An alternative approach to study periodically fully-developed flow and heat transfer problems subject to isothermal heating conditions

Periodically fully-developed flow (PFD) and heat transfer in a channel subject to isothermal conditions must either be formulated as an eigenvalue problem and solved iteratively or the PFD solution must be extracted as a part of developing flow (DF) solution by considering the entire flow domain. The first approach is mathematically complex and the second approach is computationally inefficient. In this work, an alternative approach is proposed wherein a PFD flow solution is used as an input to all modules of a DF domain and the PFD temperature field is extracted by monitoring variation in module-averaged Nusselt number. The proposed method was validated by comparing results obtained by the proposed method with results in the literature for three sample problems: flow between parallel plates, flow over round tubes in parallel plate channel, and flow in a parallel plate channel with staggered plate fins. Flow and energy equations were solved by using a control volume based finite element method in conjunction with SIMPLER algorithm. Results obtained by the proposed approach compared very favorably with the results published in the literature.