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Help with some sort of formula to determine resistance to heat

  1. Feb 11, 2019 at 7:26 AM #1
    I am not that smart when it comes to math. But I was wondering if there is a formula calculator or something online that would help me with the example of a problem. For instance if the attic is 130 degrees and I have a 14 inch round metal duct to my air conditioner in the Attic is there a way to calculate how long the insulation will prevent heat from getting into the duct? Say my duct has 50 degree air in it, and the attic is 130 degrees is there a way to calculate the resistance and time to temperature change of using say r19 insulation around the pipe? This is not just for this I have been wondering if I added a smaller second water heater in series and created a small room under my house and super insulated it how long would it hold the temperature in the tank? Does this make sense?
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  3. Feb 11, 2019 at 9:06 AM #2


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    In both these cases, it's not a matter of 'how long it will prevent'. It's a matter of 'the rate that heat will pass through' from one place to another, for a given temperature difference.
    Depending on your level of technical ability and how prepared you are to get into the topic, there is a mass of information which is used by heating Engineers. The rate of heat transfer across a metal sheet or tubing is very easy if you know the material. There are tables of values of thermal conductivity of many different constructional materials.
    This is not a difficult subject in principle but it is hard to nail all the factors that affect the way heat travels into or out of a room or house. There are many on-line resources that could help with your ducting question. If the duct is a long one and there are large temperature differences, it would probably be worth lagging the duct to remove heat loss through it pretty effectively.
  4. Feb 11, 2019 at 9:43 AM #3
    Lagging the duct? What do you mean?
  5. Feb 11, 2019 at 10:19 AM #4


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  6. Feb 11, 2019 at 3:26 PM #5


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    Good search terms are duct heat loss.

    If your duct insulation is about 2" thick, it would have an R-value of about 5. That number takes into account certain practical realities involving insulation installation. A 14" duct is 3.7 feet around. The temperature difference is 130 - 50 = 80 deg F. Assume 30 feet of duct (randomly picked number).

    The heat gain/loss is calculated as: BTU's per hour = Area / R-value X temperature difference. Putting numbers into an example calculation, the heat gain is 30 feet long X 3.7 feet around / 5 (R-value) X 80 deg F = 1780 BTUH.

    That's not a lot, normally the largest source of heat loss is duct leakage. If the joints in your ductwork are not sealed, you could easily be losing 25% of the money you are spending on air conditioning and also 25% of capacity. If your air conditioner has trouble keeping up on a hot day, that could be one reason why. The same calculation works for heating. The heat flow is just in the other direction.

    All of which is why my house (built in 2012) has an insulated crawl space with ductwork in the crawl space. Since the crawl space is conditioned space, the ductwork is neither sealed nor insulated. In winter, the temperature in the crawl space is about one degree warmer than the space above, and we have nice warm floors. And a low heating bill.
  7. Feb 11, 2019 at 9:36 PM #6
    Actually, this i going into my detached garage/workshop. It is a 2 ton heat pump. I seriously contemplated putting ductwork in conditioned space, but was worried about headroom. I may someday get a lift and was afraid it would interfere.
    I plan on seling everything with mesh tape and matic before insulating. I actually thought of wrapping with r 15 bats, unfaced, then using the silver relectix radiant barrier as a vapor barrier.
    It is a 30x30 building. I would have a 14 inch trunck about 20 feet long. I would have 4-8 inch supply ducts coming off of this trunck to 4 diffusers in the ceiling, spaced 7.5 feet from each wall if that makes sense.
  8. Feb 12, 2019 at 8:06 AM #7


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    Not really, no....but that doesn't necessarily mean it's wrong - it may just be a different approach. So let's take a step back:

    Ordinarily this type of problem would be a steady state heat transfer problem. Heat flows in at one rate and you size an air conditioner to pump heat out at the same rate (or vice versa).

    But you're asking about time. So I'll ask: why does it matter how long it takes a duct or a tank of water to heat up? Are you trying to keep it cool for an indefinitely long period of time (steady state) or is there a reason why you need to know how long it takes to heat up to a certain temperature (transient)? Both problems can be solved, but we'll need to understand why you seem to be asking about the transient case when the steady state is the more common.
  9. Feb 12, 2019 at 8:51 AM #8


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    My shop is only 24 X 26, and the heater is a fan coil unit using hot water from the house hydronic system. No ductwork because no need for ductwork. The blower develops enough velocity to throw the air completely across the room, which makes for complete mixing. There is even temperature through the entire shop. My shop is well insulated, a poorly insulated shop might benefit from ductwork.

    It looks homemade because it is. I originally had a commercial fan coil unit in there, but made such a loud annoying noise (think of the fan coil unit in a cheap motel) that I replaced it. The sheet metal was bent with a brake made from a couple pieces of angle iron, water coil from somewhere (I forget), blower from Amazon, and the installation was by a local HVAC contractor.

