Solar radiation absorption in solar ponds

The local rate of absorption of the solar radiation in a solar pond is determined for the direct component at angles of incidence from 0° to 75° with 15° intervals as well as for the diffuse component by the exact treatment of the radiation problem. The effects of bottom reflection, the pond depth, the type of radiation on the thermal performance of the pond are examined, and a new rigorous approach is presented for treating diffuse radiation as a direct beam. The fraction of the solar radiation absorbed within the first 10 cm of water is determined under various conditions. The local rate of solar energy absorption at any depth and at any incidence angle can readily be computed from a fourth-degree polynomial expression, the coefficients of which are tabulated for different incidence angles and bottom reflectivities.     

Modeling the performance of a solar pond as a source of thermal energy

The use of solar ponds is becoming more attractive in today's energy scene. A major advantage of solar ponds over other collectors is the ability to store thermal energy for long periods of time. The solar pond comprises a hydraulic system subject to processes of heat and mass transfer. The design of this system and the related equipment requires a thorough knowledge of the pond heating-up process and expected thermohaline structure within the pond. The current study considers that convection currents in the pond are inhibited by the salinity distribution, and applies a finite difference implicit model in order to investigate the interaction among physical variables represented by various dimensionless parameters. Variables which are included in the analysis comprise the solar radiation input and absorption as it passes through the pond; diffusion and dispersion of heat within the pond; absorption of heat at the bottom of the pond; and withdrawal of heat from layers within the pond. The physical variables generate 3 dimensionless variables associated with the pond's heating-up process. A 4 dimensionless variable is associated with the heat utilization. The analysis represented in this paper concerns the interaction between these dimensionless parameters and its implications.     

Effect of bottom reflectivity on ground heat losses for solar ponds

A two-dimensional ground heat loss model is used to investigate the effect of bottom reflectivity on ground heat losses for solar ponds. In the model, convection boundary conditions are used between water and ground. The convection heat transfer coefficient is estimated using the correlations given for heated or cooled flat plates. The local rate of absorption of the solar radiation in the pond is determined for the direct and diffuse components by the exact treatment of the radiation problem. The fractions of heat adsorbed by the pond bottom that is transferred to soil and to water are investigated for different bottom reflectivities.     

Heating/melting of a fused silica particle by convection and radiation

The effect of internal absorption and emission of radiation on the heating/melting process of small fused silica particles is analyzed. The particle is considered to be semitransparent to radiation, and the radiative transfer theory is used to predict the local volumetric absorption/emission rate. The transient energy equation with conduction and radiation accounted for is solved to predict the temperature distribution in the particle and the solid–liquid interface position after the melting has started. The radiative transfer calculations are carried out on the spectral basis using published spectral optical property data for fused silica. Results of parametric calculations for different diameter particles, surroundings temperatures and external flow conditions are reported and discussed.     

Near-infrared light heating of a slab by embedded nanoparticles

Exposed to spectral and uniform light, the heating of a one-dimensional, conducting and radiatively participating medium due to embedded absorbing and scattering nanoparticles is solved. Spherical harmonics approximation is used to solve the radiative transfer equation and the finite difference explicit method is used to find the temperature distribution in a generic slab having both boundaries subjected to convection. The host medium is transparent to spectral radiation and the temperature distribution is obtained when the temperature of the irradiated boundary reaches a desired point specified to ensure that any temperature in the medium does not exceed its melting temperature. It is found that the variation of the concentration and configuration of the embedded nanoparticles, particularly gold nanoshells, changes the radiative transfer spectrum, which leads to an alteration in the local heat generation spectrum and the resulting temperature distribution in the medium. It is shown that a gold nanoshell configuration with a great amount of scattering increases the internal diffuse radiation, which creates a more even radiative distribution, while a configuration with a great amount of absorption promotes a high amount of absorption in the entry region and very little in the rear region, leading to the formation of a large temperature gradient between the two boundaries. The present study provides a framework from which the photothermal heating of nanoparticle mixtures in non-transparent host media may be applied.     

