# Energy flows in a heating system – how and where heat moves around

This article applies simple school physics to heat energy flows in a heating system in an attempt to understand how heating systems can behave, and misbehave, and to provide guidance on some settings and basic measurements. Metric units are generally used.

I hope you find it reasonably clearly written, even if a little demanding in places. However, it didn’t start with a well-formed plan. I use writing to force myself to organise my thoughts and some of the material here had been posing unresolved and nagging questions in my mind. Where I came upon answers it was by stumbling around, so if they appear obvious to you, they weren’t to me!

The simplest situation to consider is a heated property which has reached a steady state – the house and outdoor temperatures are constant. The simple diagram below (art was never my strong point) illustrates the flow of energy.

The term “house temperature” is a rather loose concept as different parts of the house will be at different temperatures. To keep ideas simple, we can think of it as the temperature at the house’s room thermostat.

In the illustration, fuel (gas) flows along the pipe to the boiler, but the concepts are the same for oil, electricity or wood.  The chemical energy in the fuel is converted to heat by burning it with oxygen in the boiler. (Oxygen forms just over one-fifth part of air, nearly all the rest being nitrogen, which is little affected by passing through the boiler.) The heat from the hot gases is transferred to the heating system water within the boiler’s heat exchanger.

The next transfer is from the heated water in the radiator system (that is, any radiator system including underfloor) to the fabric of the building which is warmed for our comfort. As the building isn’t perfectly insulated, heat is lost to the outside environment.

For the temperatures to be steady, the heat losses must be perfectly balanced by the heat supplied by the boiler, and this is maintained by thermostatic devices – one or a combination of room thermostat, boiler thermostat and thermostatic radiator valves (TRVs). A modern boiler may be able to modulate, that is adjust, its rate of burning gas to achieve this. Older boilers are either on or off, and burn for a period, then rest, such that over time, the average power balances the heat lost. (In reality, the boiler power required may be lower than a modern boiler’s minimum power, so it too burns and rests in succession.)

 Energy and power   We’re equipped by nature to perceive energy in the form of light, heat, sound and motion, and the conversion of mechanical energy to heat by friction so we have some intuitive understanding of it, and this article doesn’t try to be too deep and meaningful. The metric unit of measurement is the joule.   Power is the rate at which energy is transferred from one place or one form, to another. The measurement unit, equivalent to the joule per second, is the watt, though kilowatts are commonly used for households and appliances. 1 kilowatt = 1000 watts and is abbreviated kW.   Domestic energy consumption is usually stated as so many kilowatt-hours. If a boiler runs at 5kW for an hour, the energy used is 5 kilowatt-hours, or 5kWh.

Summary: when the temperatures of a heated property and outdoors are steady the (average) boiler power equals the loss rate from the building. If the building loses heat at the rate of 2 kilowatts, 2 kilowatts, on average, is demanded from the boiler.

The building loss rate can be quite modest. My small semi-detached house is relatively poorly insulated (solid 9 inch brick wall, no cavity). During the coldest week of winter of January 2013 (not the coldest winter, admittedly), the boiler demand, averaged over the week, was 4 kilowatts (4kW), which included hot water demand as well as central heating. The power averaged over the year May 2013-2014 was 1.4kW and the cheapest week averaged 0.65kW. We can see that a boiler capable of producing say 24kW is going to spend most of its time not burning gas.

The box below shows you how to calculate average power, should you wish. Of course you could just measure gas consumption but the virtue of converting to kilowatts (or kilowatt-hours) is to allow comparison with other heat sources.

Note that it’s not easy to accurately quantify the effectiveness of energy saving measures as outside temperatures are so variable from week to week and year to year. Hence the importance of facilities like that at Salford University where an entire reconstructed house is enclosed within an environmental chamber, enabling meaningful measurements to be made.

