This work describes the development of a methodology that couples one-dimensional (1D) network elements with three-dimensional (3D) spatial computational fluid dynamic (CFD) elements to analyse shell-and-tube heat exchangers with dense tube bundles. The one-dimensional (1D) elements represent the tube flow while the spatial elements represent the external auxiliary flow. This reduces the computational expense significantly as compared to full CFD analysis of the same system, whilst a detailed transient temperature distribution can still be obtained. The methodology uses a unique combination of relaxation algorithms, a polynomial regression mapping procedure, and discretisation methods to create a coherent numerical methodology. Simulations are performed on a TEMA-FU type shell-and-tube heat exchanger. The methodology was validated against full CFD and indicates errors between the calculated logarithmic mean temperature differences (LMTD) of less than 2% over a range of turbulent flow conditions. Various combinations of media for primary and auxiliary fluids are considered, to test the applicability and robustness of the methodology. Finally, a transient simulation of timed step inputs for the flow rate and temperature of both primary and auxiliary fluids, also corresponds with a full CFD analysis. It is concluded that the proposed 1D-CFD method is effective for simplifying the analysis of flow through tube bundles.