Chapter 17.6, Problem 62E

Heat flux The heat flow vector field for conducting objects is F = –k▿T, where T(x, y, z) is the temperature in the object and k > 0 is a constant that depends on the material. Compute the outward flux of F across the following surfaces S for the given temperature distributions. Assume k = 1.

62.     $T\left(x,y,z\right)=100e^{-x^2-y^2-z^2}$; S is the sphere x² + y² + z² = a²