Heat pump vs furnace

The traditional way to heat a house with electricity, is electric resistance heating (also called electric 'baseboard' heating): Electricity is converted into heat by running it through a resistor.

We calculated the efficiency of the U.S. electric generating sector at about 30%. That means that a natural-gas burning furnace would only have to have an efficiency of better than 30% to beat out electric baseboard heating.

But an electric heat pump does not convert electricity into heat, but rather uses electricity to move thermal energy from one place to another.

Imagine a cold house on a hot day: Once you've opened a window, it would not take *any energy at all* for heat from the outside to flow inside and "heat" your house!

Most of the time, though, we want to heat our houses on days when it's cold outside. An electric heat pump can perform the trick of moving heat from a cold place (outside) to a warmer place: This is exactly what a refrigerator is routinely doing!

The question you'll look into is whether such a device--even if it's powered by electricity generated from burning a fuel like natural gas--with all the attendant heat losses according to the 2nd law--Can such an electric device beat out the much simpler furnace that just burns natural gas piped into your home? or not?

You will compare two ways of extracting chemical energy from natural gas as heat, and ending up with heat in your house:

• One is a natural gas-burning furnace.
• The second is the process of generating electricity from natural gas and using the electricity to run a heat pump.

You will look for the best appliances which are already on the market. The best natural gas electric generation plants, high efficiency gas furnaces, and electric "air source" heat pumps.

Write up your answers to the numbered questions below in a document. Preferably, use CoCalc to author a Jupyter notebook, that you export to .pdf and hand in on Moodle.

Furnace

A furnace is a fairly simple machine for burning fuel and delivering the heat to your house. But even such a "simple" machine is nowadays a bit more complicated than meets they eye.

The number used to compare furnace efficiencies is the Annual fuel utilization efficiency (AFUE): It's the overall heat delivered to your house divided by the heat of combustion of the fuel that you burn. Furthermore, it takes into account seasonal factors and inefficiences in real equipment--For example, furnaces are more efficient when they're warmed up, than when they're cold; they might exhaust some of the heat up the chimney instead of capturing it to heat your indoor air, etc.

To allow for comparing with the heat pumps, I will write about the coefficient of performance (COP) of the furnace: $$c_\text{furnace}$$ which is the dimensionless ratio of heat energy delivered to your house divided by the combustion energy of the fuel that you start with.

Below are the questions I'd like you to investigate. But write up your responses coherently in the form of a short report. Answer the questions and show your calculations. Also, define the variables and acronyms you use. For example, explain what $C_{hp}$ and "HSPF" are. Finally, draw some conclusions from this comparison about future prospects for heat pump technology vs furnace technology.

1. The wikipedia article on AFUE claims the most efficient natural gas furnaces are "condensing" furnaces. Find out what a condensing furnace is, and explain in a few sentences the principle behind them, and why they are more efficient than non-condensing ones.
2. Look on the websites of two different furnace manufacturers (home equipment, not commercial purposes) and find the model that they sell with the highest AFUE. Some common brands: Carrier, Rheem, Trane, American Standard, Lennox, Bryant. Report the two AFUEs and link to the webpages.

The total COP, $c_\text{furnace}$ for burning natural gas to produce heat isjust the (highest) AFUE value you can find. This is for some sort of US 'average' climate determined in the (ANSI) standards used for measuring AFUE.

Air source heat pump

The total process from burning natural gas to heat via heat pump is more complicated. First the natural gas is burned in a utility plant to generate electricity. Call the efficiency of this process $\eta_\text{gen}$.

Some energy is lost during transmission from the generating plant to your house. If 5% of the energy is lost in transmission, the efficiency coefficient for energy transmission is 100%-5%=95%, call this $\eta_\text{tr}$.

A heat pump runs electric motors to compress a fluid in a refrigeration cyle. It does work to *move* heat from a cold reservoir (outdoor air) to a hot reservoir (inside). Electric motors can have a very high efficiency of transforming electrical $\to$ mechanical energy, often upwards of 95%. (An electrical motor is not a heat engine, so it's not limited by Carnot efficiency). The theoretical efficiency of a heat pump typically drops as the outside air temperature drops. So in order to evaluate the efficiency of a heat pump, we should test its output at a variety of temperatures, and weight according to our climate.

The Heating Seasonal Performance Factor (HSPF) is a standards-based protocol for measuring the total heat delivered (in BTU) divided by the input energy required (in Watt*hours), averaged over the course of a year of a typical US climate. So, it already includes factors such as the conversion of electricity to mechanical energy inside the heat pump.

To calculate the coefficient of performance, $c_{hp}$ of a heat pump (the heat pump alone), you will need to multiply its HSPF (units of BTU/(w*hr)) by the number of watt hours in a BTU: 0.293 w*hr/BTU.

Then, the ratio of heat delivered to your house to combustion energy in the natural gas will be: $$c_\text{system} = \eta_\text{gen} \eta_\text{tr} c_\text{hp}.$$ Questions:

3. Document a value for $\eta_\text{gen}$ for a natural gas plant: Try to find a fairly up-to-date number. Show the value you found, link to the website you found it on, and write one sentence on why I should trust this website.
4. Document a value for $\eta_\text{tr}$ in the same way.
5. According to our class deliberations on Carnot efficiencies... What's the best theoretical COP we could expect for a heatpump running between Goshen's quick-n-dirty-October-April average temperature of 38 F and 68 F.
6. Find the HSPF for the most efficient models available from two different manufacturers (for home use). Link to the citations. Convert these HSPFs to $c_\text{hp}$ values. This $c_\text{hp}$ number can be greater than 1.

   We calculated in class for a Carnot heat pump that we could get to $c_\text{hp}$ greater than 10.

7. Calculate the total coefficient of performance $c_\text{system}$ using the best, currently available air source heat pump you could find.
8. Compare your ratios of heat delivered / combustion heat for the furnace and the heat pump (for the whole system).
9. In the process that runs through the heatpump--generation, transmission, heatpum--Where are the engineering improvements that could be made to any of the steps along the way that could increase the COP further? See if you can find a source (on or offline) that discusses this, document it, and just list one or two of the improvements that could be made and an estimate of how high the COP might be pushed.
10. Are there engineering improvements that could be made to furnaces? See if you can find a source (on or offline) that discusses this, document it, and just list one or two of the improvements that could be made and an estimate of how high the coefficient might be pushed.