 How to measure your boiler’s average power   Let’s say we want the average power over a week. We take an initial reading from our gas meter, and a second one after a week has elapsed. The difference gives the amount of gas burned over the week. Suppose the first reading is taken at 9am on a Sunday morning and the second at noon the following Sunday, 3 hours later in the day, 7 days later. The number of hours between the readings is 7 x 24 + 3 = 171.   We’ll start with a metric meter, calibrated in cubic metres, written from now on as m3. The initial reading, picked at random is 08642, and the second, 08693, a difference of 51m3. So the hourly usage is 51/171, close to 0.3m3/hour. To find the energy used, we multiply by what’s termed the calorific value of the gas. While this can vary over a range, it’s often taken to 10.75kW per m3 per hour. So the average power over that week is 0.3 x 10.75 = 3.2kW.   Now for an imperial meter, calibrated in cubic feet (ft3). The initial reading is 168855, and the second, 170338, difference 1483 ft3. To convert to m3 we multiply by 0.0283168 (or use an online converter) and obtain close to 42 m3. and hourly usage 42/171 = 0.246m3/hour. Multiplying by 10.75 gives the average power over the week as 0.246 x 10.75 = 2.64kW.   A spreadsheet makes all this a doddle.   Note that extended use of other gas appliances such as a gas fire, will add to the demand.

Heat transfer by circulating water

The typical central heating system in the UK is “wet” – circulating water transfers heat from boiler to property via radiators or underfloor heating pipes (an underfloor pipe network acts as a very large radiator).

It takes energy to warm a substance and diligent scientists have measured how much is required for very many substances, assigning to each a “specific heat capacity” – specific to each substance. We’re lucky – we can just look up the figure. It tells us how much energy we need to raise the temperature of a kilogram of stuff by 1 celsius (or kelvin). For water, it’s close to 4200 joules or 4.2 kilojoules, and if you do look it up, you may see 4.187 kJ/kgK (joules per kilogram per kelvin), sometimes written as 4.187 kJkg-1K-1 which is different notation for exactly the same thing. Specific heat capacity is given the symbol C.

If we want to know the amount of energy needed to increase the temperature of a substance by an amount DT (delta T), we use the formula:

E = m.C.DT

where m is the mass of the substance and the dots mean multiplication (m x C x DT).

In a central heating system energy is transferred by moving water, circulated by a pump, and the rate at which energy is transferred, the power, is proportional to the rate at which the mass is moved, which is the flow rate.  which could be measured in kilograms per second, but as 1 litre of water has a mass of 1 kilogram, it’s more convenient to express the flow rate it terms of volume of water moved per second, units litre/second or l/s or ls-1.

So….    Power transferred = flow rate x C x  DT

The importance of this is that it shows us that in principle, we can achieve a given power transfer by heating water through a large temperature difference at a low flow rate, or a small temperature difference and high flow rate, and all points in between.

The circulating water in a heating system leaves the boiler with a certain flow rate along the flow pipe, having been heated by through a temperature difference of DT. It is pumped though the pipes and radiator system and returns to the boiler along the return pipe with exactly the same flow rate (water is pretty much incompressible so what leaves must come back), having been cooled through exactly DT. This means that:

The (heat) power transferred from the boiler to the heating water is exactly the same as the power transferred from the heating water to the property.

(This is something I hadn’t twigged before writing this article. Note that “transferred to the property” includes heat lost from pipes as well as radiators.)

High or low flow rate – which is better?

There’ll be more about this later, but lower flow rates, with larger temperature differences, are better for condensing boilers in particular. If the temperature of the water returning to the boiler is hotter than 53 celsius, the boiler won’t condense. High flow rates are also noisier and more prone to giving rise to undesirable “cavitation” (see http://en.wikipedia.org/wiki/Cavitation ).

 Radiators – mostly convectors really   The word “radiator” implies that most of the heat transferred to the room is in the form of radiation – infrared. In fact most heat is transferred by convection (circulating air) and some do indeed refer to “convectors”. The truth of this can be seen in their design. A double panel radiator has the same frontal area as does a single panel one and would therefore radiate pretty much the same amount of power. However the two panels and associated fins provide a much larger surface area to warm the air in close proximity which expands, becoming less dense and rises, pulling in cooler air from below and setting up a convection current. This enables the double panel radiator to transfer heat at a considerably higher rate.

Warming up the house (and cooling it down) – leaving the steady state behind

The first part of the document dealt with a property at stable temperature with the boiler making up for losses only. However, it had to reach that temperature in the first place, which is why boilers provide much greater powers – we don’t want to wait ages for our living quarters to warm up. The fabric of the building and its contents all require energy to warm them. We can bundle everything together and refer to a building’s heat capacity (unit joule/kelvin) – the amount of energy needed to increase the temperature by 1 celsius.

