Problem 2A To prevent the rover's hemispherical drill head from freezing, your team is asked to model its steady state temperature conditions. The drill radius is also b. Using the following PDE and boundary/initial conditions, derive an analytical solution to the drill's temperature distribution T(ru): 18 18 PDE: · ¹ ² ( ²² ) - ¹ ² [(²-²)] + ₁ = 0 + +Go=0 ² or ôr Domain: 0≤r

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 2A
To prevent the rover's hemispherical drill head from freezing, your team is asked to model its
steady state temperature conditions. The drill radius is also b. Using the following PDE and
boundary/initial conditions, derive an analytical solution to the drill's temperature distribution
T(ru):
18
at
PDE:
+ 4 (-²²) - - - [(-²) +
+
(1-μ²
+ Go = 0
ôr
Ôμ
Domain: 0≤r<b, 0≤u≤1, where μ = cos
8T
OT
BCs:
+H.T(r=b, u) = 0, and
= 0, where Go and H are constants.
ar
âμ
r=b
μ=0
Transcribed Image Text:Problem 2A To prevent the rover's hemispherical drill head from freezing, your team is asked to model its steady state temperature conditions. The drill radius is also b. Using the following PDE and boundary/initial conditions, derive an analytical solution to the drill's temperature distribution T(ru): 18 at PDE: + 4 (-²²) - - - [(-²) + + (1-μ² + Go = 0 ôr Ôμ Domain: 0≤r<b, 0≤u≤1, where μ = cos 8T OT BCs: +H.T(r=b, u) = 0, and = 0, where Go and H are constants. ar âμ r=b μ=0
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