?For the following exercises, the heat flow vector field for conducting objects i
Chapter 6, Problem 323(choose chapter or problem)
For the following exercises, the heat flow vector field for conducting objects i \(\mathbf{F}=-k \nabla T\), whereT(x, y, z) is the temperature in the object and k > 0 is a constant that depends on the material. Find the outward flux of F across the following surfaces S for the given temperature distributions and assume k = 1.
\(T(x, y, z)=-\ln \left(x^{2}+y^{2}+z^{2}\right)\) ; S is sphere \(x^{2}+y^{2}+z^{2}=a^{2}\) .
Text Transcription:
F = -k nabla T
T(x, y, z) = -ln (x^2 + y^2 + z^2)
x^2 + y^2 + z^2 = a^2
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