## Posts Tagged ‘Heat Transfer Coefficient’

### Cold Weather Measurements of Heat Transfer Coefficient

December 11, 2022

Friends, it’s winter and the weather is reassuringly cold: average daily temperatures in Teddington are around 0 °C. And as I wrote the other week, that offers the opportunity to make measurements of the Heat Transfer Coefficient of a dwelling.

People with Gas Boilers

This is especially valuable for people with gas boilers who are thinking about getting a heat pump.

When the outside temperature is around 0 °C, the average heating power required to heat the majority of UK homes is typically in the range 5 kW to 10 kW.

Most gas boilers have a full power of 20 kW to 30 kW and so can heat a home easily. To keep the temperature just right, the boilers cycle on and off to reduce their average output to the required level. For most houses there is no possibility that a boiler will be undersized.

Heat pumps operate differently. They are typically less powerful than boilers and the maximum heat pump output must be chosen to match the maximum heat requirement of the house.

By measuring the daily use of gas (kWh) by a boiler on a cold day one can estimate the size of heat pump required to heat the dwelling to an equivalent temperature.

I wrote about this at great length here, but at its simplest one just takes the amount of gas used on a very cold day (say 150 kilowatt hours) and divides by 24 (hours) to give the required heat pump power in kilowatts (150/24 = 6.3 kW).

People with Heat Pumps

But the cold weather is not just for people with gas boilers: Heat pump custodians and people heating their house electrically can gain insights when it’s cold.

Starting on 1st December I looked up:

• the average daily temperature;
• the daily heat output from the heat pump (in kWh);
• the daily electricity consumption of the heat pump (in kWh);

The internal temperature was a pretty stable 20 °C throughout this period. So I first worked out the so-called temperature demand: that’s the difference between the desired internal temperature and the actual external temperature.

I then plotted the daily heat output from the heat pump (in kWh) versus the average daily temperature demand (°C). The data fell on a plausible straight line as one might expect. Why? Because the colder it is outside, the faster heat flows out through the fabric of the dwelling, and the greater the rate at which one must supply heat to keep the temperature constant.

In the graph below I have re-plotted this  but instead of using the average daily heat output from the heat pump (in kWh) I have divided this by 24 to give the average daily heat pump power in kilowatts.

Click on graph for a larger version. Graph of average heating power (in kW) versus temperature demand (°C) for the first 10 days of December 2022. Notice that the line of best fit does not go through the origin.

The maximum heat output from the 5 kW Vaillant Arotherm plus heat pump varies with the external temperature, but for flow temperatures of up to 45 °C, it exceeds 5.6 kW.

The maximum daily average power for the first 10 days of December is just over 3 kW, so I think the heat pump will cope well in even colder weather. Indeed I could probably have got away the next model down. But it does seem to be a general rule of heat pumps that one ends up with the model one size above the size one actually needs.

Click on image for a larger version. Specifications for the Vaillant Arotherm plus heat pump. For the 5 kW model at an external temperature of -5 °C and heating water for radiators to between 40 °C and 45 °C, the maximum output is between 5.6 kW and 6 kW.

The slope and intercept of the graph

The slope of the graph is approximately 0.166 kW/°C or 166 W/°C. This figure is known as the Heat Transfer Coefficient for a dwelling. It is the figure which characterises the so-called fabric efficiency of a dwelling.

However, as I noted many years ago when I looked at this problem using gas boiler measurements, the straight line does not go through the origin. The best-fit line suggests zero power output when the external temperature is 2.8 °C below the internal temperature.

This would imply that the heat flow through the fabric of the building was not proportional to the difference between the inside and outside temperature.

The reason for this is that there are other sources of heating in the house, and not all the heat pump output goes into the house. Specifically:

• People: each person heats the house with around 100 W, about 2.4 kWh/day.
• Electrical Items: All the electricity consumed by items in the house ends up as heat. For my home this amounts to around 10 kWh/day.
• Hot Water: Heat pump output that heats domestic hot water is mostly lost when the hot water is used. My guess for this house is that this amounts to around 3 kWh.day.

So to estimate the actual amount of heat dissipated in the house I should really take the heat pump output and:

• Add 2.4 kWh/day for each person in the house
• Add 10 kWh/day for all the electrical items
• Subtract 3 kWh/day for the hot water lost.

Together this amounts to adding 9.4 kWh/day to each heating estimate. Pleasingly, plotting the same graph with these corrections, the graph now intercepts within 0.5 °C of the origin. To me this indicates that I am now accounting for all the significant sources of heat within the house reasonably well.

Click on graph for a larger version. Graph of average heating power (in kW) versus temperature demand (°C) for the first 10 days of December 2022.

I haven’t included any solar gain in these estimates because at this time of year solar gain is generally very low unless a home has large south facing windows. Previously I have noted that solar gain seemed to be much more important in spring and autumn with longer and generally sunnier days.

COP

I also took the opportunity to evaluate how the daily averaged coefficient of performance (COP) varies with external temperature. This is based on readings from a heat meter and an electricity meter which monitors the heat pump.

The COP values below 3 are a little bit lower than I would like, but still acceptable. On subsequent cold days I will be seeing if there are adjustments I can make to the heat pump operation which can improve this.

Click on graph for a larger version. Graph of daily average COP versus daily average outside temperature (°C) for the first 10 days of December 2022. Extrapolating the trend suggests that the COP would reach unity at a temperature of – 12 °C.

Out of curiosity, I also evaluated the heat output using the Vaillant SensoApp. The figures were massively in error. For example, on 10th December the app suggested the total heat delivered to the house by the heat pump was 58 kWh. In fact the correct answer was 73.9 kWh.

Conclusion

Cold weather offers an opportunity to assess the so-called Fabric Efficiency of a dwelling by direct measurements of its Heat Transfer Coefficient.

The cold weather will be with us for a few more days so there’s still a chance to make measurements in your dwelling.