Optimum taper for thermal conduction paths in electronic equipment

Walls must often serve as conduction heat paths in many industrial applications. For the general case where heat is uniformly supplied to a wall or plate, the heat to be conducted down the wall to a heat sink, the question arises whether the wall should be of uniform thickness or tapered, for a given volume of material. The wall giving the smaller temperature drop could be considered the better design in utilizing the given weight of material. In many cases the wall is thin and long, and the problem can be reduced to one-dimensional heat transfer as shown.