Let’s start with the heating system at steady temperature as we considered before, and look at what happens when the programmer turns off the heating for the night in the late evening.

The rate of cooling (the rate of energy loss, in other words, the power) is highest at the outset, where the temperature is highest, and falls as the property cools. The loss rate is proportional to the difference between the warm property and cooler surroundings (this is Newton’s law of cooling) and a graph of temperature against time follows a curve like this (an “exponential” cooling curve):

This particular curve shows a property at 20 celsius cooling towards an outside temperature of 10 celsius and the heat capacity has been chosen such that it takes about 24 hours to cool to outside temperature (near enough that is – mathematically, it never quite gets there). If the heating is turned off for 8 hours at night, we can look at just this part of the curve:

In the morning, when the heating goes back on, the temperature is close to 13 celsius.

The heat capacity is the same as for the cooling curve and in this example, the boiler maximum power is 18kW. The graph goes up to 20.5 celsius, at which point the thermostat set for that temperature would cease to demand heat.

The line looks superficially straight, but curves, with a decreasing slope as the temperature rises. This is due to increasing heat loss as the property warms above the outside temperature.

 Thermostat hysteresis   Thermostats turn off the demand for heat at a higher temperature than the point where they turn on. The difference is commonly around 1 celsius, so a thermostat set to 20 celsius may turn on the demand at 19.5 and turn it off at 20.5. The 1 celsius gap is called hysteresis. It’s necessary to have one, otherwise the boiler would be turning on and off in quick succession, unnecessarily and inflicting wear and tear on components such as fans and gas valves.

Back to the circulating heating water:

The power output of domestic boilers in the UK mostly falls in the range 10 to 40kW. All the heat produced has to be removed from the boiler by the circulating water, otherwise the boiler heats up and its safety devices stop it burning (older boilers) or modulate to lower power (modern boilers), to avoid overheating.

 Boiler – not a boiler at all The word “boiler” is a misnomer, a hangover from the steam age – “boilers” contain safety systems to prevent them boiling. The American/Canadian word furnace is much more accurate. It helps to think of a heating system from the point of view of the “boiler” – a furnace with a cooling system. If the furnace isn’t cooled by the circulating water, it reduces power or stops burning gas.

We earlier looked at the power moved around the heating system by circulating water

Power transferred = flow rate x specific heat capacity of water x  DT

From this we can work out the flow rate needed to keep the boiler burning by removing the heat from its heat exchanger at least as fast as it is generated:

The volume flow rates give the volume of water that needs to be moved through the boiler heat exchanger and heating system in a given time. The flow velocity (speed of the water) depends on the size of the pipe. The commonest situation in domestic heating systems is 22mm diameter copper pipe flow and return pipes from and to the boiler, and the table shows the water velocity for this – the water is moving quite swiftly – the higher figure in the table is close to 6mph – we can out-run the water but it’s faster than a brisk walk. The lower figure is close to typical walking pace.

As we would expect, the greater the temperature difference between flow and return, the lower the required flow rate. Domestic central heating circulating pumps tend to have a maximum flow rate of around 3.5m3/hour. As the above table shows, they can support a 40kW boiler and a temperature difference of 11 celsius between flow and return.

(The figure of 11 celsius used to be the target for radiator balancing for non-condensing boilers. For condensing boilers, the target is 20 celsius, in an effort to keep them condensing, with a return water temperature lower than 53 celsius – see earlier.)

The flow rate and velocity scale for less powerful boilers, so, for example, the minimum flow rate for a 15kW boiler and 20 celsius temperature difference would be 1.71 x 15/40 = 0.64m3/hour.

Setting the pump speed – slow is good

Circulating pumps commonly have three speeds – three flow rates – which one to use? Given that one can change speed with little apparent effect, it may seem a little arbitrary. However, as there are drawbacks to high flow rates, as covered earlier, the answer is to use the lowest speed that allows the boiler to burn continuously at its highest power in the coldest weather with all thermostatic valves open. While this answer might seem like a case of “every assistance short of actual help”, the pragmatic approach is to use the lowest speed and increase it if, during cold weather, the boiler cuts off the flame too soon and the property doesn’t get warm as it should. As the table shows, the highest speed should only be needed for the most powerful boilers.

