1. Heat Flow in a Copper Rod Alexander Williamson Dr. Bruce Thompson Ithaca College

2. A p p a r a t u s

3. Sample Data Set

4. Analytical Model T1T1 T2T2 z z+dz Heat Flow

5. Temperature vs Distance

6. Temperature vs Time

7. Data and Model Compared The problem: Heat is being lost to convection and radiation effects.

8. Convective and Radiative Heat Loss Adds new term to partial differential equation. h : transfer coefficient for free air σ : Stefan-Boltzman constant T a : ambient room temperature r: radius of the rod T1T1 T2T2 z z+dz Heat Flow Heat Loss

9. Solving The New PDE Analytical solution is impossible, so … Analytical solution is impossible, so … Now we turn to Matlab ’ s PDE solver! Now we turn to Matlab ’ s PDE solver! Breaks up rod into n pieces along z and time into m time steps Breaks up rod into n pieces along z and time into m time steps At first, very inconsistent: irrelevant parameters changed function drastically At first, very inconsistent: irrelevant parameters changed function drastically Realized amount of heat added was changing Realized amount of heat added was changing Needed more detail near z=0 and t=0 Needed more detail near z=0 and t=0 Changed from linear to logarithmic steps Changed from linear to logarithmic steps

10. First solved original PDE with new method to confirm its accuracy

12. Next, added in heat loss factor and renormalized method for calculating the peak time and amplitude Looks good! Almost perfect!

13. Next, added in heat loss factor and renormalized method for calculating the peak time and amplitude UH-OH! Looks good! Almost perfect!

14. Next steps Adding an “ effective z ” Adding an “ effective z ” Heat conducting epoxy around resistor conducts heat ~1000 times more slowly Heat conducting epoxy around resistor conducts heat ~1000 times more slowly Rough trials indicate more like 3:2 ratio than 2:1 ratio Rough trials indicate more like 3:2 ratio than 2:1 ratio After Consistent Model After Consistent Model Try other materials Try other materials Have gold rod to make similar apparatus Have gold rod to make similar apparatus

15. The End Thanks for listening.