The objective of this paper is to present a methodology for optimal de
sign of cooling systems for multi-cavity injection mold tooling. After
the part layout and the injection mold are designed, the methodology
optimizes cooling system layout in terms of cooling channel size, loca
tions, and coolant flow rate. The mold cooling design is modeled as a
non-linear constrained optimization problem. The objective function fo
r the constrained optimization problem is stated as minimization of bo
th a function related to part average temperature and temperature grad
ients throughout all the cavities. The constrained optimal design prob
lem is solved using Powell's conjugate direction with the penalty func
tion method. The objective function is evaluated using finite element
analysis solving the transient heal conduction problem. A matrix-free
Jacobi conjugate gradient algorithm of Galerkin finite element method
is utilized to simulate transient heat conduction.