January 28, 2022

By: Luke Hollinshead

To understand “heating”, we must understand heat losses, because really, there would be no need for heating without them!

Heat losses occur due to heat being transferred from inside a property through walls & windows etc (fabric heat losses) and being transferred, via drafts of warm air, through gaps in the fabric, which is replaced by cooler outside air (ventilation & infiltration losses).

First of all, let’s establish what “Heat” is.

Heat is simply thermal energy. It is the result of particles bouncing around at ”different speeds”.

The faster the particles move, the higher the kinetic energy. We call the average kinetic energy temperature.

So the higher the kinetic energy, the higher the temperature. Don’t mix up heat and temperature! They’re not the same.

Temperature is the speed of the particles, and heat is the number of particles in motion.

Imagine you’re in a room and you light a small candle, which is burning at about 1000˚C. Will the candle heat up the room? No, of course not (unless it was a particularly big candle!).

Now imagine a radiator in the same room, which is 70˚C. Will the radiator heat the room?

Yes, it will because the radiator has more heat, even though it’s a much lower temperature than the candle.

Rule number 1 about heat is the conservation of energy. This is important because it means that we can’t simply create new energy, we can only transfer it from one thing to another.

Rule number 2 is also important and relevant to understand when talking about heat losses. Rule number 2 states, quite simply, that things with higher temperatures will always be “attracted to” and tend towards cooler things.

In other words, hot stuff really likes cold stuff and will only ever move in the direction of cold stuff. It’s kind of like dropping a ball.

A ball can only ever fall towards the ground; it can never fall up! This is the flow of kinetic energy.

Faster-moving particles bump into slower-moving particles, which causes the slower ones to speed up a bit and the faster ones to slow down a bit.

This will continue to happen until all the particles are all bouncing around at the same speed.

We call this, equilibrium.

In simple terms, if you placed a hot cup of coffee on a table, the heat from the cup would move in the direction of the table and of course, heat that part of the table up.

So the cup is cooling down because it’s giving up heat to the table.

This will continue to happen until the coffee cup, and the table is the same temperature, which would then mean that no more heat can be transferred. They’re at equilibrium.

This is also known as “Newton’s Law of Cooling”. Important - there must always be a difference in temperature (∆T) for heat to flow.

If you remember from school, there are 3 ways that heat energy can be transferred: conduction, convection and radiation, all of which play a big part in heating systems of course.

Let’s first talk about conduction. Conduction is pretty easy to get your head around as it’s the heat transfers due to physical contact between mediums.

So when you touch a glass of ice water, it feels cold because heat from your skin is flowing (using conduction) to the glass.

This is exactly what is happening in a property when we are talking about fabric heat losses. I guess you could also think of “heat loss” as “heat gain”, but to outside.

Either way, it’s simply heat transfer, and as we know, heat can only move in one direction: hot to cold.

This is of course undesirable, because the more heat we lose, the more heat we need to add to compensate.

Importantly, the bigger the difference in temperature between inside and outside, the bigger the rate of heat transfer. Think of it like this:

Imagine a 10-litre bucket. The sort of thing you’d use to wash a car.

You fill it up with water from the tap until it’s at the 5-litre mark.

You then drill some holes in the bottom of the bucket and of course, the water will just leak out.

This is like your heat loss. Bigger holes would obviously represent a larger rate of heat loss.

To try to maintain the water level at the 5-litre mark, you’d have to open the tap again, but just enough so that the amount of water flowing into the bucket, is the same as the amount leaving.

In this analogy, the tap is the boiler, as it’s compensating for what is being lost.

So, to reduce the transfer of heat from inside to outside, we insulate our properties. This reduces how conductive the fabric of the property is and makes it “more difficult” for heat through conduction to occur.

As you look deeper into fabric heat losses, you will inevitably stumble across things like U–Values and R-Values.

U-Values are very commonly associated with heat losses and insulation.

The lower the U-Value, the better the insulation. But what actually are U and an R values?

In simple terms, when referring to fabric heat loss, a U-Value is a measure of how much heat will be conducted through a specific material.

It’s measured in units W/m²K (watts per meter squared kelvin).

An R-Value is basically the opposite and is a measure of how resistive a specific material is to heat conduction.

It’s measured in m²K/W (meters squared kelvin per watt). So U and R-Values are reciprocals (opposites) of one another.

But still, what does this mean? What actually are W/m²K and m²K/W?

