Materials selection for a cooling plate using control area diagrams

Merit indices are used to rank materials and are of fundamental importance in materials selection. Traditionally, merit indices have only been available for elementary design cases. In the present paper merit indices are generalised to cooling systems where heat flow and strength are design criteria in a materials optimisation framework. A cooling tube and a cooling plate are considered. A new concept, merit exponent is used that is related to the merit indices. A definition of the merit exponent is given also for cases with many design variables. In each design case a number of merit exponents are involved. It is a nontrivial task to identify which they are and when each of them is applicable. For this purpose control area diagrams (CAD) are used. A CAD is a diagram with the controlling properties on the axes, and areas where one or more constraints are active. For the cooling systems the controlling properties are heat conductivity and strength. The active constraints define the relevant merit exponent. The constraints involve the controlling properties and geometrical variables. Principles are established for how to set up the CAD and to derive the merit exponents.

► A procedure for deriving merit exponents when multiple property constraints are active is outlined.
► The principles are illustrated for cooling systems (tube and plate).
► Control area diagrams (CAD) for the active constraints for cooling systems are formulated.
► The procedures do not require analytical solutions and are applied in FEM.