(Solved): The heat flow vector field for conducting objects is F=kT, where T(x,y,z) is the temperature ...

The heat flow vector field for conducting objects is $F=?k?T$, where $T(x,y,z)$ is the temperature in the object and $\mathrm{k}$ is a constant that depends on the material. Compute the outward flux of $\mathbf{F}$ across the surface $S$ for the given temperature distribution. Assume $k=1$. $T(x,y,z)=50e^{?x?y};S$ consists of the faces of the cube $?x??1,?y??1,?z??1$. The outward flux is (Type an exact answer.)