## Using Radiators with Heat Pumps

Click for a larger image. A typical dual-panel radiator transfers heat from the hot water flowing through it to the room in two quite distinct ways. By direct heating of the air in contact with the metal surfaces, and by radiation from the outer metal surface.

Switching to heating a house with a heat pump rather than a gas boiler is not entirely straightforward. But it is much easier if one can keep using one’s existing radiators.

But heat pumps operate most efficiently when circulating water at lower temperatures – ideally 40 °C or so. However radiators don’t work so well at these lower temperatures, so in the worst case it might be possible that not enough heat will be transferred to the house to keep it (and you!) warm.

In this article I thought I would explain how radiators work and how one can estimate how well they will work when the water flowing through them is at lower temperatures.

The key to understanding radiators is that radiators transfer heat to the room using two quite distinct physical mechanisms:

• convection.

And in fact, convection is generally more important that radiation. Let’s look at each mechanism in turn.

The heat transferred by radiation occurs mainly from the outer panel facing the room and the amount of heat transferred (in watts) is given by a fancy formula.

Click for a larger version.

The power radiated into to the room depends on:

• The Stefan-Boltzmann constant 5.67 x 10^-8 W/m^2/K^4
• The front surface area of radiator in m^2 i.e. height (m) x width (m)
• The physical property of the surface known as emissivity – typically 0.9 for many painted surfaces.
• The difference between the temperature of the radiator surface and room temperature. But the it is not just the simple difference between the temperatures. It depends on the difference between the 4th power of absolute values of the temperatures.
• To find the absolute temperature one adds 273.15 K to the temperature in degrees Celsius. So a room temperature of 20 °C corresponds to 293.15 K (kelvin) and a flow temperature of 50 °C corresponds to 323.15 K

The graph below shows the amount of power radiated from the front surface of a radiator at various temperatures

Click for larger version. The heat radiated by a typical radiator with a surface area just over one square metre. Warming the temperature of the surface from 30 °C to 40 °C results in 57 W of additional heat transfer to the room. Further warming the temperature of the surface from 40 °C to 50 °C results in 63 W of additional heat transfer to the room.

The emissivity of the radiator has a maximum value of one – and so can’t be increased very much from it’s typical value of 0.9.

So to radiate more heat from a radiator one must either increase its area, or its flow temperature.

The heat transferred by convection occurs at the all the vertical heated surfaces of the radiator.

Click for a larger version. For a radiator with 2 heated panels, convection is induced on 4 vertical surfaces.

Heat is transferred by direct contact between the air and the painted surface. Since the heated air has lower density, it become buoyant and a self-sustaining upward air flow is developed.

It is difficult to develop an exact formula that describes the heat transfer process, but most simple analyses assume that heat transfer is proportional to the temperature difference between the radiator and the room.

However, at higher temperature differences, the moving air speed increases and this further improves heat transfer to the air. This leads to a slight non-linear dependence on the radiator temperature.

Convective and radiative heat transfer can be calculated using complex mathematics at this web site.

The graph below shows the amount of power transferred by convection from the front surface of a radiator at various temperatures.

Click for larger version. The heat transferred by convection from just the front surface of a radiator is compared with the heat radiated the front surface of the same radiator as in the previous figure. Warming the temperature of the surface from 30 °C to 40 °C results in 36 W of additional convective heat transfer to the room. Further warming the temperature of the surface from 40 °C to 50 °C results in 39 W of additional convective heat transfer to the room.

However even a single-panel radiator can transfer heat convectively from two surfaces (front and back). And a double-panel radiator can transfer heat from 4 surfaces (the front and back of each panel).

And we can increase the convective heat transfer further from a radiator by more adding vertical surfaces for air to flow past. For example, for example, the figure below shows the design of several Stelrad Radiators. There are several additional ‘corrugated’ fins with a length which exceeds the basic width of the radiator.

Click for a larger view. These are cross-sections of radiators showing different numbers of panels and fins. All the radiators have roughly the same radiated output 317 W: this is proportional to the frontal area. But the overall power outputs are 1568 W for the K1 model, 2155 W for the P+model, 2770 W for the K2 model. This extra power is achieved by additional convective heat transfer from the panels and the fins which can have a much larger surface area than the panels. All figures assume 70 °C water flow.

Summary

For a single panel radiator, with no fins, radiation and convection contribute roughly equally to heat transfer.

But for more complex radiators with additional fins and panels, convection is much more important for heat transfer. For the K2 radiator in the figure above, convective heat transfer is 8 times larger than radiative heat transfer.

The physical models of heat transfer are too complicated to calculate for every variety of radiator. So there is a standard curve adopted for calculating overall (radiative and convective) heat transfer for water flow at lower temperatures.

This standard curve is shown as a dotted line in the figure below. It matches the physical models reasonably well, but predicts a slightly lower heat output.

Click for larger version. The heat transferred by convection from the four vertical surfaces of double panel radiator, and the heat radiated the front surface of the same radiator. Their sum is shown in black and the standard de-rating curve is shown as a dotted line. Operating the radiator at 70 °C (dangerously hot) results in a total heat output of 1072 W. Cooling the temperature of the surface to in (roughly) almost a 50% reduction in heat transfer to the room. Cooling further to 40 °C the de-rating is close to 70%. And using a flow temperature of 30 °C will result in an 85% reduction in heat out put compared with the nominal radiator specification.

But the summary is simple. The nominal heat output of a radiator is specified assuming that the room is at 20 °C and the water flowing through the radiator is at an average temperature of 70 °C.

