Chapter 14.6, Problem 61E

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.

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