封闭腔不透明表面辐射传递系数统计分析

基于蒙特卡罗法定义封闭腔内不透明表面辐射换热的辐射传递系数,并与角系数、哥布哈特系数进行比较,发现其在反映综合考虑表面材料物性以及空间几何位置的能量传输特性过程中更具有通用性。统计分析辐射传递系数概率分布和置信度水平,推导封闭腔内辐射传递系数的平均相对和绝对误差公式,为用蒙特卡罗法求解辐射换热中所确定的计算精度和计算工作量提供了参考依据。     

Modeling thermal behavior and work flux in finite-rate systems with radiation

We apply thermodynamic analysis in modeling, simulation and optimization of radiation engines as non-linear energy converters. We also perform critical analysis of available data for photon flux and photon density that leads to exact numerical value of photon flux constant. Basic thermodynamic principles lead to expressions for converter’s efficiency and generated work in terms of driving energy flux in the system. Steady and dynamical processes are investigated. In the latter, associated with an exhaust of radiation resource measured in terms of its temperature decrease, real work is a cumulative effect obtained in a system composed of a radiation fluid, sequence of engines, and an infinite bath. Variational calculus is applied in trajectory optimization of relaxing radiation described by a pseudo-Newtonian model. The principal performance function that expresses optimal work depends on thermal coordinates and a dissipation index, h, in fact a Hamiltonian of the optimization problem for extremum power or minimum entropy production. As an example of work limit in the radiation system under pseudo-Newtonian approximation the generalized exergy of radiation fluid is estimated in terms of finite rates quantified by Hamiltonian h. The primary results are dynamical equations of state for radiation temperature and work output in terms of process control variables. In the second part of this paper these equations and their discrete counterparts will serve to derive efficient algorithms for work optimization in the form of Hamilton–Jacobi–Bellman equations and dynamic programming equations. Significance of non-linear analyses in dynamic optimization of radiation systems is underlined.     

A useful integral function and its application in thermal radiation calculations

A new integral function has been discovered. The present function is found to be useful in computing the spectral emissivity of an isothermal volume containing either soot or gaseous species, or both. Examples of its application are discussed herein.     

The contribution of the thermal radiation of the inner surfaces of a room on its thermal losses

The temperature difference between the surfaces of the internal and the external walls of a room causes a heat flux from the internal to the external walls through radiation and finally to the environment through conduction. This thermal flux, which is different to the thermal losses due to the conductance of the external walls, is a function of the thermal and the structural characteristics of the walls. In the present work a simple analytical expression is given, which relates the thermal losses due to radiation and the total thermal losses due to radiation and convection directly to the structural characteristics of the room, that is the reflectivity of the internal surfaces, the conductance of the external walls, the ratio of the external to the internal wall surfaces and the temperatures of the internal space of the room and the environment. This relationship has been verified by experiments carried out on an experimental arrangement which simulates this phenomenon.     

Entransy expression of the second law of thermodynamics and its application to optimization in heat transfer process

Based on theories of thermodynamics, the energy equation in terms of entransy in heat transfer process is introduced, which not only describes the change of entransy, but also defines the entransy consumption rate. According to the regularity of entransy change in heat transfer process and the effect of entransy consumption rate on the irreversibility of heat transfer process, it can be found that entransy is a state variable, from which a new expression for the second law of thermodynamics is presented. Then by setting entransy consumption rate and power consumption rate as optimization objective and constraint condition for each other, the Lagrange conditional extremum principle is used to deduce momentum equation, constraint equation and boundary condition for optimizing flow field of convective heat transfer, which are applied to simulate convective heat transfer coupling with energy equation in an enclosed cavity. Through the numerical simulation, the optimized flow field under different constraint conditions is obtained, which shows that the principle of minimum entransy consumption is more suitable than the principle of minimum entropy generation for optimizing convective heat transfer process.     

