Computer codes were developed to study the performance of compact heat exchangers (CHEs) operating in self-sustained oscillatory flow (SSOF) regimes. The methods were based on a control volume-based finite element (CVFEM) method for geometric discretization and the explicit first stage, single diagonal coefficient, diagonally implicit, Runge–Kutta (ESDIRK) method for temporal discretization. The developed codes were validated for both steady and unsteady cases. A study of nine geometrically related domains of flat tubes in staggered configurations was performed. Grid independence was established subject to double cyclic conditions—periodically fully developed flow and heat transfer in the stream-wise direction and cyclic or repeating flow and heat transfer in the cross-stream direction. The maximum Reynolds number was established at approximately 2000 for the cases studied to avoid the turbulent flow regime. Parameters of interest like Nusselt number, friction factor, and pumping power were calculated for steady and SSOF regimes. An approach was proposed to determine critical Reynolds number (Recrit) for the SSOFs such that for Reynolds number below Recrit the flow remains steady, and above Recrit, the flow exhibits the characteristics of SSOFs before finally transitioning to fully turbulent conditions. The results indicated a sensitivity of performance parameters to transverse spacing but not to longitudinal spacing.