## Wall And Roof Transfer Functions

Conduction transfer functions are used by the TFM to describe the heat flux at the inside of a wall, roof, partition, ceiling, and floor. Combined convection and radiation coefficients on the inside (8.3 W/m2-K) and outside surfaces (17.0 W/m2-K) are utilized by the method. The approach uses sol-air temperatures to represent outdoor conditions and assumes constant indoor air temperature. Thus, the heat gain though a wall or roof is given by

£ bn (te,9-n6) rc £ Cn - £ dn (4e,9-n6/A) n = 0 n = 0 n = l

where qe,9 = heat gain through wall or roof, at calculation hour 9 (W). A = indoor surface area of wall or roof (m2).

n = summation index (each summation has as many terms as there are non-negligible values of coefficients). tefl-n6 = sol-air temperature at time 9-n6 (°C). trc = constant indoor room temperature (°C). bn, cn, dn = conduction transfer function coefficients.

Conduction transfer function coefficients depend only on the physical properties of the wall or roof. These coefficients are given in tables (ASHRAE, 1997). The b and c coefficients must be adjusted for the actual heat transfer coefficient (Uactual) by multiplying them with the ratio Uactual/Ureference.

In Eq (6.4), a value of the summation index n equal to 0 represents the current time interval, n equal to 1 is the previous hour, and so on.

The sol-air temperature is defined as te = t0 + aGt/h0 - e6R/h0 (6.5)

where te = sol-air temperature (°C). t0 = current hour dry-bulb temperature (°C). a = absorptance of surface for solar radiation. Gt = total incident solar load (W/m2).

6R = difference between longwave radiation incident on the surface from the sky and surroundings and the radiation emitted by a blackbody at outdoor air temperature (W/m2). h0 = heat transfer coefficient for convection over the building (W/m2-K). e 6R/h0 = longwave radiation factor = -3.9°C for horizontal surfaces, 0°C for vertical surfaces.

The term a/h0 in Eq. (6.5) varies from about 0.026 m2-K/W for a light-colored surface to a maximum of about 0.053 m2-K/W. The heat transfer coefficient for convection over the building can be estimated from h0 = 5.7 + 3.8 V (6.6)

where h0 is in W/m2-K and V is the wind speed in m/s. PARTITIONS, CEILINGS, AND FLOORS

Whenever a conditioned space is adjacent to other spaces at different temperatures, the transfer of heat through the partition can be calculated from Eq. (6.4) by replacing the sol-air temperature with the temperature of the adjacent space.

When the air temperature of the adjacent space (tb) is constant or the variations of this temperature are small compared to the difference of the adjacent space and indoor temperature difference, the rate of heat gains (qp) through partitions, ceilings, and floors can be calculated from the formula qp = UA(tb - h) (6.7)

where

A = area of element under analysis (m2).

U = overall heat transfer coefficient (W/m2-K).

(tb - t) = adjacent space-indoor temperature difference (°C).

### GLAZING

The total rate of heat admission through glass is the sum of the transmitted solar radiation, the portion of the absorbed radiation that flows inward, and the heat conducted through the glass whenever there is an outdoor-indoor temperature difference. The rate of heat gain (qs) resulting from the transmitted solar radiation and the portion of the absorbed radiation that flows inward is qs = A(SC)(SHGC) (6.8)

where

A = area of element under analysis (m2). SC = shading coefficient.

SHGC = solar heat gain coefficient, varying according to orientation, latitude, hour, and month.

The rate of conduction heat gain (q) is q = UA(to - ^) (6.9)

where

A = area of element under analysis (m2). U = glass heat transfer coefficient (W/m2-K). (to - ti) = outdoor-indoor temperature difference (°C).

### PEOPLE

The heat gain from people is in the form of sensible and latent heat. The latent heat gains are considered as instantaneous loads. The total sensible heat gain from people is not converted directly to cooling load. The radiant portion is first absorbed by the surroundings and convected to the space at a later time, depending on the characteristics of the room. The ASHRAE Handbook of Fundamentals (2005) gives tables for various circumstances and formulates the gains for the instantaneous sensible cooling load as:

where qs = rate of sensible cooling load due to people (W).

N = number of people.

SHGp = sensible heat gain per person (W/person).

The rate of latent cooling load is ql = N(LHG p) (6.11)

where ql = latent cooling load due to people (W).

N = number of people.

LHGp = latent heat gain per person (W/person).

### LIGHTING

Generally, lighting is often a major internal load component. Some of the energy emitted by the lights is in the form of radiation that is absorbed in the space and transferred later to the air by convection. The manner in which the lights are installed, the type of air distribution system, and the mass of the structure affect the rate of heat gain at any given moment. Generally, this gain can be calculated from 