Poor heating water circulation – symptoms, causes and cures:

The first sign of trouble most people experience is simply that their property isn’t comfortably warm, and naturally, suspicion falls initially on the boiler, which in many cases is actually fine.

The first thing to look for is whether the boiler is burning briefly and then shutting off the flame. If so, the next check is to feel the heating pipes close to the boiler – they are most likely 22mm diameter. Be careful as it’s likely that the “flow” pipe will be extremely hot. Then if possible, locate the heating pipes further from the boiler. If these are both cool, there’s a circulation problem, and the boiler is ceasing to burn because the heat it generates is not being removed.

Lack of water?

The next thing is to ensure that there is an adequate amount of water in the heating system. For those with open-vented systems with a header or “feed & expansion” tank at the highest point in the system, typically the loft, the level of water in the tank should be checked. If the water level is below the outlet pipe, the float valve may be stuck and moving it may release it.

If your system is filled, look at the pressure gauge, which may be on the boiler (labelled 9 in the example upper image below) or located with the expansion vessel in the cupboard housing the hot water storage cylinder (lower left image).

(Some boilers indicate pressure on an electronic display.)

If the gauge is reading is at or close to zero, you’ll need to get some water into the system, and the only place water can get in is the filling loop. The filling loop may be integral to the boiler or employ a silvery braided hose like the one shown:

Pump?

Having made sure there’s enough water in the system, if the symptoms of poor circulation persist, the next suspect on the list is the circulating pump, which may be an item on its own or within the boiler. Sometimes a failed or failing pump betrays itself by the sound it makes and it’s worth listening to it by placing a screwdriver blade in contact with the pump body and an ear to the screwdriver handle. A pump in good condition runs quietly. Rattles and screeches from a pump are not good signs.

Another symptom of a pump in need of replacement is if its body gets hot while the heating water is cool – the pump body temperature should be close to that of the circulating water.

Note that if the system’s been operated with inadequate water, the pump can be damaged by running dry, even for a period of minutes.

Sometimes there is flow round the system and the central heating pipes become warm but the pump is operating with reduced performance even with radiator valves open. Without means of measuring flow it’s not obvious that the pump is failing and one just has to decide to change it as an act of faith.

Motorised valve?

In a heating system with a “regular” (or “heat-only”) or system boiler, it may be that the system is producing hot water but not heating the house. This could be due to a motorised valve not opening because its motor has failed or there is no power to it – try opening the valve manually using its lever while the boiler is working for hot water. If the central heating pipe now gets hot, there’s your answer.

(Motorised valves may fail to work after their summer holidays – the peak time for emergency calls to British Gas is in the autumn when the heating season resumes – many more than in the depth of winter. It can be worth giving them a light tap, which sometimes frees up the mechanism. To prevent the problem occurring, run the heating system for brief periods during the summer.)

Bypass open?

If there’s no obvious problem but the boiler still only burns briefly, it’s worth feeling the return pipe to the boiler. If this is hot, it may be there’s a bypass valve which is letting too much water flow back to the boiler than through the rest of the system. (I once spent a good while on a radiator balancing mission only to find a gate valve used as the bypass had been fully opened some while past by a “helpful” uncle.)

Air lock?

Air locks tend to occur in hot weather and are more common in open-vented rather than sealed systems. Air gets into the system somehow, possibly at a “microleak” and works its way to pipework with an unfortunate layout where there is what amounts to an inverted “U”. There it sits, breaking the path of water and stopping the flow. This can be why a heating system doesn’t work after being off for the summer. Air locks can be shifted using high pressure mains water from a hose attached to a heating system system drain point. This can take time and several attempts.

Corrosion?

Air in the heating water and insufficient corrosion inhibitor chemical causes corrosion within radiators and black magnetite iron oxide in the system. It may stay in the radiators but can move around, blocking up the narrowest water channels, which are likely to be in the boiler. Heating water is commonly taken for granted and neglected, sometimes with expensive consequences as a power-flush may be needed as part of the remedy. Heating system water filters are a good investment as they are designed to stop magnetite from reaching the boiler.

