In: Physics
a solid material that has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by w(x, y, z) has heat flow given by the vector field F = ?K?wand rate of heat flow across a surface S within the solid given by?K ?? ??S ?w dS. Find the rate of heat flow out of a sphere of radius 1 meter inside a large cube of copper (K=400kilowatts/m-k) with temperature function given by w(x, y, z)=20?5(x2+y2+z2)?C