Numerical computation of 3D heat transfer in complex parallel heat exchangers using generalized Graetz modes

Numerical computation of 3D heat transfer in complex parallel heat exchangers using generalized Graetz modes. OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. a b s t r a c t Keywords: Generalized Graetz mode Parallel heat exchangers Optimal weak-variational formulation Functional minimization We propose and develop a variational formulation dedicated to the simulation of parallel convective heat exchangers that handles possibly complex input/output conditions as well as connection between pipes. It is based on a spectral method that allows to re-cast three-dimensional heat exchangers into a two-dimensional eigenvalue problem, named the generalized Graetz problem. Our formulation handles either convective, adiabatic, or prescribed temperature at the entrance or at the exit of the exchanger. This formulation is robust to mode truncation, offering a huge reduction in computational cost, and providing insights into the most contributing structure to exchanges and transfer. Several examples of heat exchangers are analyzed, their numerical convergence is tested and the numerical efficiency of the approach is illustrated in the case of Poiseuille flow in tubes.