# 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 is a constant that depends on the material. Compute the outward flux of F across the given surface S for the given temperature distribution. Assume k=1.   T(x,y,z,)=−7ln( x2 +y2 + z2) S is the sphere x2+y2+z2=a2

Question
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 is a constant that depends on the material. Compute the outward flux of F across the given surface S for the given temperature distribution. Assume k=1.

T(x,y,z,)=−7ln( x2 +y2 + z2)
S is the sphere x2+y2+z2=a2