# Transient Heat Transfer Analysis

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.)

Views: 2048

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:

## Discussion Forum

### Transient Heat Transfer Analysis

Started by James White. Last reply by James White Dec 10, 2013.

### Trying to find %age energy saving from variety of upgrades in 10K sf multifamily house

Started by George M. Matthews. Last reply by Guy DuBois Mar 18, 2013.

### Using Average Monthly Temperature to Model Home Energy Use

Started by James White. Last reply by James White Dec 28, 2012.

### How about simulation in the multifamily context?

Started by Evan Mills. Last reply by Don Hynek Jan 23, 2012.

### Modeling Domestic Hot Water Systems

Started by James White. Last reply by Steve Waclo Nov 24, 2010.

• View All

## Latest Activity

jackie harsha added a discussion to the group Marketing Energy Efficiency

### Informative video about energy and its implications

Like many, I’ve been struggling with the differences between what consumers say and what they…See More
Friday
jackie harsha joined James Sayers's group

### Marketing Energy Efficiency

Sharing ideas, tools and examples of promoting energy efficiency to consumersSee More
Friday
Ajmain Azraf posted blog posts
Friday
Robert Post added a discussion to the group Job Board

### Hiring Residential BPI BA Energy Auditors In Philadelphia Area

Please reach me if interested and we can plan a call to discuss this opportunity. This is a full…See More
Friday
Robert Post joined Diane Chojnowski's group

### Job Board

This group is for posting jobs related to all aspects of the home performance industry including…See More
Friday
John Fulton posted a photo

### Roman Blinds For Living Room

Perfect Blinds to cover Long Window. Roman Blinds for your Drawing Room, Seating Space, Corner…
Friday
Robert Post posted a blog post

### Hiring BPI BA Professionals in Philadelphia Area

Please reach me if interested and we can plan a call to discuss this opportunity. This is a full…See More
Thursday

## Events

• ### Better Buildings Peer Exchange Call: Making an Impact: Low-Income Energy Efficiency Programs

February 23, 2017 from 1pm to 2:30pm – Eastern Time

## Home Energy Pros

Welcome to Home Energy Pros – the unique digital community by and for those who work in the home energy performance arena.

Home Energy Pros was founded by the developers of Home Energy Saver Pro (supported 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. Please honor our Guidelines