Heat Flow Suppose the temperature at a point in 3-space x, y, z in a body is given by T = u(x, y, z). Then the heat flow is defined as the vector field F=K delta mu where K is an experimentally determined constant called the conductivity of the substance. The rate of heat flow across the surface S in the body is then given by the (vector) surface integral K delta mu middot dS Suppose the temperature u in a metal ball is directly proportional to the square of the distance from the center of the ball, with the proportionality constant 'c'. Find the rate of heat flow across a sphere S of radius R centered at (0, 0, 0). You may use your calculator to computer the resulting integral. Hint: Recall that the distance between the origin and a point in 3-space x, y, z is given by d = x-1 + y-1 + z-2. Try to choose an appropriate coordinate system to compute the resulting flux integral! You may apply the Divergence Theorem to computer the resulting flux integral as well.