The influence of solar and long-wave radiation on the thermal gain of a room with opaque external wall

The thermal gain of a room is influenced by the solar radiation, the environmental (long-wave) radiation and the radiation of the internal walls of the room considered as gray bodies at different temperatures. In the present work a relation is obtained that includes the influence of the above radiations on the thermal gain of the room. This analytical relation was confirmed experimentally, mainly with respect to the influence of the internal room radiation on the thermal gain.     

Enhancement of PCM melting in enclosures with horizontally-finned internal surfaces

A numerical model for simulating the melting of a phase change material (PCM) housed within an internally-finned metal enclosure is developed. A finite volume approach, utilizing the temperature-transforming model for phase change, is used to predict the conjugate heat transfer in the cavity walls and fins, as well as within the molten PCM. The influence of the number of fins, the fin length and thickness, and the hot wall temperature on the melting process is reported. With horizontal fins, rapid melting occurs during the early stages of the phase change, followed by a second, slow melting regime. Analytical correlations are developed that can be used to quickly estimate melting rates during both melting regimes, and it is shown that the predictions of the correlations are in good agreement with those of the detailed model.     

Transient thermal analysis of semitransparent composite layer with an opaque boundary

Transient coupled radiative and conductive heat transfer in a two-layer, absorbing, emitting, and isotropically scattering non-gray slab is investigated by the ray tracing method in combination with Hottel's zonal method. One outer boundary is opaque, and another is semitransparent. The radiative energy transfer process in a semitransparent composite is divided into two sub-processes, one of which considers scattering, the other does not. The radiative transfer coefficients of the composite are deduced under specular and diffuse reflection and combined specular and diffuse reflection, respectively. The radiative heat source term is calculated by the radiative transfer coefficients. Temperature and heat flux are obtained by using the full implicit control-volume method in combination with the spectral band model. The method presented here needs only to disperse the space position, instead of the solid angle. A comparison with previous results shows that the results are more accurate.     

Analysis of entropy generation during natural convection in porous enclosures with curved surfaces

The natural convection is analyzed via the entropy generation approach in the differentially heated, porous enclosures with curved (concave or convex) vertical walls. The numerical simulations have been carried out for various fluids (Prandtl number: Pr_m?=?0.015, 0.7, and 7.2) at various permeabilities (Darcy numbers: 10^?5?≤?Da_m?≤?10^?2) for a high value of Rayleigh number (Ra_m?=?10⁶). The finite element method is employed to solve the governing equations and that is further used to calculate the entropy generation and average Nusselt number. The detailed spatial distributions of S_θ and S_ψ are analyzed for all the wall curvatures. Overall, the case with the highly concave surfaces (case 3) is the optimal case at low Da_m, whereas the cases with the less convex surfaces (cases 1 and 2) are the most efficient cases at high Da_m.     

A model of the thermal restoration transient state of an opaque wall after the interruption of solar radiation

The temperature distribution of an outer wall of a room subjected to solar radiation goes through a transient state until it reaches a thermal equilibrium state. After an interruption of solar radiation, the temperature profile on the wall cross-section, starting from the latter thermal equilibrium state, returns through a transient state to the initial thermal equilibrium state. The transient state between the above two equilibrium states is called the thermal restoration transient state of the wall. The duration of the thermal restoration transient state depends on the structural characteristics of the wall and on the thermal parameters of the room–environment system. The influence of the thermal restoration transient state on the evaluation of the ability of an opaque wall to store and exploit solar radiation and on the computation of the resulting thermal gain of the room during the thermal restoration of the wall is important, because it acts as a flywheel. In the present work analytical expressions yielding the temperature profiles and the duration of the transient state as a function of thermal and structural characteristics have been developed. An analytical model for the thermal gain of the room during the thermal restoration of the wall also was developed. An experimental verification of the duration of the transient state of the thermal restoration was made.     

