Network models for maximization of heat transfer under weight constraints

Of concern is a network in which the conductance of certain branches are variable. The problem posed is the maximization of the joint conductance subject to a bound on the <t norm of the variable conductances. It is shown that at P an optimum state the conductance of a variable branch is proportional to the 2/(p+l) power of the current through the branch. l*his relation together with a dual variational principle leads to a "duality inequality giving sharp upper and lower estimates of the maximum joint conductance. Such a network serves as a discrete model for a cooling fin subject to a weight limitation. Thus the model shows what analogous properties should hold for the cooling fin. Prepared under Research Grant DA-ARO-D-31-124-71-G17, Army Research Office (Durham). NETWORK MODELS FOR MAXIMIZATION OF HEAT TRANSFER UNDER WEIGHT CONSTRAINTS by S. Bhargava and R. J. Duffin