I have put together an Excel spreadsheet that calculates the temperature profile through a wall that is heated by the sun.

It use the matrix [K]{T} + [C]{dT/dt} = {S}, where [K] is the heat transfer, {T} is the temperature at the various nodes, [C] is the thermal capacitance of the node, and {S} is the thermal heat gain of the outer node. A copy of the spreadsheet and matrix math is attached.

The math equations have not been verified for accuracy or errors, but it is kind of fun to play around with the variables to see how the temperature profile in the wall changes throughout the day.

(Note that an earlier version of this post had the attached Excel file as a *.zip file.  It has been replaced with an Excel version.)

Tags: difference, element, finite, heat, transfer, transient

Views: 849

Attachments:

Replies to This Discussion

Does this assume that all the heat the face is not leaving, or does it account for convetive currents on the face taking some heat away? Does it assume no wind? What boundry factors have you set up?

The spreadsheet calculates whether heat is going in or out.  Yes, it accounts for convective currents removing heat from the surface.  You can specify any interior or interior convective heat transfer coefficients or air temperatures that you want.  You can also specify the amount of solar gain that the wall receives based on the absorption coefficient.  A perfectly black surface would absorb all of the solar heat (Absorbtivity = 1.0) and a perfectly reflective surface would have zero absorbtivity. I used it recently to model the heat transfer in and out of cold storage rooms that is kept at 32F.

I'm working on an updated model that provides the thermal properties for different building materials and different convective heat transfer coefficients for wind, no wind, surface orientation etc. 

In addition to calculating the heat flow through walls, the spreadsheet could also be used to calculate how quickly the outside of your coffee cup would warm up after filling it with coffee.

This is a nice graphic.  I have a question on how you captured the data -- did you set temperature probes at increasing depths into the brick wall, or are these extrapolated from the delta between interior and exterior temperatures?  Thank you.

The values are all calculated for each node based on the physical characteristics that are input into the model.

To, Ti, hi and ho are inside and outside temperatures and convective heat transfer coefficients,

K is the Conductance (Conductivity/Thickness) of each layer

ρ is the layer's density, and

Cp is the specific heat of the material.

Attached is a detailed description of how I derived the calculations that are used in this transient heat transfer analysis.

Attachments:

RSS

Home Energy Pros

Home Energy Pros was founded by the developers of Home Energy Saver Pro (sponsored by the U.S. Department of Energy,) and brought to you in partnership with Home Energy magazine.

Latest Activity

John Proctor commented on Kurt Shafer's blog post What is your opinion about members promoting products here?
"Kurt: So my question is how does your device work? PSC motors generally do not reduce their…"
2 hours ago
John Proctor commented on Christopher Morin's blog post How do You Test a TXV?
"Correction 32 is the melting point, not the saturation temperature."
2 hours ago
Richard Beyer replied to Mike Kandel's discussion Our Homes Suck – And That's Why Our Kids Have Sinus Problems
""I have no interest in bantering or arguing with you." AGREED! I look at these…"
4 hours ago
tedkidd replied to Mike Kandel's discussion Our Homes Suck – And That's Why Our Kids Have Sinus Problems
"Todd, it appears Richard is more about getting the last word than about learning a new thing.…"
4 hours ago
Todd Collins replied to Mike Kandel's discussion Our Homes Suck – And That's Why Our Kids Have Sinus Problems
"Richard,  I don't believe I am missing any points.  As I mentioned... I have no…"
4 hours ago
Richard Beyer replied to Mike Kandel's discussion Our Homes Suck – And That's Why Our Kids Have Sinus Problems
"Todd, Your missing the point. I can only suggest for you to read all the links attached within that…"
5 hours ago
Tom Conlon replied to Tom Conlon's discussion Whole House Fans - Love 'Em or Not?
"Excellent snapshot, Griffin. You didn't happen to notice the fan manufacturer's name on…"
6 hours ago
Brandon Walton replied to Brandon Walton's discussion 12 Things Every Home Performance Contractor Should Have on Their Work Truck
"Thanks Don! "
7 hours ago
Griffin Hagle replied to Tom Conlon's discussion Whole House Fans - Love 'Em or Not?
"I was aware of but unfamiliar with them until moving to Southern California in 2012. After seeing…"
11 hours ago
tedkidd commented on Scott Mellberg's blog post Lessons from Energy Efficiency Advisors: Getting Homeowners Onboard with Home Performance
"David,  I don't think forcing people to do things works out well for anyone.  Any…"
12 hours ago
David Eakin commented on Scott Mellberg's blog post Lessons from Energy Efficiency Advisors: Getting Homeowners Onboard with Home Performance
""I believe it is our job to educate the consumer, understand the problems, help them…"
12 hours ago
Profile IconGary Fitzgerald, LOUIS ANDERSON and Jeremy Hargreaves joined Home Energy Pros
12 hours ago

© 2014   Created by Lawrence Berkeley National Laboratory.

Badges  |  Report an Issue  |  Terms of Service