This thesis provides an assessment of various computational strategies for modellingthe turbulent flow and heat transfer around in-line tube banks. The research has directapplication to the heat exchanger of an Advanced Gas-cooled Reactor (AGR).The suitability and accuracy of different Computational Fluid Dynamic (CFD) techniqueswere investigated first on generic square in-line tube banks where experimentaldata are available. The assumption of flow periodicity in all three Cartesian directionsis initially investigated whereby the domain size was varied. Wall-resolved Large EddySimulations (LES) predict an increasing flow asymmetry with decreasing tube spacing.Two dimensional (2D) and three dimensional (3D) Unsteady Reynolds AveragedNavier-Stokes (URANS) models were simulated at the tube spacing known to be closeto the flow pattern transition from symmetric to asymmetric. Marked differences wereobserved between the flow pattern predicted by turbulence models resolving the boundarylayer and those that rely on wall functions. Ultimately, an improved understandingof the flow physics and heat transfer mechanisms encountered within in-line tube bankswas gained.The assumption of flow periodicity was then removed and the effects of confiningwalls were investigated by reproducing experimental conditions. The correct pressureforces and heat transfer around the central tubes could only be accurately predictedwhen the walls in the crossflow direction were modelled. The inclusion of walls in thespanwise direction gave rise to small flow asymmetries which have been reported onsimilarly-spaced in-line tube banks.The latter half of the thesis focuses on the reasons for the enhanced thermal mixingand 3D secondary flow patterns observed in the in-line section of the AGR heatexchanger. A wall-resolved periodic LES was conducted at the lower Reynolds numberof 11,000 along with URANS calculations of the full experimental conditions atboth Reynolds numbers 11,000 and 66,000. These calculations required the use of HighPerformance Computing (HPC) facilities. Large 3D secondary flow structures werepredicted that produced the same level of crossflow temperature drifting as that reportedexperimentally. Multiple upward and downward flow paths were observed whichqualitatively explained why the experimental temperature profiles reported at differentspanwise locations indicated multiple spirals (or secondary vortices).Quantification of the levels of thermal diffusion were investigated using both decayingtemperature spikes and blanked tube platens. Thus the CFD provided recommendationsabout the thermal diffusivity assumptions used by the AGR heat exchangercode.