# What is the cost of heating of a 60k sqm building to 27 degrees celsius vs 20 degrees celsius? [closed]

How can I calculate the cost of heating a building such as http://group.canarywharf.com/estate-building/5_north_colonnade/ ?

Its size: 59,142 sq m / 636,600 sq ft

The temperature is in many places more than 27 degrees celsius. I would like to show, that an investment in better heating control would pay off quickly, if the temperature was reduced to 20 degrees celsius.

• what you actually want to compare is maintaining the temperature. That's easier to calculate by estimating how much energy is lost at 27°C and how much less it would be at 20°C – ratchet freak Jan 17 '17 at 10:29
• Welcome to Engineering! This looks like a "homework question" (notice the quotation marks). In order for such questions to be answered in this site, we need you to add details describing the precise problem you're having. What have you tried to solve this yourself? Please edit your question to include this information. – Wasabi Jan 17 '17 at 10:30
• it's definitely not a homework question, it's a real life problem and I have no idea how to solve it – Nickpick Jan 17 '17 at 10:31
• You would probably want a professional to look at this specific building then. There's no equation to determine energy saved by lowering the temperature a set amount per square foot. You could make estimates based off of the change in energy, but I doubt it would be accurate. A lot of this has to do with what energy systems the building already has, what equipment it's using and the normal conditions that it operates in. It could be most cost effective to just throttle the heating down. It may make sense to gut the heating system and install something new and efficient... – JMac Jan 17 '17 at 11:59
• Yes i know, but to show that I would like to have an estimate how this can be calculated. That's exactly the point. – Nickpick Jan 17 '17 at 12:00

This is a heat transfer problem

You can get a first order estimate by considering only conductive heat transfer, neglecting radiative and convective. Simplifying it even more, (again we don't know anything about your building, so this is the best we can do)

q = k*dT

where q is the RATE of heat transfer, dT is the temperature difference between outside and inside, and k is a constant that we determine experimentally.

Let's assume it's 10 degrees C out. The average difference between 20 and 10 is 5 (that is, dT changes every time the temperature changes, but we're simplifying, so let's set it to somewhere in the middle). So we'll let dT = 5. So, per hour (or minute, or second) you have 5*k units of heat exiting the building.

Versus 8.5*k units of heat per hour if the temperature is set to 27 C.

So, how much do you pay per unit of heat? Multiply that by 3.5, and there's the savings

Keep in mind this is a VERY rough estimate. I've neglected a LOT of factors. Your problem may be a matter of configuring the HVAC system for optimal air flow, or getting new insulation. I'm neglecting the shape of your building vs how the wind/sun impact it all day/season/year long.

• the price would be £0.05 per kWh. What would that mean in terms of yearly cost? – Nickpick Jan 17 '17 at 14:13
• The average difference between 20 and 10 degrees is always 10 degrees, not 5 degrees. You'd have 10k and 17k (the ratio of the two should still be the same). – JMac Jan 17 '17 at 14:23
• JMac, did you read the part after it, where I said dT is constantly changing? This is a first order estimate, so I assumed temperature went linearly (which it doesnt!) from 20 to 10. Let f(x) := x-10, represent the temperature difference as a function of temperature; integrate f(x) from 10 to 20, divide by ten, and you should get 5. – Mohammad Athar Jan 17 '17 at 14:29
• @user2539738 but if you're keeping your building heated at 20 C, then you won't have temperature fluctuations as large as 5 or 10 C, rather the temperature will probably vary from 19 - 21 or 18 - 22 C. Therefore your average temperature difference between the inside of the building and outside would still be approx. 10 C, not 5 C – BarbalatsDilemma Jan 17 '17 at 14:55
• BarbalatsDilemma, good point! thanks. The difference wouldn't be more than a couple of degrees, which for this estimate, we can ignore! – Mohammad Athar Jan 17 '17 at 15:11

This webpage has a variety of equations including heat transfer/loss of windows, walls, and thermal properties of common building materials. http://www.engineersedge.com/heat_transfer/heat_transfer_table_content.htm

• Welcome to Engineering! So as to avoid link-rot, please expand your answer to include the relevant information from the link provided, at least the most essential points. Feel free to quote directly from the source. – Wasabi Jan 19 '17 at 2:19