heatflow%due%to%aplume%(kz + ip)(kz — ip) e k4t2pcp 2õ2 —i27r kz zo z 00 dkz (kz + — ip) 4tkp...
TRANSCRIPT
-
Heat Flow Due to a Plume
Evan Hirakawa November 8, 2010
-
• Only boundary condi?on:
T (x, y, 0) = 0
• Gaussian heat source:
-
Heat Conduc?on Equa?on:
with the source, H:
-
Fourier Transform x and y:
Now Fourier Transform z:
-
Now solve for T(k):
-
Inverse Fourier Transform for z:
-
Now create image to sa?sfy boundary condi?on, T(z=0) = 0
-‐now inverse transform x & y numerically
• σ = 60000/(2*sqrt(2 * log(2))) m
• A = .948 W/m2 (amplitude)
• k = 3.3 W/(m*K) (thermal conduc?vity)
• κ = 8 x 10^-‐7 m2/s (thermal diffusivity)
-
FWHM = 10 km
-
FWHM = 30 km
-
FWHM = 60 km
-
FWHM = 100 km