Topography optimisation using a reduced-dimensional model for convective heat transfer between plates with varying channel height and constant temperature

This paper proposes a reduced-dimensional model for the structural optimisation of conjugate heat transfer between parallel plates with constant temperature and a fluid channel of varying height. The model considers heat conduction and convection through a planar reduced-dimensional version of the convection-diffusion equation. To significantly reduce the computational time for the optimisation process, assumptions on the through-thickness velocity and temperature fields are made, allowing to transform a three-dimensional problem to a two-dimensional one. The accuracy and limitations of the model are investigated through an in-depth parametric analysis and are seen to be acceptable in the context of optimisation when considering the reduced computational cost. To allow for the optimisation of varying topology and topography, the local channel height is linearly interpolated based on the design field. The height parametrisation combined with the reduced-dimensional model provides physical meaning to intermediate design variables and removes the traditional requirement of 0–1 discrete solutions for topology optimisation. This allows the free switch between topology and topography optimisation, but it is illustrated through various examples that only topography changes are relevant for the treated problems. Two optimisation examples, a square heat exchanger and a manifold heat exchanger, demonstrate that the reduced-dimensional model is sufficiently accurate to be applied to structural optimisation. In comparison with shape optimisation using a full three-dimensional model, it is demonstrated that topography optimisation using the reduced-dimensional model can achieve equivalent optimised designs at a significantly lower computational cost. Graphical abstract