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: 862

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

Aaren Stewart posted a discussion

Let's solve this HVAC quiz!!!

Answer these three simple problems of your HVAC systems, let's see how much you know your system…See More
17 minutes ago
Chris Laumer-Giddens posted a blog post

Mini-Split Heat Pumps are Quirky, Especially their Capacity

Mini-Split Heat Pumps are Quirky and Still EffectiveThe name "mini-splits" generally refers to heat…See More
9 hours ago
Jan Green posted an event

Solar Course for Appraisers at SRP's Pera Club

November 13, 2014 to November 14, 2014
"As the US continues to search for energy alternatives, properties improved with solar PV…See More
9 hours ago
Hal Skinner replied to Hal Skinner's discussion What an RCC can do with no R- insulation in the walls.
"Just like paint.  RFoller and brush or strong airless sprayer.  It has the consistency of…"
12 hours ago
Hal Skinner replied to Hal Skinner's discussion What an RCC can do with no R- insulation in the walls.
"ty and thermal emission leveld of many materials including bricks and white paint.  They do…"
13 hours ago
Hal Skinner added a discussion to the group The RCC Classroom (Radiant Control Coatings)
Thumbnail

Walmart goes green in Texas

We applied cour RCC to 5 Walmart superstores in Texas.  Worked great and they wanted it.  Then they…See More
13 hours ago
Kim Tanner replied to Trip Smith's discussion Where to spend my marketing dollars?
"Direct mail doesn't do very much, in my opinion, unless you have awesome coupons! Honestly,…"
13 hours ago
Hal Skinner replied to Hal Skinner's discussion What an RCC can do with no R- insulation in the walls.
"Mornn Trip and Bud, In this case all I can do is report it exactly as it was told to me.  I…"
14 hours ago

© 2014   Created by Lawrence Berkeley National Laboratory.

Badges  |  Report an Issue  |  Terms of Service