To understand this, we must first sort of reverse engineer where these units came from.

Since fabric heat losses are all about thermal conduction, let’s start with thermal conduction (how conductive material is).

We know that conduction is the heat transfer due to physical contact between two mediums, but how can we measure it?

Well, this is the hard bit to get your head around. Thermal conduction defines the proportional relationship between two other properties of a material.

This is the thermal conductivity coefficient. It’s a unique “constant” for any given material that is given the symbol “λ” (Lamda) or sometimes “k” (lowercase k).

Its units are W/mK (watts per meter kelvin). The two properties that this coefficient relates to are the “heat flux” and “temperature gradient” of a material.

Heat flux - this is defined as the rate of heat transfer per unit area. Its units are W/m² (watts per meter squared).

So this is a measure of the number of watts that are being transferred for every 1 square meter of a material.

Temperature gradient – this is defined as the change in temperature over a specific distance between two points.

Its units are K/m (degrees kelvin per meter). So it’s simply the difference in temperature between one side of a material to the other.

Or, the temperature difference relative to a materials thickness. Or, the change in temperature for every meter…

Right. Is your head hurting? Let’s try to make some sense of this.

We are basically saying that any given material has a thermal conductivity value, which is the relationship between that materials heat flux and temperature gradient…

\[Thermal\hspace{3mm} Conductivity = {{Heat\hspace{3mm} Flux} \over Temperature\hspace{3mm} Gradient}\]

Or

\[λ = {{W/m²} \over K/m}\]

But earlier we said that thermal conductivity (λ) has units ** W/mK** (watts per meter kelvin)? That is

\[{{W/m²} \over K/m}\]

Is the same as

\[{{W÷m²} \over K÷m}\]

which is the same as

\[{{W} \over m²} ÷ {{K} \over m}\]

which is the same as

\[{{W} \over m²} X {{m} \over K}\]

which is the same as

\[{{Wm} \over m²K}\]

which is the same as

\[{{W} \over mK}\]

which Is the same as

*W/mK*

So…… *λ = W/mK*

Still with me? Right! Now we understand thermal conductivity, we can see how the U & R-Values come about.

Let’s start with the R-Value, which we said is the thermal resistance of a specific material and has the units ** m²K/W**.

The R-Value is therefore, defined as the thickness (in meters) of a material, divided by that material’s thermal conductivity.

\[R \hspace{3mm} Value = {{Thickness} \over Thermal \hspace{3mm}Conductivity}\]

Or

\[R \hspace{3mm} Value = {{m} \over λ}\]

Again, we can break down the above to see how we got to the units for the R-Value, which are:

\[{{m} \over λ}\]

is the same as

\[{{m} \over W/mK}\]

which is the same as

\[{{m} \over 1}÷{{W} \over mK}\]

which is the same as

\[{{m} \over 1}X{{mK} \over W}\]

which is the same as

\[{{m²K} \over W}\]

which is the same as

*m²K/W*

So……R-Value = *m²K/W*

Now we can see where the R-Value comes from.

Finally, this means we are able to see where the all-important U-Value comes from too.

Remember, we said that the U-Value is the reciprocal of the R-Value, which means they are the inverse of each other.

Therefore, the U-Value is 1 divided by the R-Value.

\[U \hspace{3mm} Value = {{1} \over R\hspace{3mm}Value}\]

Once more, we can break this down to see where the U-Values units (W/m²K) come from too.

\[{{1} \over R}\]

is the same as

\[{{1} \over m²K/W}\]

which is the same as

\[{{1} \over 1}÷{{m²K} \over W}\]

which is the same as

\[{{1} \over 1}X{{W} \over m²K}\]

which is the same as

\[{{W} \over m²K}\]

which is the same as

*W/m²K*

So……U-Value = *W/m²K*

Okay. We’re all good on what a U-Value is and where it comes from. But how can we apply it to heating design?

Well, U-Values are everything when it comes to fabric heat losses. They give us crucial information that is specific to the materials that a property is constructed from.

This can be used to determine how much heat is going to be lost through thermal conduction, under design conditions.

When we talk about design conditions, we are referring to the biggest variable factor that will affect a properties fabric heat loss. Temperature!

Or more accurately, the temperature difference between inside a property and outside. So “design conditions” are really just the worst case scenario that the heating system is likely to encounter.

This is simply the difference between the ideal inside, comfortable living temperature (21˚C) and the regional average lowest outside temperature.