Computation of diffuse solar radiation

A technique for computing the spectral and angular (both the zenith and azimuthal) distribution of the solar energy reaching the surface of earth and any other plane in the atmosphere has been developed. Here the computer code LOWTRAN is used for getting the atmospheric transmittances in conjunction with two approximate procedures: one based on the Eddington method and the other on van de Hulst's adding method, for solving the equation of radiative transfer to obtain the diffuse radiation in the cloud-free situation. The aerosol scattering phase functions are approximated by the Hyeney-Greenstein functions. When the equation of radiative transfer is solved using the adding method, the azimuthal and zenith angle dependence of the scattered radiation is evaluated, whereas when the Eddington technique is utilized only the total downward flux of scattered solar radiation is obtained. Results of the diffuse and beam components of solar radiation received on surface of earth compare very well with those computed by other methods such as the more exact calculations using spherical harmonics and when atmospheric conditions corresponding to that prevailing locally in a tropical location (as in India) are used as inputs the computed values agree closely with the measured values.     

Effects of particulate concentrations on temperature and heat flux distributions in a pulverized-coal fired furnace

A simple methodology for numerical modelling of total heat transfer in an axisymmetric, cylindrical pulverized coal-fired furnace is introduced. The solution for the flow field and energy equations are coupled with the solution of the radiative transfer equation. The SIMPLER code is employed to solve all the equations numerically. The radiation part is modelled using the first-order spherical harmonics approximation. The radiative properties of the gases and particulates such as soot, coal/char and fly-ash are obtained locally to account for the temperature and concentration distribution effects. Using a k - ε model, the turbulence closure is obtained. Parametric studies are performed and are presented graphically to demonstrate the effects of particulate concentrations on the distributions of medium radiative and physical properties, temperature, and the wall total and radiative heat fluxes.     

Generalized radiative transfer equation for porous medium upscaling: Application to the radiative Fourier law

Many porous media cannot be homogenized as Beerian semi-transparent media. Effective extinction, absorption and scattering coefficients can indeed have no physical meaning for small or intermediate optical thicknesses. A generalized radiative transfer equation (GRTE), directly based on the extinction cumulative distribution function, the absorption and scattering cumulative probabilities and the scattering phase function is established for this optical thickness range. It can be solved by a statistical Monte Carlo approach. For a phase of a porous medium that is optically thick at local scale, the GRTE degenerates into a classical Beerian RTE. In these conditions, a radiative conductivity tensor is directly obtained, by a perturbation method, and expressed with the radiative coefficients of this RTE and temperature. As illustrations, exhaustive radiative conductivity results are given for a set of overlapping transparent spheres within an opaque phase and for opaque rod bundles.     

NATURAL CONVECTION AND RADIATION IN A SQUARE ENCLOSURE

Natural convection of a radiating fluid in a square enclosure is studied numerically. The coupled momentum, energy, and radiative transfer equations are solved by an iterative procedure. The solutions to the equation of radiative transfer are obtained by the discrete ordinates method using S4 and S8 quadratures. The method is based on control volume formulation and is fully compatible with the SIMPLER algorithm used to solve the momentum and energy equations. The effects of optical thickness and scattering on the flow and temperature fields and heat transfer rates are analyzed. The changes in the buoyant flow patterns and temperature distributions due to the presence of radiation in inclined or heat generating enclosures are also studied. Comparative results obtained by the P-I differential approximation are presented.     

Modeling of the radiation field in a parabolic trough solar photocatalytic reactor

We calculate the distribution of absorbed radiation inside a solar photocatalytic reactor, by means of radiative transfer theory. The reactor configuration is that of a glass tube illuminated by a parabolic trough collector, where the catalyst consists of titanium dioxide micro-particles suspended in water. The calculations are made within the framework of the P1 approximation, which allows to solve analytically the radiative transfer equations. The obtained solution is used to study the effect of catalyst concentration on the degradation of pollutants, by means of a general kinetic model. The results obtained display the main features which are observed in experiments reported in the literature.     

