# Heat Transfer - Void Space Dynamic Insulation

Hi,
I currently have a project running involving dynamic insulation. I am struggling to develop a 1D transient analytical model to compare to my experimental results. I have used the separation by variables method in the most basic form over 1 solid material but have failed to adapt this to 3 layers with one being air. The problem involves a solid material(EPS-100mm)>air void(18mm)>solid material(Concrete block-100mm). I've tried to illustrate the problem in the attached photo to help with visualizing it.
Any guidance/help/pointers in the right direction would be greatly appreciated.

Regards,
Distressed Student

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Chestermiller
Mentor
Why don't you just solve it numerically? (At least, that's what I would do.)

Chet

Why don't you just solve it numerically? (At least, that's what I would do.)

Chet
Hi Chet,
I have obtained a numerical solution using the finite difference method on Matlab but unfortunately my supervisor wants an analytical solution to valid the experiment. This model is then ideally implemented into an easy-to-use spreadsheet version to estimate the carbon-reduction, energy-use-reduction and cost saving performances of 3 different house archetypes with void space dynamic insulation installed.
Steve

Chestermiller
Mentor
Hi Chet,
I have obtained a numerical solution using the finite difference method on Matlab but unfortunately my supervisor wants an analytical solution to valid the experiment. This model is then ideally implemented into an easy-to-use spreadsheet version to estimate the carbon-reduction, energy-use-reduction and cost saving performances of 3 different house archetypes with void space dynamic insulation installed.
Steve
Steve,

Maybe you can tell us a little more about the particulars of this problem. It might be possible to make some approximations that simplify things. My understanding is that you are solving a transient heat transfer problem in which the thermal boundary conditions are changing with time. For the most part, the heat flow is 1D. What is the thermal diffusivity of the two 10 cm thick wall materials? What are the specific boundary conditions? What is the time scale for the time dependent boundary condition variations? What is the flow rate of the air through the channel (per unit width)? What is the condition on the entering air? Is the heat flow steady state with a superimposed transient variation?

Chet

Steve,

Maybe you can tell us a little more about the particulars of this problem. It might be possible to make some approximations that simplify things. My understanding is that you are solving a transient heat transfer problem in which the thermal boundary conditions are changing with time. For the most part, the heat flow is 1D. What is the thermal diffusivity of the two 10 cm thick wall materials? What are the specific boundary conditions? What is the time scale for the time dependent boundary condition variations? What is the flow rate of the air through the channel (per unit width)? What is the condition on the entering air? Is the heat flow steady state with a superimposed transient variation?

Chet
Chet,
Technically, you are right to understand the thermal conditions are changing with time, however with regard to my experiment, the thermal boundary conditions are relatively constant as the micro-house is located in an air-conditioned laboratory. The thermal diffusivity of the EPS insulation and concrete block are 1.33x10^-3 m²/s and 8.5x10^-8 m²/s, respectively. The boundary conditions are as follows: The inside of the micro-house is at a constant 60 °C and the laboratory is maintained at 22 °C. The time scale is just 0 to till a steady state is reached. The experiment was repeated with 3 different air inlet flows: 0 m^3/s, 0.016 m^3/s and 0.033m^3/s (drawn in via a fan attached to the pipe). The width of the channel is 1.70m, height 2.0m and 0.018m thick. The air entering the insulation will just be at the laboratory room temperature (22 °C) initially and will slowly recover the heat otherwise lost and then the pre-warmed air is fed back into the micro-house. I believe the heat flow is steady state with a superimposed transient variation.

***EDIT: Just to be clear as I didn't state this, the inside temperature varies. Once the room has reached 60°C the heater is switched off and the data is acquired until the heat flux etc reaches a steady state (cool-down mode). Once this is obtained the heater is switched back on(heat-up mode) and again the data is acquired. This is completed for each air inlet flow rate. The transient response is then to be obtained.***
Steve

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Chestermiller
Mentor
So the air flows through the wall, starting at the outside temperature, and being released inside, correct? Is there a header to distribute the air, and a collection header for the air? How does the air get back out of the micro house again (return vents??). When there is no air flowing, is the heat load what you expect? Do you have measured air temperatures going into the room at the various flow rates?

Chet

So the air flows through the wall, starting at the outside temperature, and being released inside, correct? Is there a header to distribute the air, and a collection header for the air? How does the air get back out of the micro house again (return vents??). When there is no air flowing, is the heat load what you expect? Do you have measured air temperatures going into the room at the various flow rates?

Chet
Yes that is correct. Not quite sure what you mean by header, but the channel contains uniform, bi-directional airflow through the entire wall area. There is an exhaust pipe/vent on the opposite side of the micro-house. Yes, I've got air temperatures going into the room and thermocouples, velocity, humidity and heat flux sensors at relevant areas. A datalogger collects all the sensor information every minute.
The picture below better illustrates the situation:

However, in my case I only have the inner leaf>air void>insulation(Acting as the external leaf). The spacer in my case is not a sheet as such, more metal strips to maintain the spacing. This shouldn't effect the air flow.

As for the 1D solution I am just working out an effective density, specific heat capacity and thermal conductivity and treating it as one material which is obviously not the case and very inaccurate. Would it be correct to say air flow will not have an effect on 1 dimensional heat transfer through the wall?

Chestermiller
Mentor
Yes that is correct. Not quite sure what you mean by header, but the channel contains uniform, bi-directional airflow through the entire wall area. There is an exhaust pipe/vent on the opposite side of the micro-house. Yes, I've got air temperatures going into the room and thermocouples, velocity, humidity and heat flux sensors at relevant areas. A datalogger collects all the sensor information every minute.
The picture below better illustrates the situation:
View attachment 81140
However, in my case I only have the inner leaf>air void>insulation(Acting as the external leaf). The spacer in my case is not a sheet as such, more metal strips to maintain the spacing. This shouldn't effect the air flow.

As for the 1D solution I am just working out an effective density, specific heat capacity and thermal conductivity and treating it as one material which is obviously not the case and very inaccurate. Would it be correct to say air flow will not have an effect on 1 dimensional heat transfer through the wall?
I don't think it would be correct to say that, unless you are referring to the heat transfer through the individual layers. The air temperature is changing as it flows from the inlet to the outlet and the air has thermal inertia, so it carries heat in that direction. The thing to do is to first model the problem at steady state, focusing on the air flow heat transfer. Then start modeling the system response to transients. The transient problem might require some good heat transfer experience to model, depending on the specific time scales for the variation. It might be possible to solve analytically, but it might require numerical solution. What I'm saying is that you might want to consider hiring a heat transfer consultant.

Chet