We call this the “design outside temperature” or “DOT”.

This could be anywhere between 1˚C to -5˚C in the UK, depending where the property is. You could design a system with whatever inside and outside temperature you like.

You could design for an internal temperature of 35˚C and DOT of -100˚C if you like! However, this would be ridiculous for many reasons.

Firstly, 35˚C would be really really uncomfortable inside and the likelihood of it ever reaching -100˚C in the UK is nil.

Secondly, the system would be huge! The heat source, the pipes the emitters, everything! This would be impractical and very very expensive.

Thirdly, the system would spend it’s whole working life being oversized. This is true for normally sized systems actually.

We’re realistically only going to reach DOT around 1% of the year, so our heating systems could spend 99% of the time being in fact, “oversized”.

It is obvious from this that the smaller the temperature difference between inside and outside, the smaller the rate of conductive heat loss.

So what information about a property do we need in order to find out how much heat it’s going to lose through the fabric that it’s constructed from?

Simple:

- Internal design temperature
- Design outside temperature (DOT)
- Surface area of the property
- U-Values of the property

Of course, the walls, the roof, the windows etc are all made from different materials and therefore, all have different U-Values and of course, different surface areas too.

This is why generally, you would calculate heat losses of all of these separately and add them all up for the total property fabric heat loss.

So you can see that the only variable is the outside temperature. We are always going to design to a comfortable living temperature inside.

Unless the property is made from elastic, the surface area can’t change and the U-Values are absolutely fixed too, since they’re a property of the specific building materials.

From this, we can simply say that fabric heat loss is a result of: Surface Area x U-Value x (inside temp – outside temp).

Heat Loss = A x U x ∆T

Or

Q = AU∆T

Knowing this, we are able calculate the rate of heat loss per every degree of temperature change. Since A and U are fixed, they become the constant that defines the proportionality between Q and ∆T.

(AU) = Q/∆T

You have a 2.4 m x 3 m wall made from 102 mm thick brick. It has a U-Value of 2.97 W/m²K. The inside temperature is designed to be 21˚C and the design outside temperature is -3˚C.

We can calculate the walls heat loss under these conditions like this:

- Area of wall (A) = 2.4 m x 3 m = 7.2 m²
- U-Value (U) = 2.97 W/m²K
- Temperature difference (∆T) = 21˚C – (-3˚C) = 24˚C
- Q = AU∆T

Q = 7.2 m²x 2.97 W/m²K x 24˚C = 513.2 W

Now to find out the fabric heat loss per degree of temperature change. W/K (watts per kelvin).

You simply take the fabric heat loss (Q) of 513.2 W and divide it by ∆T of 24˚C. That is, Q/∆T, which we already said is equal to AU right?

So to further tie all of this together:

Q/∆T = A x U Or W/K = m²x W/m²K,

\[W/K={{m²} \over 1}X{{W} \over m²K},\]

\[W/K={{W m²} \over m²K},\]

\[W/K={{W} \over K},\]

*W/K = W/K*

So that’s fabric heat losses, but as mentioned, that’s not the only way heat losses occur. We also have to factor in ventilation and infiltration losses.

These are heat losses due to air changes within a property.

Air changes are due to both controlled and uncontrolled air leaks through gaps in the fabric of the property and through purpose made ventilation.

Each type of room will also have a specific amount of stated required air changes per hour, for ventilation purposes.

This simply means that the air that leaves the property is replaced by outside air, which needs to be heated up to the designed internal temperature.

This of course significantly contributes to the total heat losses of a property.

Remember, this isn’t NASA, so we can only assume that these air changes are indeed taking place.

I guess in newer properties, the specific ventilation requirements are more easily accounted for, since these may be carried out using more accurate means of natural ventilation and the use of mechanical ventilation.

In older properties, it’s harder to say, but they do exist of course, so we must factor them in.

In general, ventilation and infiltration is a little easier to calculate.

During the design stage, the designer will dictate the amount of ventilation that each room requires in terms of air changes per hour (ACH), according to current standards.

Again, whether these air changes are actually happening in reality is another matter, but we have to design around something.

The trickle vents in windows, for example, should provide the designed natural ventilation stipulated by building requirements, in theory. As should MVHR systems etc.

So when we are specifying how many air changes per hour (ACH) a particular room requires, what does it depend on?

Well, most obviously, the main factor is the type of room. Bathrooms will need more ventilation than say, a living room!

