Theoretical analysis of thermal radiative equilibrium via a radiosity method

We propose a theoretical consideration of thermal radiative equilibrium via a radiosity method. According to G. Kirchhoff's research on cavity radiation, the condition of radiative equilibrium arises in a cavity in which the internal wall temperature is uniform. Furthermore, by considering the balance of energy on the wall surfaces in the cavity, the relationship, emittance ? = absorptance α, is obtained. Adversely, in the present study, we developed a method to prove the conclusion of the uniformity and uniqueness of radiative equilibrium in the cavity (independent of the emittance of the interior wall surfaces) by considering the relationship ? = α on the wall surfaces to be a supposition. Using the concept of radiosity, we proved that the radiosities on the internal wall surfaces can be kept uniform in the enclosed system of thermal radiative equilibrium. This knowledge is advantageous for inspecting the benchmarks of various programs for radiative analysis. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20372     

Thermal analysis of roof-spray cooling

Roof-spray cooling systems have been developed and implemented to reduce the heat gain through roofs so that conventional cooling systems can be reduced in size or eliminated. Currently, roof-spray systems are achieving greater effectiveness due to the availability of direct digital controls (DDC). The objective of this paper is to develop a mathematical model for the heat transfer though a roof-spray cooled roof that predicts heat transfer based on existing weather data and roof heat transfer characteristics as described by the transfer function method (TFM). The predicted results of this model are compared to the results of existing experimental data from previously conducted roof-spray cooling experiments. The mathematical model is based on energy balances at the exterior and interior surfaces of the roof construction that include evaporative, convective, radiative, and conductive heat transfer mechanisms. The transfer function method is used to relate the energy balances at the two surfaces that differ in amplitude and phase due to the thermal resistance and thermal capacitance characteristics of the roof. The model is shown to yield relatively good predictions of heat transfer rates through the roof. The calculation method shows promise as a relatively simple means of predicting heat gains based on calculation procedures that are similar to those frequently used by practicing engineers. © 1998 John Wiley & Sons, Ltd.     

Materials for radiative cooling to low temperature

The clear sky can act as a heat sink. Cooling to low temperatures is possible with materials which are strongly emitting in the 8–13 μm band and non-absorbing elsewhere. In this paper we discuss the resource for radiative cooling and its implementation with thin solid films (SiO_0.6N_0.2 coatings on Al) and with slabs of certain gases (C₂H₄, C₂H₄O and NH₃ backed by Al). Results are given on spectrophotometric infrared reflectance and transmittance, computed parameters which govern the predicted cooling performance, and some preliminary field tests.     

闭式冷却塔内冷却盘管传热热阻分析

通过对闭式冷却塔内冷却盘管各热阻的数量级分析,认为在实际计算中,管壁导热热阻比其它热阻小一个数量级,计算中可忽略,但其余热阻均不可忽略。影响盘管总热阻大小的因素很多,从数学上分析了各热阻对总热阻的影响,找出影响盘管总热阻的主次因素,为冷却盘管的研究、设计及运行管理提供参考。     

A study of a polymer-based radiative cooling system

A radiative cooling system consisting of unglazed flat plate radiators, water as heat carrier and a reservoir is presented. The radiators are twin-wall sheets made of a modified PPO (polyphenylenoxid) resin, which are proposed as low cost roof integrated modules. The thermal performance of a system with a radiator aperture area of 5.3 m² and reservoir volume of 280 l has been investigated in experiments for Oslo climate. A parameterisation for the cooling performance of a tilted radiator surface for clear and cloudy atmospheres is proposed and applied to model the experimental results. The impact of the tilt angle, the aperture area and the reservoir volume on the cooling performance has been studied in simulations. The feasibility of a radiative cooling system designed for a single-family house at southern latitudes has been modelled. Except for mid-summer ambient temperature and high relative humidity, the simulations show that the radiative cooling system seems to cover the demand.     

The radiative cooling of selective surfaces

We have realized a selective surface with optical properties matched to the atmospheric window 8–13 μm. With respect to a black radiator, this surface is considerably more effective for cooling by exposition to the clear sky: in particular, a cooling effect is obtained also during the day. Theoretical results and experimental data are presented.     

Condensation of water by radiative cooling

Atmospheric humidity can be condensed as dew and used for example in small-scale irrigation. In arid locations, the most favourable conditions for dew collection persist in the late night and around sunrise. We study the possibility to use a dew collector for condensing atmospheric water vapour by exploiting the effect of radiative cooling. In particular, we study pigmented polymer foils with high solar reflectance and high thermal emittance. Suitable pigments are a mixture of TiO₂ and BaSO₄ particles or a novel SiO₂/TiO₂ composite. We calculate the condensation rate under different climatic conditions and report on initial field tests.     

