# Heat gain through walls

The heat gain through a wall is the sum of the relatively steady-state flow (often simply termed ‘transmission’) that occurs because the inside air temperature is less than that outside, and the unsteady-state gain resulting from the varying intensity of solar radiation on the outer surface of the wall. The phenomenon of unsteady-state heat flow through a wall is complicated by the fact that a wall has a thermal capacity, and so a certain amount of the heat passing through it is stored, being released to the interior (or exterior) at some later time.

Two environmental factors are to be considered when assessing the amount of heat entering the outer surface of a wall:

(i) the diurnal variation of air temperature, and

(ii) the sinusoidal-type variation of solar intensity.

Figure 7.14 presents a simplified picture. At (a), under steady-state conditions, the graph of temperature through the wall is a straight line, the slope of which depends on the difference between the temperatures of the inner and outer surfaces and on the thickness of the wall. The calculation of heat gain under such circumstances is exactly the same as for the more familiar case of steady-state loss:

Heat flow from a point : ‘—► Movement of a point : —►

 ,Pr ‘X ,Pr ^ fr Wall Wall Wall Wall

(a) (b) (c) (of)

Fig. 7.14 Temperature gradients in a wall subjected to an unsteady heat input on the outside.

Q=U(tr-t0) (7.17)

Where Q is the rate of heat flow in W rrT2

U is the thermal transmittance coefficient in W irf2 K-1

Tr and?0 are the air temperatures in the room and outside, respectively.

A heat gain occurs if t0 exceeds tr.

The CIBSE Guide expresses the steady-state heat transfer through a wall in terms of the inside environmental temperature, instead of the inside air (dry-bulb) temperature, tT. Environmental temperature is a hypothetical temperature that gives the same rate of heat transfer as that determined by more complicated methods. It is defined as one-third of the mean air temperature plus two-thirds of the mean radiant temperature in the room. Air conditioning systems control air temperature, not environmental temperature, hence equation

(7.17) is adequate and is widely used.

Figure 7.14(b) shows the effect of raising the outer surface temperature. The temperature at the point Pb is greater than that at point Pa. Such an increase could be caused by the outer wall surface receiving solar radiation. Heat flows away from Pb in both directions because its temperature is higher than both the air and the material of the wall in its vicinity. If the intensity of solar radiation then diminishes, the situation in Figure 7.14(c) arises.

Since heat flowed away from Pb, the value of the temperature at Pc is now less than it was at Pb. When the surface temperature rises again, the situation is as shown at (d). It can be seen that the crest of the wave, represented by points Pa, Pb, Pc, Pd etc., is travelling to the right and that its magnitude is reducing. Further crests will follow the original one because a wave is being propagated through the wall as a result of an oscillation in the value of the outside surface temperature. Eventually the wave will reach the inner surface of the wall and will produce similar fluctuations in surface temperature. The inner surface temperature will have a succession of values corresponding to the point Pr as it rises and falls. Thick walls with a large thermal capacity will damp the temperature wave considerably, whereas thin walls of small capacity will have little damping effect, and fluctuations in outside surface temperature will be apparent, almost immediately, as similar changes in inner surface temperature.

It is possible for the inner surface temperatures to be less than room air temperatures, at certain times of the day, for walls of sufficiently heavy construction. A wide diurnal range of temperature can give this result. This outside surface temperature falls at night, by radiation to the black vault of the sky, and the effect of this is felt as a low inside surface temperature at some time later. At such a time, the air conditioning load will be reduced because of the heat lost into the wall from the room. Figure 7.15 presents a simplified picture of this.

 Fig. 7.15 Temperature gradient in a wall showing the possibility of heat flow outwards under Unsteady state conditions.

Posted in Air Conditioning Engineering