In this paper three-dimensional flows with conjugated heat transfer in multi-fluid and multi-channel compact heat exchangers are investigated. The underlying numerical solution method for the three-dimensional steady and unsteady incompressible Navier-Stokes and energy equations is presented, which combines efficient numerical techniques and parallel computing. The method is based on blockstructured grids with collocated arrangements of variables, a fully conservative finite volume discretization, an iterative pressure-correction method of SIMPLE type, a special parallelized ILU solver, a nonlinear multigrid method, and a grid partitioning technique.