Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature: that is, F-KVT, which means that heat energy flows from hot regions to cold regions. The constant k is called the conductivity, which has metric units of Jim-s-K or Wim-K. A temperature function T for a region D is given below. Find the • SSF.no --SS. VT-nds across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral. Assume that k=1. T(xyz)-65²-²-²D is the sphere of radius a centered at the origin net outward heat flux Fonds-k

Prove the second part of each law: AU (BNC) = (AUB) N (AUC) Distributive laws AN (BUC) = (ANB) U (ANC) ANB AUB AUB = A0B De Morgan's laws

ac Use ac. ethod

3 : 5 = _____: 15