Chapter 6.6, Problem 323E

For the following exercises, the heat flow vector field for conducting objects $\text{F}=-k\nabla T$ , where $T(x,y,z)$ is the temperature in the object and $k>0$ is a constant that depends on the material. Find the outward flux of $\text{F}$ across the following surfaces S for the given temperature distributions and assume $k=1$ .

323. $T(x,y,z)=\text{In}(x^2+y^2+z^2)$ ; $S$ is sphere $x^2+y^2+z^2=a^2$ .