This paper presents a three-dimensional geometric optimisation of cooling channels in forced convection
of a vascularised material with the localised self-cooling property subjected to a heat flux. A square configuration
was studied with different porosities. Analytical and numerical solutions were provided. The
geometrical configuration was optimised in such a way that the peak temperature was minimised at
every point in the solid body. The optimisation was subject to the constraint of a fixed global volume
of solid material, but the elemental volume was allowed to morph. The solid material was subject to a
heat flux on one side and the cooling fluid was forced through the channels from the opposite direction
with a specified pressure difference. The structure had three degrees of freedom as design variables: the
elemental volume, channel hydraulic diameter and channel-to-channel spacing. A gradient-based optimisation
algorithm was used to determine the optimal geometry that gave the lowest thermal resistance.
This optimiser adequately handled the numerical objective function obtained from numerical simulations
of the fluid flow and heat transfer. The numerical results obtained were in agreement with a theoretical
formulation using scale analysis and the method of intersection of asymptotes. The results
obtained show that as the pressure difference increases, the minimised thermal resistance decreases.
The results also show the behaviour of the applied pressure difference on the optimised geometry. The
use of the optimiser made the numerical results to be more robust with respect to the optimum internal
configurations of the flow systems and the dimensionless pressure difference.