Evaluation of the ability of an opaque wall to store and exploit solar radiation

The ability of an external opaque wall of a room to perform two functions, i.e. to store the thermal energy when it reaches thermal equilibrium under solar radiation, and to exploit the stored thermal energy during the transient phenomenon of the wall thermal restoration after the interruption of solar radiation flux, was analysed. Analytical expressions have been obtained for the ability of the wall to store and exploit solar radiation, and for the resulting thermal gain of the room during the transient state of its thermal restoration.     

Evaluation of solar radiation and its application for photovoltaic/thermal air collector for Indian composite climate

In this paper, an attempt has been made to evaluate cloudiness/haziness and atmospheric transmittance factors for the composite climate of New Delhi, India by considering the hourly data of global and diffuse radiation obtained for (i) the city region, experimentally observed and (ii) the flat land region obtained from the Department of Indian Meteorology, Pune. Cloudiness/haziness factor for the two models have been determined using simple regression analysis for clear sky condition for New Delhi. The comparison between the cloudiness/haziness and atmospheric transmittance factors for the composite climate of New Delhi for both the models and regions have been made. It has been observed that the cloudiness/haziness and atmospheric transmittance factors obtained by both models gave fair agreement within an accuracy of 0.57%. It has also been observed that there is a significant effect of region on beam and diffuse radiation due to cloudiness/haziness factors as expected. Further the data of solar radiation obtained from the Department of Indian Meteorology, Pune, have been used to evaluate the monthly performance of photovoltaic thermal (PV/T) air collector. It has been found that an overall thermal efficiency and exergy efficiency of PV/T air collector were about 50 and 14%, respectively. Copyright © 2006 John Wiley & Sons, Ltd.     

Conjugate turbulent natural convection with surface radiation in air filled rectangular enclosures

Conjugate turbulent natural convection and surface radiation in rectangular enclosures heated from below and cooled from other walls, typically encountered in Liquid Metal Fast Breeder Reactor (LMFBR) subsystems, have been investigated by a finite volume method for various aspect ratios. The formulation comprises the standard two equation k–ε turbulence model with physical boundary conditions (no wall functions), along with the Boussinesq approximation, for the flow and heat transfer. As far as radiation is concerned, the radiosity – irradiation formulation for a transparent fluid of Prandtl number 0.7 has been employed. The conjugate coupling on the walls has been handled by using a fin type formulation. The Rayleigh number based on the width of the enclosure is varied from 10⁸ to 10¹² and the aspect ratio is varied from 0.5 to 2.0. Detailed results including stream lines, temperature profiles, and convective, radiative and overall Nusselt numbers are presented. A correlation for the mean convection Nusselt number in terms of Rayleigh number and aspect ratio is proposed for design purposes. The influence of the wall emissivity and the external heat transfer coefficient on the heat transfer from the enclosure has also been investigated.     

Calculation of the distribution of incoming solar radiation in enclosures

Solar heat gains are an important factor in the calculation of cooling loads for buildings. This paper aims at introducing an improved methodology to calculate the distribution of incoming solar energy on the internal surfaces of closed spaces with multiple openings. The independent numerical methodology is based on the view factor theory and in order to justify and prove its functionality, it has been linked to the commercial software of TRNSYS, which normally uses a surface area ratio based algorithm for the same process. For the simplified building structures that have been examined, there are noticeable differences in the spatial and temporal distribution of the absorbed solar energy. The proposed approach is indeed an improvement over the surface area ratio method, having a strong physical basis with relatively little extra computational effort.     

High flux boiling applied to microelectronics thermal control

This discussion of the application of nucleate pool boiling to the cooling of microelectronic devices begins with recollection of several of Professor Westwater's important early contributions to boiling. Early studies of immersion cooling of electrical equipment are cited and the evolution of this technology to cooling of microelectronic devices is outlined. The important issues related to the current applications of immersion cooling are discussed. These issues include single-phase natural convection, incipient boiling, established boiling, enhanced boiling, and critical heat flux. The work done by Professor Westwater and his students over twenty years ago is now providing important insight into the critical heat flux as encountered in microelectronic chips.     