Salt gradient stabilized solar pond collector

This paper presents a theoretical analysis of a salt gradient solar pond as a steady state flat plate solar energy collector. We explicitly take into account the convective heat and mass flux through the pond surface and evaluate the temperature and heat fluxes at various levels in the pond by solving the Fourier heat conduction equation with internal heat generation resulting from the absorption of solar radiation as it passes through the pond water. These evaluations, in combination with energy balance considerations, enable the derivation of the expressions for solar pond efficiency of heat collection as well as the efficiency of heat removal. The efficiency expressions are Hottel-Whillier-Bliss type, prevalent for flat plate collectors. Numerical computations are made to investigate the optimization of geometrical and operational parameters of the solar pond. For given atmospheric air temperature, solar insolation and heat collection temperature, there is an optimum thickness of nonconvective zone for which the heat collection efficiency is maximum. The heat removal factor is also similar to that of a flat plate collector and the maximum efficiency of heat removal depends on both the flow rate and the temperature in the nonconvective zone.     

Effects of changes in the atmosphere on solar insolation

A review of the nature of solar radiation and the spectral distribution of its energy is presented. The attenuation of solar radiation by scattering and absorption and the effects of atmospheric pollutants on radiation attenuation with an estimate of the long-term effects of pollutants is discussed.     

Inverse radiation analysis of simultaneous estimation of temperature field and radiative properties in a two-dimensional participating medium

An inverse radiation analysis is presented for simultaneous estimation of temperature field and radiative properties including absorption and scattering coefficients in a two-dimensional rectangular, absorbing, emitting and scattering gray medium from the knowledge of the exit radiative energy received by charge-coupled device (CCD) cameras at boundary surfaces. The backward Monte Carlo method was introduced to describe the radiative heat transfer for its efficiency. The inverse problem is formulated as an optimization problem and solved by the least-square QR decomposition (LSQR) method. The effects of measurement errors, optical thickness and search step length on the accuracy of the estimation were investigated and the results show that the temperature field and radiative properties can be reconstructed accurately for the exact and noisy data.     

Effect of light scattering on the performance of a direct absorption solar collector

Recently, a solar thermal collector often employs nanoparticle suspension to absorb the solar radiation directly by a working fluid as well as to enhance its thermal performance. The collector efficiency of a direct absorption solar collector (DASC) is very sensitive to optical properties of the working fluid, such as absorption and scattering coefficients. Most of the existing studies have neglected particle scattering by assuming that the size of nanoparticle suspension is much smaller than the wavelength of solar radiation (i.e., Rayleigh scattering is applicable). If the nanoparticle suspension is made of metal, however, the scattering cross-section of metallic nanoparticles could be comparable to their absorption cross-section depending on the particle size, especially when the localized surface plasmon (LSP) is excited. Therefore, for the DASC utilizing a plasmonic nanofluid supporting the LSP, light scattering from metallic particle suspension must be taken into account in the thermal analysis. The present study investigates the scattering effect on the thermal performance of the DASC employing plasmonic nanofluid as a working fluid. In the analysis, the Monte Carlo method is employed to numerically solve the radiative transfer equation considering the volume scattering inside the nanofluid. It is found that the light scattering can improve the collector performance if the scattering coefficient of nanofluid is carefully engineered depending on its value of the absorption coefficient.     

RADIATION-CONDUCTION INTERACTION IN A PLANAR,ANISOTROPICALLY SCATTERING MEDIUM WITH FLUX BOUNDARY

Steady, combined radiation and conduction heat transfer in an absorbing, emitting, and anisotropically scattering planar medium is investigated theoretically. The problem is considered with a constant net heat flux imposed at one boundary and a constant temperature at the other. Both specular and diffuse reflectivities are included. The influence of radiation heat transfer is obtained by solving the exact integral equations of radiative transfer with the nodal approximation technique. The technique reduces the integral equations into a discrete system of algebraic equations and permits obtaining exact numerical solutions for any scattering-phase function. Temperatures are obtained from the energy equation with an iterative procedure. The effects of scattering anisotropy as well as radiation parameters such as albedo and wall reflectivities on temperatures are analyzed.     

