# Physical Phenomena

11.3.2.1 Introduction

In this section the basic physical models for the simulation of the dynamic thermal behavior of a building are given. The description starts with the trans­fer of heat and solar radiation through the building envelope, then summa­rizes the various ways that this energy is distributed in the room, shows the methods to calculate the instantaneous space sensible load (in other words, the cooling or heating load of the room), and finally deals with the outdoor conditions. In addition, a short overview of the modeling of HVAC compo­nents and systems is given.

11.3.2.2 Heat-Transfer Processes

Heat is transferred by means of three quite different mechanisms:

• Thermal conduction

• Thermal convection

Conduction

Conduction is the heat transfer due to spatial temperature differences (temperature gradient) without any macroscopic material movement. Conduc­tion is important in solids and depends essentially on the material properties (Fig. 11.27).

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differ­ences (buoyancy forces), the heat transfer is termed Free convection. Typical ex­amples are the cold down-draft along a cold wall or the thermal plume upward along a warm verrical surface. Forced convection takes place when fluid move­ment is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe.

Kach body having a temperate above absolute zero radiates energy in the form of electromagnetic waves. The amount of energy emitted is dependent on the temperature and on the emissivity of the material. The wavelength or frequency distribution (the spectrum) of the emitted radiation is dependent on the absolute temperature of the body and on the surface properties.

Long-wave radiation (infrared radiation) is in the range of 0.8-100 |xm, short-wave radiation (visible as light) is in the range 0.4-0.8 p. m, and solar radiation is in the range 0.3-3.0 |i, m.

11.3.2.3 Heat-Exchange Processes in the Room

Heat-Balance Equations

The air temperature of a room at any given time is given by a hear-balance equation which includes the heat flux exchanged by convection at each wall element (A • Qc), the heat flow exchanged by ventilation (<&„), the convective part of hear flow due to internal heat gains (<!>„;), the convective part of heat flow due to the HVAC system (<I>hc)T and the variation of energy in the room air(c M dffa/dt):

+ + = (1L13)

I =■ i

The individual hear fluxes in (Eq. 11.13)—<7r. ^c^Hc—are a^so time —

Dependent.

The convection term Qc is given by (hc, convective heat transfer coeffi­cient; fls, inside surface temperature of wall element J; 0^, room air tempera­ture):

<tc, = h40‘-9*>- <ll-14>

The internal surface temperature of each wall element / is given by a heat — balance equation:

Tfh,/’ *7sr./ A X ‘ ’Pit,/ — 0 , (11.15)

Where Qlr is the heat flux by long-wave radiation exchange with other internal surfaces, QSr is the heat flux due to the absorbed short-wave radiation, Qt is the heat flux by convection, Qcd is heat flux by conduction, is the heat flux

Due to rhe radiative component of the internal heat gains, and <piu is the view factor between source and surface / (Figs. 11.29 and 11.30).

The humidity ratio of a room at any given time is given by a latent hear balance equation including the water vapor flows due to infiltration F), To ventilation to moisture transport through envelope elements

(Mw D), to internal sources (Mw j), and to the HVAC system (MK,;,), and the variation of moisture content in the zone air mass M (M dxa/dt):

AW+ + + = M (11.16)

All heat flux and moisture flux elements in Eqs. (11.13) To (11.16) Are also time-dependent.

The heat transferred into a room by solar radiation (short-wave radiation) strongly influences the room climate. Direct and diffuse solar radiation are generally considered separately (Fig. 11.31). Reflections normally are not con­sidered in building simulation codes. According to this assumption, the direct radiation is attributed to the surfaces hit by the beam, while diffuse radiation is distributed to the individual surfaces in the room either according to the area of each surface (area-weighted approach) or according to the geometric situation as seen from the transparent surface (view-factor method, see also long-wave radiation exchange later). At the wall surface, the energy balance is

Long-wave

 A RaHtarinn H Solar F-y

 Diffus

FIGURE 11.31 Radiation fluxes at the building facade: the solar radiation components (direct or beam, diffuse, and reflected radiation from the ground or other buildings) and the components of the radiation back from the building facade (reflected solar and thermal infrared radiation from the building envelope).

Established by long-wave radiation exchange to other surfaces, by con­vection to the room air, and by heat conduction into the wall construc­tion.

Proper consideration of solar radiation exchange between two rooms through a transparent element is important when analyzing atria, sun — spaces, or glazed double facades.

