A Tale of Two Houses by Bowman and Tande

Part IV—Finding an Answer

After much thought and considerable scribbling, you come up with a single equation that describes how these factors are interrelated:

As you look at the equation, it seems vaguely familiar. Suddenly remembering where you’ve seen it before, you jump up to go find it.

“Hey! Have you figured out…?” yells Uncle Bubba.

“I’ve almost got an answer,” you reply, cutting him off as you run upstairs.

Quickly closing the bedroom door, before Bubba and Bill can follow, you begin looking for the backpack with your school books. You pull out a copy of McCabe, Smith, and Harriot and flip through it until you find the section on heat transfer and discover that, not only is your equation in the book, but it is famous enough to have a name: Fourier’s Law.

Confident that you are on the right track, you decide you are ready to do some calculations. You look up values for thermal conductivities in the textbook, use the house dimensions to estimate the surface area of each house, and make some reasonable estimates for wall thickness and temperatures. Soon you have an answer and return downstairs to talk to your uncles.

Estimate the missing values and calculate the heat lost/gained from each house.

Uncle Bubba’s House	Uncle Bill’s House
Area (A): _____ft²	Area(A): _____ft²
Effective Conductivity (k): 15 BTU in/(ft² °F day)	Effective Conductivity (k): 50 BTU in/(ft² °F day)
Temperature Difference (ΔT): _____°F	Temperature Difference (ΔT):______°F
Thickness (x): _____inches	Thickness (x):_____inches
Q :____________ BTU/day	Q :____________ BTU/day

Originally published at http://www.sciencecases.org/heat_transfer/case4.asp