• The estimated heat output with a flow temperature of 50 °C is reduced to ~50% of the standard output.
• The estimated heat output with a flow temperature of 40 °C is reduced to ~30% of the standard output.
• The estimated heat output with a flow temperature of 30 °C is reduced to ~15% of the standard output.

The standard de-rating factor F is given within 1% by this formula:

where both temperatures are expressed in degrees Celsius.

So what temperature should I set my hot water flow?

This is difficult to work out. But I think the procedure work like this.

• First work out how much heat is required to heat a home on a cold winter day. In the south of England where I live this typically corresponds to an outside temperature of about -2 °C. Based on my weekly readings of the gas meter on the coldest week last winter (average temperature 0.2 °C) the peak heating required for the house was around 72 kWh/day – or around 3000 W.
• Next one considers all the radiators and measures their height and width. Analysing the Stelrad data for about 40 different radiator sizes I saw that:
• K1 type radiators are rated at about 1600 watts per square metre,
• K2 type are rated at about 2800 watts per square metre.
• I then guessed that my old single-panel no-fin radiators will give roughly 700 watts per square metre.
• Collating all the data I arrived at a table like that below.

Click for a larger version. Analysis of all the radiators in the house estimating first their ‘standard output’ and then their output with a flow temperature of 40 °C.

• This table suggests that a flow temperature of 40 °C, the radiators should output 3214 watts of heating – which just about matches the 3000 watts required in the coldest weather.

So I am hopeful that my existing radiators will work fine with the new heat hump at the reasonably low flow temperature of 40 °C.

According to the specifications of my 5 kW Vaillant Arotherm plus (excerpt below) with a flow temperature of 40 °C through the radiators, the seasonal coefficient of performance should be over 4.

If most of the electricity is purchased at night using the Octopus Go rate of 5p/kWh, this means that the cost per kWh of heating will be around 1.25 p/kWh i.e. around 30% of the cost of heating with gas.

Click for a larger version. Excerpt from the operating specification of the Vaillant Arotherm Plus heat pumps. The 5 kW model is highlighted in blue. At 40 °C flow it claims to be able to deliver 6 kW of heat when the external temperature is – 5 °C, with a seasonal coefficient of performance of 4.13.

One final issue is whether the heating is in the right places in the house. The bedrooms are often very warm, and our kitchen is the coldest room, having only a single old single-panel radiator and this may need to be upgraded.

### 9 Responses to “Using Radiators with Heat Pumps”

Thank You for this discussion. I find it fascinating on many levels.

Our projects tend to examine every aspect of creating a comfortable home: the building envelope, the heat source, windows, humidity, etc.

In general – the greater the surface area of the radiating surface the higher the perceived comfort. This reason begets using the entire floor space as a radiator or the entire ceiling. Sometimes – we crate very large wall radiators or other contrivances.

The water (or glycol) moving the heat from the source to the radiator typically is 48C.

Our systems (the entire house) is designed to work well at -25C.

I think the climate in the UK would mean a design temperature of maybe -5C???

It is my belief that attempting a system using existing radiators originally designed to work at a temperature of ~60C may not be satisfactory.

It is my experience (40 years) that the perceived heating comfort of a radiation from the entire floor space is unrivalled.

• protonsforbreakfast Says:

Hi. Yes, Typically design temperatures in the south are – 2 °C but further north – 5 °C would be reasonable.

The reason that I think the radiators *will* work is that insulation I put on the walls before last winter has reduced the heating demand by half. Without that I would agree with you.

And yes, if I could have underfloor heating with a low constant heat. But it is important to me that I remain married – and my wife will only accept a certain level of disruption.

Best wishes

Michael

2. PeterG Says:

In my experience, one problem with radiators as convectors is that over long time periods, the fins collect layers of dust that impede their efficiency as convectors, and they are not particularly easy to clean.

• protonsforbreakfast Says:

Peter

That is a very good point. Our radiators are dusty. In fact – everything in the house is dusty.

My plan is to see if it works this winter. If it doesn’t then I will need to think of an alternative!

M

3. Joe Kelleher Says:

Would somehow adding fans or other means of forced convection to the radiators help at all? Obviously not what radiators are designed for, but may be a simple and cheap modification.

4. David H Says:

Thank you for a very practical approach. I have talked to quite a few people living here in Melbourne Aus, who would like to move from a gas boiler to a heat pump, and typically struggle to find a heating company who will recommend it, unless they replace all their radiators.

I noticed you tried this last year, how did it go over winter?

• protonsforbreakfast Says:

David, Good Morning,

It went very well over winter. The house did not deviate by more than ± 0.5 °C from 20.5 °C for the whole winter. If you browse back through the blog there are a few articles about the flow temperature at various outdoor temperatures. For Example

https://protonsforbreakfast.wordpress.com/2022/04/08/march-2022/

It seems that my estimate that the radiators would produce enough power with a flow temperature of 40 °C was correct. Most of the time flow temperatures were in their low 30’s degrees Celsius.

In the Twitter circles that I inhabit there is much talk of the desirability of a ‘low-loss header’. I described this component in this article.

https://protonsforbreakfast.wordpress.com/2021/06/10/heat-pumps1/

It is like an “impedance matching” device. It allows the heat pump to operate with a high flow and a low impedance path. But the heat pump does not directly force water through the radiators. This is done by a separate circulation pump which feeds off the low-loss header. This allows heat pumps to operate with non-ideal pipework and radiators. Does this feature in your installers plans for your home?

Any way: best wishes for your ‘journey’.

Michael