1. CONDUCTION IN A DIELECTRIC FILM ALEJANDRO GUAJARDO-CUELLAR ADVISOR: DR. MIHIR SEN acknowledgements : CONACYT

2. OUTLINE MOTIVATION DESCRIPTION OF THE PROBLEM MATHEMATICAL MODELS SOLUTIONS RESULTS CONCLUSIONS FUTURE WORK

3. MOTIVATION HEAT TRANSFER IN MICRO AND MACRO SCALES CANNOT BE DESCRIBED IN THE SAME WAY AS MACRO SCALE. DIFFERENT APLICATIONS CAN BE FOUND WHERE HEAT TRANSFER IN MICRO SCALE IS A FIGURE OF MERIT. CARBON NANO TUBES, INTEGRATED CIRCUITS.

4. SOME SAMPLES http://www.nec.com/global/corp/H0602.html http://www.ewels.info/.../nanotubes/tube.angled.jpg http://www.ipt.arc.nasa.gov/interconnect1.html

5. PROBLEM PROPOSED L T1T1 T0T0 x T= T 0 at t=0

6. Fourier law

7. HYPERBOLIC MODEL

8. DIFUSSION BY RANDOM WALK

9. Tzou proposed the following equation: This PDE does not have close solution. Tzou et al proposed an algorithm to solve the equation based in Laplace Transform. Shiomi and Maruyama studied Non-Fourier heat conduction in a single-walled carbon nanotube. They use molecular dynamics and the equation (1) and compare the result. Suggesting that equation (1) describes the phenomenon due they obtain similar results as molecular dynamics (1)

10. Results

13. CONCLUSIONS The models give different behavior for the same problem, the steady state solution is reached at different times. The same behavior for fourier and random walk is obtained. The second derivative in time in the hyperbolic heat equation gives the wave-like behavior meanwhile the first derivative works as a damping of the wave. This results give more understanding of the mathematical models proposed.

14. FUTURE WORK EXTEND THE PROBLEM TO 2-D STUDY WITH MORE DETAIL THE RANDOM WALK MODEL, AND TRY TO SOLVE THE PROBLEM WITH UNBALANCED PROBABILITY, OR STORAGE OF ENERGY OF THE DEFECT. APPLY THE RESULTS TO A SPECIFIC PROBLEM, LIKE CONDUCTION IN A CARBON NANO-TUBE.