Convective Heat Transfer at Surfaces

The kind of convective heat transfer—forced convection or natural (at floor, wall, or ceiling)—must be considered and taken into account by- selecting appropriate values for the convective heat transfer coefficient H( (see Eq. (11.14)). Thus, the heat transfer coefficient implicitly assumes the flow situation at the surface. Normally, coefficients for convective heat transfer are considered as a preset constant parameter (the coeffi­cient may be defined as variable, however, depending on other parame­ters). Therefore, the selection of appropriate values is crucial. Values for heat transfer coefficients can be found in several references; a compre­hensive summary is given in Daskalaki.1

All surfaces in a zone exchange long-wave radiation with each other. The net energy transmitted from one surface to another is dependent on the surface temperatures, the surface emissivity, the area, and the orienta­tion of the two surfaces relative to each other. For long-wave radiation, the surface emissivity is assumed to be angle independent. The geometric relation of the two surfaces is described by the view factor. If multireflec­tions are taken into account, the net radiation heat exchange is calculated using exchange factors (e. g., according to Gebhart2).

Internal Heat Gains (Casual Gains)

In industrial applications, internal heat gains are very often the most im­portant factor affecting the thermal indoor climate. Typical heat sources are machines, appliances and equipment, and all kind of processes taking place in the room. Artificial lighting and people further contribute to the internal heai load in the room.

In the simulation, the time dependency of the energy release of such sources is defined in so-called schedules. The heat sources transfer energy to the room air by convection and to the surfaces by long-wave radiation. In principle, heat sources can be modeled by two kinds of parameterization!

• Heat source with defined surface temperature and area

• Heat source with predefined total gain and the split between convective and radiative heat release

In the case of a given surface temperature, the amount of energy released is determined by the parameters for the convective and radiative heat ex­change. As far as convection is concerned, these are the temperatures of the heat source surface and room air, respectively, and the heat transfer coeffi­cient. The radiative heat exchange is determined by the view factors and the temperatures of the surrounding surfaces.

In the second approach, the energy release is split by a predefined (mostly constant) factor between convection and radiation. The convective part is di­rectly transferred as energy gain to the room air, while the radiative part is distributed to the surrounding walls by the area-weighted method or the view-factor method.

Heat gains from internal loads normally are sensible heat. Nevertheless, many processes release a significant amount of moisture. Also, occupants pro­duce relevant amounts of latent heat, especially at high metabolic rates and at high air temperatures.

Ventilation

When air flows at a certain rate through the space, energy is transported in relation to the difference between supply and extract air temperature. Such airflow can be induced by natural or mechanical ventilation. See Section 11.5 on the interaction between naturally induced airflows and the thermal behav­ior of the room.

Heat Storage In the Room

Normally, the heat storage capacity of the air in the space can be ne­glected. Machines, tools, equipment, etc. situated in the room may have a sig­nificant influence on the thermal behavior of the room and must be considered in the simulation.

11.3.2.4 Outdoor Conditions

Outdoor Air Temperature

Outdoor air temperature is an important factor regarding the building en­ergy balance. Outdoor air temperature affects the heat transfer through exter­nal walls and roofs and the heat transfer by ventilation. Moreover, outdoor air

Temperature is a driving force for natural ventilation, as the difference be­tween indoor and outdoor air temperature causes the stack effect.

Outdoor Air Humidity

Outdoor air humidity strongly affects the latent cooling load and energy requirements during summer season. Year-round outdoor air humidity must be considered when studying condensation conditions.

Wind

Wind affects the convective heat transfer on external walls and is a driv­ing force for natural ventilation.

The total or global solar radiation has a direct part (beam radiation) and a diffuse part (Fig. 11.31). In the simulation, solar radiation input values must be converted to radiation values for each surface of the building. For nonhori­zontal surfaces, the diffuse radiation is composed of (a) the contribution from the diffuse sky and (b) reflections from the ground. The diffuse sky radiation is not uniform. It is composed of three parts, referred to as Isotropic, circum­solar, and Horizontal brightening. Several diffuse sky models are available. De­pending on the model used, discrepancies for the boundary conditions may occur with the same basic set of solar radiation data, thus leading to differ­ences in the simulation results.

The solar radiation absorbed on external building surfaces increases the wall surface temperature, thus leading to a change in the heat conducted through the component. In low-wind conditions, free convective flows drift up the warm external wall surface. This changes the convective heat transfer and leads to increased temperatures of supply air for natural ventilation.

Neither effect normally is accounted for in building simulation programs. Normally, for energy analysis, this is not critical, but it may have a significant effect ori natural ventilation of multistory buildings.