Another factor is the amount of uncontrollable infiltration, which depends on the building itself, in terms of the expected air leakage.

Older buildings, which are built to dated standards, have more uncontrollable infiltration and therefore, the designer would need to account for more ACH than newer buildings.

These ACH are categorised for various building standards e.g. a kitchen in a house that was built pre year 2000, would be Cat.A and would require 2 ACH.

Whereas a kitchen in a house constructed after 2006 would be Cat.C and would only require 0.5 ACH.

Other factors such as chimneys, high ceilings and building exposure also play a big part in infiltration losses too.

The way in which we calculate these losses is simple and widely used.

The factors that they depend on are the number of air changes per hour (AHC), the internal volume of the rooms, the temperature difference between the outside and inside air.

You may consider that humidity and the specific heat capacity of the air would play a role, which of course they do, but again, this isn’t NASA!

These factors remain pretty much constant under the conditions we’re dealing with, so we can use a constant value for SHC of air, as we would with water in other heating calculations.

So the basic formula for ventilation and infiltration losses can be expressed as:

Rate of heat loss = V x ACH x ∆T x 0.33

Or

Rate of heat loss per ˚C difference between inside and outside = V x ACH x 0.33

0.33 is a factor that is the product of SHC and density of air

V is the volume of the room

ACH is the number of air changes per hour

∆T is the temperature difference between the designed internal room temperature and the design outside temperature

As we did above for fabric losses, we are able to further break this down and understand why this works and how it comes about.

Let’s firstly consider that a room is simply a box filled with a fluid that we call air. Air is actually a fluid!

Let’s say that the air is at the required temperature of 21˚C and it all escapes and is replaced with new air, at a temperature of 5˚C.

We’ve lost heat and now need to replace it. If this box had 1 ACH, this would be happening once per hour.

Of course, it doesn’t happen all at once! It happens gradually and constantly but equates to the entire volume of air being replaced in an hour period.

So what we really need to know is, how much heat do we need to add to compensate for this?

Easy! This is the same as calculating how much energy it will take to heat a certain amount of water (also a fluid) up.

We have a fluid (Air), which has mass (everything has mass) and therefore, has a specific heat capacity (the amount of energy to change a certain mass of the substance by a certain temperature, usually this is joules per kg per each degree of temperature change).

From this, we can simply say that the amount of heat required to increase our boxes air temperature is expressed as:

Heat needed = M x C x ∆T

Or

Q = M x C x ∆T

M is the mass of the air that needs to be heated

C is the average specific heat capacity of the air at the conditions (approx. 1000 J/kg˚C)

∆T is the difference in temperature between the air entering the box (room) and the required temperature of the room

Now the mass of the air depends on two things: volume and density. The volume is simple, it’s the volume of the box (room).

Density changes with temperature but not so much as to make any difference for these conditions, so we can use an average value for this (1.205 kg/m³).

Mass is simply volume x density. Remember, this mass is also based on ACH-air changes per hour.

Because we work in terms of power (watts), which is energy per unit time (joules per second), we need to make sure we convert from air changes per hour to air changes per second. ACH/3600.

Q = V x ρ x C x ∆T x (ACH ÷ 3600)

ρ is the density of air

Let’s face it, that’s quite long winded, which is why you will only ever see a “simpler” version of this.

If you’re good at maths, you may have noticed that it doesn’t matter where you divide by 3600.

You can literally plonk it anywhere in the formula and the answer will be the same.

This means that we can take the constant things that will always be the same and “pre combine” them into a tidy “factor”, so the designer only needs to fill out the variables and multiply them by this “factor”.

The density and SHC of air will be constant, so we can simply take these two things and divide them by 3600.

Q = V x ∆T x ACH x (ρ x C / 3600)

Or

Q = V x ∆T x ACH x (1.205 x 1000/3600)

This is the same as Q = V x ∆T x ACH x 0.33, since 1.205 x 1000/3600 = 0.33! So the factor is 0.33.

So, we can make it even more simple by saying:

Rate of heat loss (per˚C) = V x ACH x 0.33

From this the designer only needs to input the room volume and number of air changes to know the ventilation losses per every degree of temperature difference.

Enjoyed this article? Want to know more about system design and how to become a top heating engineer?

C/O Dragon Argent Limited, 63 Bermondsey Street, London, SE1 3XF

Vat number: 364541984

Company number: 11887015

Company number: 11887015