  10. Feb 12, 2019 at 10:14 AM #9
    Mainly for the water heater question. My thought was to have my gas water heater which is inside to feed a second electric low boy water heater which would be in the crawlspace. The goal would be to build an insulation "room" to hold the temp in the second tank the same as the 1st tank as long as possible before the electrical elements have to kick in on the second tank.
  11. Feb 12, 2019 at 2:26 PM #10


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    I understand the description, but this seems to be more complicated than it needs to be for the average workshop. Unless you need very slow moving air, very quiet operation, or very uniform distribution, it is probably not necessary to run a header through the middle of the shop.

    I'd encourage a couple of options for the OP, adding to what jrmichler was showing.

    If your shop is open, with no partitions, at 30' square, a single discharge will probably be fine. To make this a little better, I'd suggest putting the air handler against the middle of one wall with a ductboard header set on top (to the ceiling), maybe 6-10 feet long. Get three/four (aimable) registers/grilles, large enough you won't have airflow issues or excessive noise. Aim them as you need them to distribute air across the shop, and put in a return where it makes sense--usually you'd stagger the header to the opposite side of the return on the floor. This AC "air dump" or "plenum dump" is very common in work areas, where HVAC systems lack of obtrusiveness is not required, or overhead equipment is an issue. A short duct system like this will tend to be noisier, but for me, I am running tools/machines/etc., and I'd rather be cool than in silence (plus I have a stereo with a volume knob). It also has the benefit of only taking up a very small part of the overhead area in the shop.

    I had a choice when I did my current shop (30'x30', with 9' ceilings), to either put in a package unit, or install a mini-split. I chose the mini-split, and it has run admirably. It has been cheaper to operate than the three large fans I kept in the garage in the Florida summer. It runs at variable load, and always (almost) circulates air, so the garage is very uniform in temperature. I really only mention this because It is a 2 ton heat pump with single low velocity discharge, and it warms and cools the shop just fine with zero ductwork, and it is VERY quiet. There are some downsides to mini-splits, however.

    I make these suggestions, because ductwork is expensive and it can cost money long term--(hot) attic duct will be a heat/money loss. Every time the unit shuts off, all the attic duct reaches the attic temperature (or close enough to it), and the unit will blow hot air until all the old air has been cleared. Also, attic duct leaks can be a substantial energy loss. Minimizing duct in the attic is not a bad thing.

    PS--My previous shop was 35x30 with a 30x20 upstairs, 2.5 ton heat pump, and it only had a single dump downstairs (14"x8") with the return, and worked well for the 35x30x10' high work area. The unit didn't run very much, no variable speed, but it was very comfortable for the gulf coast. The upstairs had 4 registers, but it was a half story with attic on three sides.

    Sorry if post has gotten too long....had to stop before I really got going.
  12. Feb 12, 2019 at 3:29 PM #11


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    It sounds like you have a long run from your gas water heater to the point of use. I have the same, so I had a two gallon electric water heater installed under the kitchen sink. We have instant hot water. Less than one cup before it comes out hot. P2120063.JPG

    I put a Kill A Watt energy monitor on it when we were away. The stand by losses are only 11 kwh per month, part of which is offset by reduced hot water usage. I never calculated, we might be offsetting the entire standby loss of the two gallon water heater.

    I have heard of adding insulation blankets to hot water heaters. Be careful, the electrical controls would be in a hotter environment than they were designed for. You can save more money be setting your water heater(s) thermostats to the lowest setting that gives you water that is just hot enough.
  13. Feb 13, 2019 at 5:37 AM #12
    My issue is not being able to operate 2 showers at the same time without running out of hot water. Shorter showers are not an option.
  14. Feb 13, 2019 at 6:57 PM #13


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    Just trying to keep track:
    1) This thread started out with a question about heat gain from a hot attic to an air conditioning duct.
    2) More information: It's for a one room shop.
    3) Change of direction: Wants to reduce standby losses in a hot water heater.
    4) Another change of direction: It's not the standby losses, it's not enough hot water heater capacity.

    If your present hot water heater does not have enough capacity, there are a couple things you can do that are less costly than adding a water heater:

    1) Are you wasting water jumping out of the way and readjusting the temperature whenever somebody else flushes a toilet or starts/stops the other shower? If so, a pressure balanced shower valve is the answer. I have them in my showers, and I do not notice any temperature change when my wife flushes either toilet, the wash machine runs, or somebody draws hot water from a faucet.

    2) A low flow shower head. With modern shower heads, low flow does not mean that the water dribbles down. But you have to choose carefully, not all shower heads are created equal. My low flow shower head works so well that I turn the flow down a little.

    3) Set the water temperature higher. This is a last resort because it increases standby losses, and reduces water heater efficiency. If you have to set the temperature above about 120 deg F, add a thermostatic mixing valve at the water heater so nobody gets burned.
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