Chapter 6.6, Problem 322E

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 $k=1$ .

322. $T(x,y,z)=100e^{-x-y}$ consists of the faces of cube $\left|x\right|\le 1$ , $\left|y\right|\le 1$ , $\left|z\right|\le 1$ .