Heatline based thermal management for natural convection within right-angled porous triangular enclosures with various thermal conditions of walls

Analysis of natural convection in porous triangles have many important energy related applications in geophysical and solar energy fields. A numerical study on heat distribution and thermal mixing during steady laminar natural convective flow inside a right-angled triangular enclosure filled with porous media subjected to various wall boundary conditions is investigated in this study using Bejan’s heatlines approach. Influence of various thermal boundary conditions and inclination angles (φ) on evaluation of complex heat flow patterns are studied as a function of Darcy numbers (Da) for various regimes of Prandtl (Pr) and Rayleigh (Ra) numbers. Studies illustrate that maximum heat transfer occurs at the top vertex for lower top angle (φ=^°15) at higher Da(Da=10⁻³). As φ increases to ^°45, the maximum heat flux at the top vertex decreases and thermal mixing increases irrespective of Da and Pr. The enhanced convection at higher Da significantly affects the heat flow distribution, which is clearly depicted by high local Nusselt numbers at Da=10⁻³. It is also found that isothermal heating of walls enhances the heat distribution and thermal mixing. Overall, it is shown that heatlines provide suitable guideline on thermal management in porous right-angled triangular enclosures with various heating strategies.     

Transient thermal energy storage in partitioned enclosures packed with microencapsulated phase change materials

In this work, transient characteristics of thermal energy storage in partitioned enclosures filled with microencapsulated phase change material (MEPCM) particles were examined experimentally and numerically. The enclosure is partitioned with aspect ratio λ and packed with different MEPCMs with melting temperatures about T_M = 28 °C and 37 °C. The top and bottom surfaces of the partitioned enclosure are, respectively, maintained at hot and cold temperatures, while the other surfaces are kept thermally insulated. The results showed that at the initial transient, the net energy storage in partitioned enclosure, Q_net, increases with the time. Finally, the Q_net approaches quickly the steady state. Additionally, higher dimensionless accumulated energy through the hot wall Q_h and cold wall Q_c are found for a case with higher hot wall temperature T_h. that the faster melting is experienced for the system with higher Stefan number and the subcooling number is the main parameter to dominate the thermal latent heat storage of the MEPCM system. In addition, better net energy storage is noted for a partitioned enclosure with a smaller aspect ratio.     

Stability of thermal transpiration flows in rectangular enclosures – Axisymmetric disturbances

Occurrence of instabilities for thermal transpiration flow of rarefied gases has been discussed in two-dimensions. Only axisymmetric disturbances have been considered due to symmetry of the basic flow. Effect of four second-order slip models (Cercignani, Deissler, Schamberg, and Beskok) and a first-order slip model (Maxwell) on the limits of the proposed instability have been examined. We have found that Beskok model is always stable to axisymmetric disturbances and Maxwell model is more stable compared with the other second order models. Variation of critical Reynolds number for different rarefaction levels (Knudsen numbers) has also been studied. Increase in Knudsen number leads to monotonic decrease in critical Re numbers.     

Solar collector surfaces with wavelength selective radiation characteristics

The use of porous materials through which a coolant is forced for the protection of surfaces exposed to high temperature gas streams has been discussed in a number of recent papers. The knowledge of the radiation properties of these materials is required if the designer is to be able to predict the porous wall temperatures to determine whether metallurgical limitations have been exceeded. With this application in mind, measurements were previously reported for the absorptivity for solar radiation of a number of porous surfaces.¹ Since that time total normal emissivity data have been obtained for the same surfaces. In viewing these results, it was discovered that these surfaces combined high absorptivity for solar radiation with a low emissivity value, and consequently their use as solar collectors is suggested. It is the purpose of this paper to describe the experimental apparatus used to obtain the radiation data and to compare the recent emissivity measurements with the solar absorptivity data for the same surfaces. For specified conditions, an efficiency is defined which allows a quantitative comparison of these with other surfaces as solar collectors.