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: 882

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

Hal Skinner replied to Kurt Shafer's discussion Where can I find the best radiant barrier to install under my roof?
"I just posted a statement and pictures of a home in Yuma AZ.  This is one I did 10 years…"
13 hours ago
Hal Skinner added a discussion to the group The RCC Classroom (Radiant Control Coatings)
14 hours ago
Tom Mallard replied to Kurt Shafer's discussion Where can I find the best radiant barrier to install under my roof?
"Anything done to raise the roofing off the sheathing works to reduce the high temperatures in the…"
16 hours ago
Michael Dunseith posted a photo

http://www.prattcenter.net/energy-champions-launch-party

Senator Kevin Parker poses with Pratt Center's Green Jobs Green New York Project Coordinator Elana…
23 hours ago
Michael Dunseith posted a status
23 hours ago
Rob Madden, Solar Home Broker posted a blog post

Phoenix 3rd Quarter Solar Resale Statistics Continue to Impress

Phoenix solar home sales were up during the third quarter of 2014, including the resale of homes…See More
yesterday
Everblue posted a status
"Green job alert! Energy Auditor in Baltimore, MD with Advanced Green Home Solutions. Check it out: http://bit.ly/1xhQuXO"
yesterday
Chris Clay replied to Isaiah Borel's discussion Blown Cellulose VS Blown Fiberglass in the Attic
"The Cold Climate Housing Research Center in Fairbanks, AK has alot of information about this…"
yesterday

© 2014   Created by Lawrence Berkeley National Laboratory.

Badges  |  Report an Issue  |  Terms of Service