Heat exchangers (HEs) are crucial processing units in industrial plants. Heat exchanger networks (HENs) are often designed for nominal operation. However, processes are becoming increasingly dynamic and should be able to operate over a range of operational periods to address changes in market, seasonality, and start-up and shutdown. HEN synthesis has been widely studied, however most approaches use simplified HE models for optimisation and analysis of the structures, assuming the largest area across all periods of operation results in a feasible HE. The detailed HE design, which includes many more practical constraints, such as variable heat transfer coefficients that are a function of velocity, may result in certain exchangers being infeasible in some operational periods. In this study, an HE design algorithm is proposed, which finds optimal shell-and-tube HEs that are feasible across any number of operational periods, which may involve different duties and fluid properties. This is the first such design algorithm presented in literature. The algorithm works via a smart enumeration algorithm, which solves a nonlinear programming (NLP) optimisation subproblem for each combination of discrete decisions (number of baffles, stream allocation, tube diameters, etc.). Each NLP solves Bell Delaware design equations across all considered periods and allows stream splitting and HE bypassing to find an optimal multi-period HE. If no feasible HE is found, a permutation algorithm is used to find the optimal combination of HEs that can fulfil the required heat duties. The algorithm is demonstrated on two examples, showcasing its performance. Future work is suggested to increase the algorithm’s computational efficiency and to include it in multi-period HEN synthesis.