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: 1184

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.  Home Energy Pros is sponsored by the Better Buildings Residential Network.

Latest Activity

John Kaye posted a blog post

FREE Home Efficiency & Safety Assessments in the Los Angeles County area.

Since last June I have been qualifying homeowners in the Los Angeles County for the Home Upgrade…See More
3 hours ago
Eric Kjelshus replied to Rod Fox's discussion Does calcification affect electric water heater aquastat temperature sensor performance?
"Those 240 Volt aquastats shut off and then on kinda quick back on.  The older the tank the…"
8 hours ago
Profile IconMike Norvell Sr and Jen Loomis joined Home Energy Pros
13 hours ago
Rod Fox replied to Rod Fox's discussion Does calcification affect electric water heater aquastat temperature sensor performance?
"Well I'd love to tell you folks I found an answer, but I did not... I went to my…"
17 hours ago
Rod Fox replied to Kevin Eigel's discussion What is the best energy auditing software?
"I've been trying to answer this question for many years and have not yet found an answer.…"
17 hours ago
Jerry Lawrence posted events
17 hours ago
Jan Green commented on Theresa L Gilbride's blog post Find out who's building some of the best-performing homes in the country today with DOE’s Tour of Zero
"Thank you for sharing! "
19 hours ago
Jan Green commented on Theresa L Gilbride's blog post Find out who's building some of the best-performing homes in the country today with DOE’s Tour of Zero
"We have one builder in Arizona on the DOE list.  Good information for a blog!"
19 hours ago

© 2015   Created by Lawrence Berkeley National Laboratory.

Badges  |  Report an Issue  |  Terms of Service