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: 867

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

Rob Madden, Solar Home Broker commented on Alicia Hobbs's blog post 5 Solar Facts that You Should Know
"From personal experience, that $20,000 savings over 20 years will be a low number based upon the…"
10 hours ago
Rob Madden, Solar Home Broker posted a blog post

Phoenix Solar Home Sales Jump in September

The number of solar home sales in Phoenix jumped 13.6 percent from the previous month, according to…See More
11 hours ago
Profile IconGina M., Brian J. Mulhern, James Tucker and 2 more joined Home Energy Pros
12 hours ago
Casey Gesell replied to Trip Smith's discussion Where to spend my marketing dollars?
"Trip, Check out our sister company Contractor Nation: https://www.contractornation.com/ Pay Only…"
12 hours ago
Casey Gesell posted a discussion

Looking for home improvement companies to join our dealer network!

My name is Casey Gesell and I'm the Business Development Manager at Dr. Energy Saver, Inc.Dr.…See More
12 hours ago
Casey Gesell replied to Trip Smith's discussion Starting a Home Weatherization Business. Considering it...
"Hi Trip, Check out our website: www.drenergysaverdealerships.com "
12 hours ago
Alicia Hobbs posted a blog post
13 hours ago
Mark Wozniak posted a status
"I am looking for energy efficiency software training in Massachusetts."
15 hours ago

© 2014   Created by Lawrence Berkeley National Laboratory.

Badges  |  Report an Issue  |  Terms of Service