Details:HeatTransfer
Heat Transfer Coefficients and Resistances
If a wall surface is warmer than its surroundings, it will give off heat. This heat transport is effected by several transport mechanisms: heat conduction through the air adjacent to the surface, convective transport by air flows, and emission of long-wave radiation. Detailed modelling of all these phenomena is extremely complicated, but fortunately it is not necessary in the context of building physics. For the temperature and flow situations encountered here, a simple proportionality with a constant coefficient is usually adequate:
| q = a · (Ja - Js) |
| q | [W/m²] | : | heat flux density | |
| a | [W/m²K] | : | heat transfer coefficient | |
| Ja | [°C] | : | ambient temperature | |
| Js | [°C] | : | surface temperature |
The heat transfer coefficient consists of two parts:
| a = ac + ar | ||||
| ac | [W/m²K] | : | convective heat transfer coefficient | |
| ar | [W/m²K] | : | radiative heat transfer coefficient | |
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convective heat transfer coefficient The air adjacent to the component surface drains heat from the component by conductive and convective heat transport. Although these are two distinct transport phenomena, they are lumped together in the term of 'convective heat transfer'. Right next to the wall, the air takes on the temperature of the wall surface. At some distance from the surface, the convective mixing of the air maintains a nearly constant temperature distribution which is determined by the indoor or outdoor climate. It's usually the latter temperature that is measured as the 'air temperature'. However, the heat transfer from the wall surface to the adjacent air is not determined by the difference between the surface temperature and the 'air temperature' but by the smaller difference between the surface temperature and the temperature of the boundary layer. The heat flow is thus less than might be expected from the air temperature. This reduction of the heat flow is formally allowed for by introduction of a 'resistance'. The reciprocal of this resistance is the convective heat transfer coefficient in the above heat transport equation.
The numerical value of the c.h.t.c. is in a complicated way dependent on the
temperature, the magnitude and direction of a possible air flow, the nature of the
wall surface etc. Only rough values can be given for general cases. With free
convection (by warming or cooling of the air) the c.h.t.c is in the range
from 3 to 10 W/m²K, with forced convection (by wind), in the range from
10 to 100 W/m²K. |
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radiative heat transfer coefficient A wall surface always exchanges long-wave thermal radiation with other surfaces in its surroundings. The corresponding heat flow depends on the temperatures (to the fourth power), the materials, the nature of the surfaces, the size and the geometrical arrangement of the involved surfaces. Since in most cases the temperatures of the other surfaces are not known, they are for the purpose of calculations in building physics usually assumed to be identical to the known air temperature. Furthermore, three of the four powers of the temperature are lumped together with the r.h.t.c. (which thus becomes temperature-dependent), and the result is a simple linear relationship analogous to the convective heat transfer (see also the discussion of the long-wave radiation exchange). The dependence on the material of the wall and the nature of the surface is negligible as long as the materials are non-metallic, which is usually the case in the context of building physics. For two close, extended, parallel, plane, non-metallic surfaces the r.h.t.c. lies between ca. 3 and 6 W/m²K.
Please note that the r.t.h.c. only applies to radiation exchange between surfaces which
are more or less at ambient temperature. Solar radiation (with a source temperature of
6000 K and a marked diurnal variation) is treated separately (see
reference: Short-wave Radiation Absorptivity). |
In compliance with recent changes in standardized terminology, WUFI now employs the heat transfer resistance, which is simply the reciprocal of the heat transfer coefficient.
For the sake of simplicity, WUFI uses either constant heat transfer resistances, or a very simple dependence on wind speed, since allowing for the ambient conditions in a detailed way would be very complex, and only in the rarest cases all the necessary boundary conditions are known.
In addition to allowing the user to provide his own preferred values, WUFI offers the following predefined heat transfer resistances for selection:
| exterior heat transfer resistance: | ||
| • | 0 m²K/W | for basement walls in direct contact with the surrounding soil |
| • | 0.052 m²K/W | for pitched or flat roofs |
| • | 0.056 m²K/W | for outer walls [1], |
These average values do not apply to greatly exposed building components or building surfaces at great height, where correspondingly lower heat transfer resistances must be substituted.
| interior heat transfer resistance: | ||
| • | 0.13 m²K/W | for basements, outer walls, roofs [2] |
The interior h.t.r. in the region of corners or edges is generally higher than this
average value. Should there be a stratification of temperature in a room, moisture
transport calculations must not allow for this by a transfer resistance based on the
mean temperature, since this results in an erroneous assessment of the moisture conditions
at the interior surfaces. If a vertical room temperature profile is to be taken into
account, this can only be done by specifying the boundary conditions as a function of
height.
The heat transfer resistances only describe heat exchange with the ambient air or with surrounding surfaces which are at a temperature close (+/- several tens of degrees) to the temperature of the building component. For the heat load due to solar radiation, see reference: Short-wave Radiation Absorptivity.
Regarding the problem of nightly radiation cooling, see reference: Long-wave Radiation Exchange.
The heat transfer resistances are entered in the dialog "Surface Transfer Coefficients".
Literature:
| [1] | Schaube, H. und Werner, H.:
Wärmeübergangskoeffizient unter natürlichen Klimabedingungen. |
| [2] | Erhorn, H. und Szerman, M.:
Überprüfung der Wärme- und Feuchteübergangskoeffizienten
in Außenwandecken von Wohnbauten. |
