bed of uniform and spherical ore particles is studied numerically and experimentally. An unsteady and two-dimensional model is developed based on the mass conservation equations of liquid phase in the bed and in the particles. The model equations are solved using a fully implicit finite difference method giving the distribution of the degree of saturation in the particles and in the bed and the vertical velocity of flow in the bed, as well as, the effect of periodic infiltration on the above distributions. To calibrate the computational model, several column tests are performed using periodic infiltration of water on 40 cm high columns composed of ore having particles smaller than 25 mm. The numerical analysis shows that (a) the results obtained from numerical modelling under the same operating conditions as used for column tests, are in good agreement with those from experimental procedure, (b) the degree of saturation of the bed and the time required to reach steady state conditions depend on the inflow of water and intrinsic permeability of the bed and (c) the velocity fluctuations and the fluctuations of the degree of saturation in the bed depend on the inflow of water, period of infiltration, height and intrinsic permeability of the bed.     

Heat transfer and phase change of liquid in an inclined enclosure packed with unsaturated porous media

In this paper, we present a mathematical model to describe the simultaneous heat and mass transfer with liquid phase change in unsaturated porous media. Two-dimensional natural convective flow in an inclined rectangular enclosure with porous material unsaturated with fluid is analyzed numerically. The parameter variations are considered for the tilted angle, the aspect ratio and the Darcy–Rayleigh number. Local and global Nusselt numbers are presented as functions of those parameters. Compared with the saturated porous material, the heat transfer characters in the unsaturated case are discussed for the identical aspect ratio and Darcy–Rayleigh number, The discussion is also made for the field synergy of fluid velocity and heat flow in natural convection.