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assumed as a function of temperature, whereas properties of solid materials were assumed as temperature-independent. Based on the combination of three modes of heat transfer, a nodal formulation of a ventilated roof structure was provided by performing an energy balance at each node. The unsteady analysis for a one-day period, with the time step of 20 s was conducted with FDM. The validation of nu-merical model revealed few disagreements with the measured data mainly due to the wind effect which was not taken into account in the model.

In 2007, Cerne and Medved [29] indicated the lack of models which could be used for prediction of unsteady two-dimensional heat flow in ventilated building struc-tures. The authors used CFD to conduct the unsteady multi-parametric analysis of a two-dimensional heat transfer problem in the low sloped roof with a forced ventilated air-cavity made from lightweight building components. The unsteady nu-merical analysis, referred to a 24 h period, was conducted with a commercial CFD software PHOENICS based on control volume method. The ambient temperature and solar radiation intensity for a standard clear-sky summer day were used to as-sess the thermal load of a building. The air-cavity in the 2D numerical model was 9 m length and 25 mm width. The effect of a corrugated thin metal sheet on convec-tive heat transfer within the cavity was neglected. A constant airflow through the cavity and an uniform air velocity profile at the cavity inlet were assumed. Three values of airflow velocity, including 0.36, 0.72 and 1.08 m/s, were considered. The radiation attenuation in the air layer of the the air-cavity was neglected. The model was positively verified with experiments. Based on results of numerical simulations, performed with a 10 min time step, it was concluded that heat flow through the ventilated structures is markedly two-dimensional.

After reviewing the literature concerning thermal modeling of conventional solar collectors it was found that the multidimensional and unsteady character of the heat transfer problem is not considered in most of theoretical analyses. The thermal models are, in general, either simplified to much or limited to a specific design.

There is an extensive research work based on unsteady one- or two-dimensional heat transfer models. Nevertheless, most of them provide a poor guidance for the thermal modeling of the convective heat transfer within the flowing fluid and the air-cavity.

More detailed analyses of the convective heat transfer phenomena within the flowing fluid and air-cavities can be conducted with CFD models. The CFD analyses of the fluid flow and three-dimensional heat transfer in conventional solar collectors are, however, computationally time-consuming therefore a number of research works on this subject is quite low. If so exist, they are usually limited to simulations conducted under steady-state conditions.

The solar collector investigated in this study is based on a ventilated roof struc-ture. More guidance for the thermal modeling of a convective heat exchange in the air-cavity may be offered by CFD analyses of ventilated roofs. Several studies in-vestigating the effect of airflow in air-cavities of ventilated roofs can be found in the literature. Most CFD models are, however, based on a two-dimensional steady-state heat transfer and does not consider the influence of air-leakage and corrugation of a roofing material as well as other roof layers on airflow within ventilated channels.

The wind effect on a convective heat exchange in ventilated channels is mostly ne-glected. The unsteady CFD models are referred to simulations of short time-periods only.

4.3 Summary

The concept of hidden solar collector is an excellent alternative to conventional solar collectors when used to power temperature applications, such as low-temperature space-heating systems dedicated for residential buildings characterized by a low heat demand or domestic hot water systems. The collector is based on a simple solar energy collection system that is made from typical polypropylene pipes located in an air-cavity of the ventilated roof. Thus, it is characterized by low manufacturing, mounting and maintaining cost. However, the main advantage that distinguishes the collector among all active energy systems is the lack of interference in the external architecture of the building.

Due to its structure, the investigated hidden solar collector is characterized by different heat transfer problems as compared to conventional solar collectors. Its thermal performance strongly depends on climate conditions. The ambient air tem-perature, solar radiation, wind speed and other meteorological data vary in time. As a consequence, the collector always operates under unsteady conditions which are non-linear in their nature. Thus, it is difficult to accurately analyze the efficiency of a hidden solar collector based on its response to average ambient climate conditions.

A reliable evaluation of a hidden solar collector presented in this study requires the annual performance analysis based on experimental investigations. Such investiga-tions are, however, impossible to be carried out at the recent stage of the research.

Therefore, theoretical and numerical investigations are the only way to reach the general objective of this study. Due to the unsteady three-dimensional heat transfer comprising a conductive, radiative, natural and forced convective heat exchange, the performance analysis does need a numerical solution. Based on the literature review concerning the thermal modeling of the heat transfer in conventional solar collectors

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and ventilated roof structures it can be concluded that CFD analysis is the best method for a solar collector presented in this study. The numerical solution for the formulated heat transfer problem is, however, very-time-expensive. Thus, a math-ematical model for the considered case must be simplified to enable an unsteady simulation of the year-round collector operation.

Chapter 5

Model formulation

The heat transfer process in a hidden solar collector is complex (comprises all heat transfer phenomena) and multidimensional (Section 4.2.1). All physical phenomena taking part in the process are significantly influenced by time-varying weather con-ditions. Thus, it is difficult to accurately analyze the efficiency of HSC based on its thermal response to average climate conditions. What is more, a major application of HSC is to supply space-heating systems using seasonal heat storage systems. Since the maximum energy extraction from heat storage systems occurs when the avail-ability of solar energy is minimum or none, it is of great importance to determine exact amount of energy collected particularly in a winter season. Hence, a reliable numerical performance analysis of the collector requires an unsteady simulation of the year-round operation under realistic climate conditions to be carried out. This study also aims at giving some recommendations to a design of HSC in order to maximize the amount of collected energy. For these purposes, the developed 3D numerical model of HSC should enable to conduct the simulation under both tran-sient and steady-state conditions. As concluded in the previous chapter, the CFD analysis is the most accurate method for a numerical solution of a heat transfer problem in HSC. The application of this method for the simulation of unsteady heat transfer in a three-dimensional full-scale model of a one roof-field containing HSC may be, if possible, very-time-expensive. Hence, the main objective of the thermal modeling was to reach a compromise between the complexity of numerical model for simulation of both unsteady and steady-state heat transfer process in HSC, the accuracy of results and the computation run-time.

In the following, the thermal modeling approach assumed in order to investigate the performance of HSC together with the steps required in implementation of the numerical model are described in detail.

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