2. Heat Flux Consider a single heat source located at the origin with temperature 25 T(x, y, z) = %3D VZ + y² + z?° (a) Calculate the heat flux across the surface s = {(x, y, z): z = /T- x² – y², x² + y? s 1} %3D as shown in the figure. (b) Repeat the calculation in part (a) using the parametrization x = sin u cos v, y = sin u sin v, z = cos u where 0sus5 and 0 < v < 2n.

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2. Heat Flux Consider a single heat source located at the origin
with temperature
25
T(x, y, z) =
%3D
Jx² + y² + z²
(a) Calculate the heat flux across the surface
s = {(x, y, z): z = I-x² - y², x² + y? s 1}
%3D
as shown in the figure.
1
(b) Repeat the calculation in part (a) using the parametrization
*= sin u cos v, y= sin u sin v, z cos u
N = cos u
where
0 s u s
and 0 < v< 2n.
ミ一2
Transcribed Image Text:2. Heat Flux Consider a single heat source located at the origin with temperature 25 T(x, y, z) = %3D Jx² + y² + z² (a) Calculate the heat flux across the surface s = {(x, y, z): z = I-x² - y², x² + y? s 1} %3D as shown in the figure. 1 (b) Repeat the calculation in part (a) using the parametrization *= sin u cos v, y= sin u sin v, z cos u N = cos u where 0 s u s and 0 < v< 2n. ミ一2
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