  Design Handbook on Passive Solar Heating and Natural Cooling (HABITAT, 1990, 162 p.)  VII. Detail design  A. General B. Solar access, shading and window protection C. Control of conductive heat flow D. Evaluation of internal heat loads E. Cross-ventilation and air flow F. Glass-mass relationship G. Air infiltration

C. Control of conductive heat flow

The rate at which heat will flow into or out of a structure is dependent on the temperature difference between inside and outside and the resistance of the various heat paths (as stated before). The designer really only has design control over the latter. The basic units and equations were introduced in chapter III including an explanation of transmittance (U-value) through homogeneous materials and groupings with air cavities such as a brick veneer wall.

In this section the concept of steady-state heat flow and quantity will be discussed.

The flow of heat through an element (wall, roof, floor etc.) between two different temperature conditions that remain steady can be described as follows: where

Q = Heat flow rate (W)
A = Area of element (m²)
(Ti - Ta) = Temperature difference (degC)
U = Transmittance (W/m² .degC)

The steady-state equation is true for conditions that do not vary, but in reality the temperature is continuously varying. The mean temperatures of each side of the element over a number of cycles can be used as an approximation of a steady-state for most purposes. This approach is widely used for simple estimations of heat flow.

Worked example No. 3

Assume the mean monthly ambient temperature. in June Is 12.7C and the inside mean temperature is 21 C. Then the temperature difference (21C - 12.7C) = 8.3 degC. The average heat loss rate through a 5-mof brick wall with render and plaster (U-value 2.3 W/m.degC) through June will be.

2 Total heat losses over time

So far attention has been paid to instantaneous values of energy flow and from this can be calculated the rate of energy flow into or out of a building. Assume a set of conditions as follows: the June mean daily temperature in Sydney is 12.7C: the building to be constantly heated to 21C with a thermostatically controlled heating system. This will create a steady state inside and so make calculations a little simpler.

The temperature difference At = 8.3C (21 12.7) and the average rate of heat flow (Q) = the U-value (U) × the area (A) × the temperature difference ( At)

The steady-state heat-flow formula is Q = U × A × at, which, being a rate and not a quantity allowance needs to be made for time to make the formula represent the quantity of energy over a specific time. So if Q = U × A × Dt then:

 G (Wh/m²) = U (W/m²) × T (hours) × Dt (temperature difference) = 2.54 × 24 × 8.3 Wh/m² = 0.5 kWh/day.m²

This is a little simplistic because it does not consider time lag in the materials, which is discussed later in this guide.

Worked example No. 4

What is the average energy saved per day in August if it is decided to insulate 25m² of brick-veneer wall? (Assume the mean indoor temperature to be 20°C.) Choose double-sided reflective foil as the insulation material, fixed to the outside of the timber frame (providing two reflective air-spaces.)

Uninsulated brick-veneer wall

U-value = 1.98 W/m² .degK

Double-sided foil insulated brick-veneer wall

U-value = 0.66 W/m² .degK

Calculate the heat loss per day; Therefore the heat saved per day is: = (1.98 - 0.66) × 25 × (20 - 12.9) × 24 × 3.6 × 10-3
= 20.24 (rounded off)
= 10Mj/day.

Where To is the mean indoor temperature and Ta is a mean daily temperature.

3. Degree-day concept

The term "heating degree days. refers to a measure of the severity of a particular climate in terms of heating to maintain thermal comfort. It has traditionally been based on a comfort level of 21 °C inside a building. In very simple terms, the amount of heat required to keep a building at that temperature will be a function of the external temperature, the amount of solar radiation entering the building and any internal gains from appliances etc., and the resistance of the external shell of the building. It has been found that the average effect of solar radiation on the temperature of a typical house is to elevate the mean internal temperature by about 3°C. On that basis it is assumed that heating would only be required if the external temperature fell below 18°C. This is a very simplistic view but it does provide a useful technique to approximate the heating load of a building. Heating degree days also permit a comparison of the severity of the winter of one place with that of another. A method of calculating the number of heating degree days for a location is described below.

The so called steady-state heat loss calculation as discussed above is only valid when a number of temperature cycles are considered, i.e., a number of days, a week, a month or a full heating season. To consider a period of a month or the full heating cycle it is convenient to use heating degree day values instead of the difference in the mean daily temperatures in the above calculation.

In Australia heating degree days are taken to a base of 18.3°C, although there are some that use a base of 15°C. This handbook presents two methods to evaluate the heating loads of a simple building; the solarch energy performance evaluation and the solarch thermal evaluation method "C". These were prepared to assist designers who did not have access to computers and sophisticated programs. The first is based on the use of heating degree day values and method "C. on a more complete knowledge of the weather data for a particular location, especially the daily amounts of solar radiation received. Heating degree day methods do not give as accurate an answer as those using sol-air temperatures (solarch method "C"), however they are quicker and can be used for simple comparisons of one construction with another. The degree-day values can be determined from basic weather data usually available from the Bureau of Meteorology.

If only the mean daily temperatures for each month are available for a specific location, then the heating degree days for each particular month can be calculated by:

DD = N (18.3- mean daily temperature for month) (where N = number of days in that month)

Example:

July, Sydney: Ta = 11.7°C
that is: 31 × (18.3 - 11.7) = 205 degree days.

The sum of all values for the heating months in Sydney is approximately 732 degree days (some references give 720 as it depends on which station values are given). if the daily mean ambient temperature is not available then it can be estimated by taking half the sum of the daily mean maximum and the daily mean minimum.

Table 14. Heating degree days (Re: 18.3C) for various cities in Australia

 Adelaide 1280 Kalgoorlie 1010 Alice Springs 660 Melbourne 1500 Brisbane 310 Tullarmarine 1800 Canberra 2270 Newcastle 770 Darwin 0 Sydney 732 Hobart 2300 Perth 775