TWO-DIMENSIONAL COMBINED CONDUCTION AND RADIATION HEAT TRANSFER: COMPARISON OF THE DISCRETE ORDINATES METHOD AND THE DIFFUSION APPROXIMATION METHODS

Heat transfer by combined conduction and radiation in a two-dimensional semitransparent medium has been investigated. The discrete ordinates method (DOM) and the Rossland diffusion approximation are used to analyze radiative transfer. Glass is considered as an example of a radiation absorbing and emitting medium, and the spectral dependence of the absorption coefficient on wavelength is accounted for. The results predicted by the DOM are in good agreement with those based on the one-dimensional integral formulation. However, when the opacity of the medium is large, the DOM suffers from the numerical smearing, which distorts the radiative flux distribution. The diffusion approximation greatly underpredicts the temperature and flux distributions in the medium, particularly when the thickness or the opacity of the medium is small. The predictions of the diffusion approximation are only reasonable for the thick layer. Hence, the approximation should be used with extreme caution to obtain quantitatively accurate results.     

Coupled radiation and flow modeling in ceramic foam volumetric solar air receivers

Ceramic foams are promising materials for the absorber of volumetric solar air receivers in concentrated solar thermal power (CSP) receivers. The macroscopic temperature distribution in the volumetric solar air receiver is crucial to guarantee that volumetric solar air receivers work steadily, safely and above all, efficiently. This study analyzes the temperature distribution of the fluid and solid phases in volumetric solar air receivers. The pressure drop in the ceramic foams and the interfacial heat transfer between the flowing fluid and solid are included in the model. The radiative heat transfers due to concentrated solar radiation absorption by the ceramic foam and the radiation transport in the media were modeled with the P₁ approximation. The energy fields of the fluid and solid phases were obtained using the local thermal non-equilibrium model (LTNE). Comparison of the macroscopic model with experimental results shows that the macroscopic model can be used to predict the performance of solar air receivers. Sensitivity studies were conducted to analyze the effects of velocity, porosity, mean cell size and the thermal conductivity of the solid phase on the temperature fields. The results illustrate that the thermal non-equilibrium phenomena are locally important, and the mean cell size has a dominant effect on the temperature field.     

New aspects of the diffusion approximation for radiative transfer

The diffusion approximation is generalized to arbitrary locally isotropic participating media. It proves to be an approximate special solution of the full equation of radiative transfer accounting for absorption, scattering, and emission. This special solution must be completed with a solution of the radiative transfer equation without emission term in order to match the boundary conditions for the radiative field. Applied to combined heat and radiative transfer this scheme offers distinct computational advantages and broad applicability. Following these ideas a simple and robust method for one-dimensional radiation–conduction computations is constructed and verified.     

Effect of radiation absorption in saline water on the performance of solar ponds

The effect of the solar radiation absorption characteristics of saline water on the performance of salt-gradient solar ponds under quasi-steady conditions is studied. Several models have been proposed to simulate the absorption of radiation in solar ponds, however, it is shown in this work that experimental data published by many authors militate in favour of representing this absorption simply by a single exponential. Pond performance is strongly influenced by the absorption characteristics. The mean pond temperature of the storage zone and the pond efficiency drop considerably as the turbidity of the water increases. The high values of the extinction coefficient result also in damping the pond temperature fluctuations and increase its time lag with respect to the insolation. The importance of using accurate in-site measured absorption data for pond design and performance prediction is emphasized.     

Thermal radiation effects in phase-change energy-storage systems

A numerical model was developed to determine the transient temperature distribution, solid/liquid interface location, and energy-storage capacity of a semi-transparent phase-change medium. The medium is bounded between two concentric cylinders and internal energy transfer occurs simultaneously by conduction and thermal radiation. The radiation transport equation was coupled with the energy equation; both enthalpy and temperature were employed as dependent variables. The spherical harmonic approximation (P-N approximation) was used to obtain solutions for the radiative heat flux. The coupled conservation of energy and moment differential equations were solved by using iterative numerical finite-difference schemes with appropriate thermal and radiant boundary and interface conditions. The numerical model was used to study the effects of radiation on solidification (melting), transient temperature distribution and energy-storage capacity of an absorbing, emitting, and isotropically scattering, semi-transparent, gray medium contained in a cylindrical annulus. The results increase our understanding of internal energy transfer and show the effects of optical properties, conduction/radiation parameter, and geometric dimensions and should lead to better designs and optimization of phase-change energy-storage systems.