Notice the paragraph headings end in question marks. Certainty is a luxury we often don’t have as we can’t see what’s going on within the pipes. The flow rate can be measured using an ultrasonic flow meter (I own one) strapped to a pipe without breaking into it, but even if we establish that there is poor flow, it can be difficult to locate the restriction. Educated guesswork must often be employed.

Setting the boiler temperature control

Boilers generally have a temperature control on the from panel – what does it do? In the case of some modern boilers, the control changes the reading on a display of temperature in celsius – this is the “flow” temperature of the water as it leaves the boiler en-route for the radiators and/or the hot water storage cylinder.  The rest of us generally have a control knob and a scale consisting of a set of dots or numbers that don’t seem to indicate anything – what’s it all about?

The scale is related to temperature – usually the further the control is rotated clockwise, the higher the flow temperature.

For heat-only (or “regular”) or system boilers, the same heating system water heats the radiators and the hot water storage cylinder. The latter takes precedence here – the temperature of stored hot water needs to exceed 60 celsius to kill Legionella bacteria, so the circulating water needs to be 65 celsius or more. This means that generally the central heating radiators are hotter than needed, but so be it.

 Thermostatic mixing valves Hot water issuing from taps at more than 60 celsius presents a hazard to young, elderly and otherwise less able-bodied people, and the answer here is thermostatic mixing valves close to the outlets. These mix in in cold water so what comes from the taps won’t scald.

On combi boilers and some sophisticated heat-only or system boilers, the temperature of the hot water can be set independently from the central heating and there’s an opportunity to try running the radiators at a moderate temperature, say 45 celsius.

Is it more economical to have the heating on constantly in cold weather, rather than operating it on a timed basis from the programmer?

Argument 1: “If you leave the heating on all the time in cold weather, the heating system only has to supply losses, whereas if you turn it off, you have to heat the house and supply losses so it saves gas to leave it on.”

Argument 2: “There’s no better way to save gas than to turn the heating off altogether overnight when it’s fine to have the house cooler. It soon warms up again so that can’t waste much gas.”

Both arguments seem plausible and based on intuition so which is correct? I’m not much of a mathematician so I’ve put simple calculations into a spreadsheet. This takes as its inputs boiler size and rate of rise of temperature (which allows the building’s heat capacity to be calculated), time for which the heating is turned off, the maximum loss power and maximum temperature difference between building and outside temperature.

If there is a significant temperature drop of the order of 10 celsius while the heating is off overnight, for perhaps 8 hours or so, turning off the heating will save energy. If the drop is considerably less, leaving the heating on may make little difference or even save a little. A small temperature drop with the heating off for some hours during cold weather implies a small property that it well-insulated or perhaps a large one with a big heat capacity in proportion to its rate of heat loss.

As noted earlier, for householders it’s not straightforward to gather reliable experimental evidence from gas meter readings, because our weather is so variable and it’s easy to be fooled. All my measurements on my fairly small property which does experience a significant overnight cooling have shown a higher gas consumption with the heating left on. Those with considerably larger properties may obtain different results.

However, in general, it’s better to use heating controls to turn off the heating system or reduce the temperature where possible, and the burgeoning industry in heating controls is not a scam.

http://www.moneysavingexpert.com/utilities/energy-saving-myths

Thermostatic radiator valves (TRVs) – a jolly good thing

Following on from this, careful work at Salford University, widely referred to, demonstrated the savings to be made by having thermostatic radiator valves – get them if you can – the payback period for installing them is attractively short.

http://www.beama.org.uk/en/news/index.cfm/tacma-research

Weather compensation

The indoor temperature is set for our comfort. It was stated earlier that the rate of heat loss from the property is proportional to the difference between inside and outside temperature. If the outside temperature rises, the losses decrease, and it would make sense to turn down the boiler’s temperature control in order to run the boiler at lower power and the radiators at lower temperature. Conversely, if the outside temperature falls. This is what weather compensation achieves automatically, the essential ingredients being a boiler that is designed for weather compensation, and an outside temperature. The end result is comfort maintained with greater economy.

References:

Composition of air:

http://www.engineeringtoolbox.com/air-composition-d_212.html

Legionella:

http://www.hse.gov.uk/healthservices/legionella.htm