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In this paper, a class of high duty counter-current heat exchangers, which are typically used in energy integrated systems, is considered. The governing dynamic equations for such exchangers are stiff first order hyperbolic PDEs, and hence show a potential towards multi-scale dynamics. Using singular perturbations, a reduced non-stiff PDE model is derived, which captures the dynamics in the slow time scale. A simulation case study is considered to illustrate these results.