A new and fast method to determine mixing and conductive cooling of thermal waters in carbonate-evaporite environments

A method is proposed, for low-temperature geothermal systems, for calculating the aquifer temperature and relative proportions of mixed thermal and shallow groundwaters from carbonate-evaporite environments. The fluid is assumed to be in chemical equilibrium with anhydrite and chalcedony in the aquifer, and mixed with diluted waters during its ascent. An attempt has been made to establish a relationship between reservoir temperature, the aqueous sulfate and silica contents of the mixed fluid, the proportion of the thermal end-member and the temperature of the adiabatic mixture. The method calculates mineral solubilities in the field context, calibrated on representative thermal springs. The method also considers the effects of conductive cooling.     

Thermal analysis and measurement of a solar pond prototype to study the non-convective zone salt gradient stability

Solar ponds combine solar energy collection with long-term storage and can provide reliable thermal energy at temperature ranges from 50 to 90 °C. A solar pond consists of three distinct zones. The first zone, which is located at the top of the pond and contains the less dense saltwater mixture, is the absorption and transmission region, also known as the upper convective zone (UCZ). The second zone, which contains a variation of saltwater densities increasing with depth, is the gradient zone or non-convective zone (NCZ). The last zone is the storage zone or lower convective zone (LCZ). In this region, the density is uniform and near saturation. The stability of a solar pond prototype was experimentally performed. The setup is composed of an acrylic tube with a hot plate emulating the solar thermal energy input. A study of various salinity gradients was performed based on the Stability Margin Number (SMN) criterion, which is used to satisfy the dynamic stability criterion. It was observed that erosion of the NCZ was accelerated due to mass diffusion and convection in the LCZ. It can be determined that for this prototype the density of the NCZ is greatly affected as the SMN reaches 1.5.     

Thermal performance analysis of a flat slab phase change thermal storage unit with liquid-based heat transfer fluid for cooling applications

This paper presents the results of a thermal performance analysis of a phase change thermal storage unit. The unit consists of several parallel flat slabs of phase change material (PCM) with a liquid heat transfer fluid (HTF) flowing along the passages between the slabs. A validated numerical model developed previously to solve the phase change problem in flat slabs was used. An insight is gained into the melting process by examining the temperatures of the HTF nodes, wall nodes and PCM nodes and the heat transfer rates at four phases during melting. The duration of the melting process is defined based on the level of melting completion. The effects of several parameters on the HTF outlet temperature, heat transfer rate and melting time are evaluated through a parametric study to evaluate the effects of the HTF mass flow rate, HTF inlet temperature, gap between slabs, slab dimensions, PCM initial temperature and thermal conductivity of the container on the thermal performance. The results are used to design a phase change thermal storage unit for a refrigerated truck.     

Thermal radiative properties of a smooth air-water interface

Thermal radiative properties for an air-water interface were calculated by considering the interface to be smooth and the water to be at uniform temperature. Monochromatic hemispherical and total normal reflectance, monochromatic and total normal transmittance, Planck mean and Rosseland mean absorption coefficients were evaluated. The wavelength interval covered by the calculations was between 0.2 and 200 μ. Other thermal radiative properties, such as emittance and absorptance, were related to the above properties, and a comparison with available results shows favorable agreement. The use of these properties in the area of remote sensing and global energy balance makes the data essential for identifying the most effective region of the spectrum and for explaining some of the naturally occurring processes where radiative transfer plays an important role.     

Thermal cooling data for figs exposed to air cooling

This paper implies the presentation of a methodology for determining the thermal cooling data in terms of the cooling coefficients, lag factors, half cooling times and seven-eighths cooling times, as well as the heat transfer coefficients of the food products. This methodology was employed to determine the thermal cooling data for the individual figs being cooled with air at the flow velocities of 1.1, 1.5, 1.75, and 2.5 m/s. The results of this study show that the cooling coefficient and lag factor varied linearly, the half cooling time and seven-eighths cooling time decreased by 21.5% and 20.9% and the heat transfer coefficient increased by 27.3% with increasing air-flow velocity from 1.1 to 2.5 m/s.     

Mushy zone equilibrium solidification of a semitransparent layer subject to radiative and convective cooling

Equilibrium solidification in a semitransparent planar layer is studied using an isothermal mushy zone model. The layer is made up of a pure material being emitting, absorbing and isotropically scattering and is subject to radiative and convective cooling. The model involves solving simultaneously the transient energy equation and the radiation transport equation. An implicit finite volume scheme is employed to solve the energy equation, with the discrete ordinate method being used to deal with the radiation transport. A systematical parametric study is performed and the effects of various materials optical properties and processing conditions are investigated. It is found that decreasing the optical thickness and increasing the scattering albedo both lead to a wider mushy zone and a slower rate of solidification.     

