In this thesis, we apply the constructal method for designing several devices. We identified tradeoffs and competition that take place in these devices, and we show how the shape and structure, i.e. the device architecture, emerges as the result of optimization under constraints.

The first system considered is a liquid stream, which is heated to reduce its viscosity, and thus friction losses. We show that there is an optimal heating to minimize the total energy input to the system, and we delineate the applicability of this method.

The second device investigated is a solenoid and its cooling system. The optimal geometry that leads to large magnetic field and low hot spot temperature has been derived. We also show that the portion of the volume occupied by the cooling system can be optimized.

A third example of systems that we optimized is a beam under sudden and intense thermal attack. The result is the optimal shape that provides high strength in the absence of a thermal attack, and long survival time in case of a thermal attack. A similar approach has been used to optimize the number and positioning of reinforcing steel bars in the beam.

The forth problem consists of finding the minimum pumping power requirement network that connects a given set of points. Fundamental rules for easily building the optimal network have been discovered and are presented in the thesis. The addition of Gilbert-Steiner points is considered, as well as the effect of gravity forces. We show that optimal networks do not have loops, and that angle conditions can be used to optimize the network.

For the last example we consider a heat-generating surface that we propose to cool with high conductivity inserts. We begin by optimizing an elemental area, and many elemental areas are then assembled to form a first construct. The new feature of this fundamental problem is that the thickness of the high conductivity blade can now be small enough to affect the thermal conductivity. We show that the transition between size-affected and bulk regions is governed by the heterogeneity of the structure.

In each case, the competition between the global objectives and constraints is the source of the optimization opportunities, and geometry emerges as a result. The work presented in this dissertation is truly multi-disciplinary:​ it combines heat transfer with many other disciplines such as physics, electromagnetism, fluid dynamics, and strength of materials.