Analytical approaches for thermal analysis of radiative fin with a step change in thickness and variable thermal conductivity

In this paper, heat transfer in a straight fin with a step change in thickness and variable thermal conductivity which is losing heat by radiation to its surroundings is analyzed. The calculations are carried out by using the differential transformation method (DTM) and variational iteration method (VIM) that can be applied to various types of differential equations. The results obtained employing the DTM and VIM are compared with a finite difference technique with Richardson extrapolation which is an accurate numerical solution to verify the accuracy of the proposed methods. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by VIM. After these verifications the effects of parameters such as thickness parameter α, dimensionless fin semi‐thickness δ, length ratio λ, thermal conductivity parameter β, and radiation–conduction parameter N_r, on the temperature distribution and fin efficiency are illustrated and explained. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj) . DOI 10.1002/htj.21000     

Separation of variables solution for non-linear radiative cooling

A separation of variables solution has been obtained for transient radiative cooling of an absorbing-scattering plane layer. The solution applies after an initial transient period required for adjustment of the temperature and scattering source function distributions. The layer emittance, equal to the instantaneous heat loss divided by the fourth power of the instantaneous mean temperature, becomes constant. This emittance is a function of only the optical thickness of the layer and the scattering albedo; its behavior as a function of these quantities is considerably different than for a layer at constant temperature.     

Thermal performance of a building coupled to an evaporative cooling tower

The thermal performance of a building fitted with an evaporative cooling tower has been evaluated in terms of discomfort index for two climates, namely, composite and hot-dry, typified by New Delhi and Jodhpur, respectively. The effects of various evaporative cooling parameters (height and cross-sectional area of the tower, packing factor, area of the pads, resistance offered to the air flow and local wind conditions) on the performance of the building have been analysed. It was found that, for given parameters of the tower and wind conditions, there is an optimum height of the tower for which the thermal discomfort condition in the building is minimum. The optimum values of the tower height for comfort conditions in the building for various other tower parameters have been obtained for each climate.     

Application of passive radiative cooling for dew condensation

Dew water was collected from several passive foil-based radiative condensers established in a variety of geographic settings: continental (Grenoble, in an alpine valley, and Brive-la-Gaillarde, in the Central Massif volcanic area, both in France), French Atlantic coast (Bordeaux), eastern Mediterranean (Jerusalem, Israel), and the island of Corsica (Ajaccio, France) in the Mediterranean Sea. In Ajaccio two large 30 m² condensers have been operating since 2000. Additional semi-quantitative dew measurements were also carried out for Komi?a, island of Vis (Croatia) in the Adriatic Sea, and in Mediterranean Zadar and Dubrovnik (both in Croatia). Dew potential was calculated for the Pacific Ocean island of Tahiti (French Polynesia). The data show that significant amounts of dew water can be collected. Selected chemical and biological analyses established that dew is, in general, potable. Continued research is required for new and inexpensive materials that can enhance dew condensation.     

Photovoltaic-thermal collectors for night radiative cooling of buildings

A new photovoltaic-thermal (PVT) system has been developed to produce electricity and cooling energy. Experimental studies of uncovered PVT collectors were carried out in Stuttgart to validate a simulation model, which calculates the night radiative heat exchange with the sky. Larger PVT frameless modules with 2.8 m² surface area were then implemented in a residential zero energy building and tested under climatic conditions of Madrid. Measured cooling power levels were between 60 and 65 W m⁻², when the PVT collector was used to cool a warm storage tank and 40-45 W m⁻², when the energy was directly used to cool a ceiling. The ratio of cooling energy to electrical energy required for pumping water through the PVT collector at night was excellent with values between 17 and 30. The simulated summer cooling energy production per square meter of PVT collector in the Madrid/Spain climatic conditions is 51 kWh m⁻² a⁻¹. In addition to the thermal cooling gain, 205 kWh m⁻² a⁻¹ of AC electricity is produced under Spanish conditions. A comparative analysis for the hot humid climate of Shanghai gave comparable results with 55 kWh m⁻² a⁻¹ total cooling energy production, mainly usable for heat rejection of a compression chiller and a lower electricity production of 142 kWh m⁻² a⁻¹.     

Thermal analysis on the cooling performance of a porous evaporative plate for building

In this paper, a wet porous cooling plate has been used for a building wall. Cooling can be achieved due to the evaporation in the porous layer. A mathematical model on the heat and mass transfer in the unsaturated porous media is developed to analyze the influences of ambient conditions and the porous layer thickness on the cooling performance of the porous evaporative plate. With a decrease in ambient relative humidity and an increase in ambient temperature, more cooling of the porous evaporative plate can be supplied for the inside of the room. The heat exchange between the inside surface of the porous plate and the air in the room should be intensified to achieve a higher cooling efficiency of the porous plate. The ambient wind speed and the thickness of the porous plate also have significant influence on the average temperature of the porous plate. All these results should be taken into account for the utilization of the porous evaporative cooling plate. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20284