Flow boiling in multi-microchannel evaporators is recognised as one of the most efficient cooling solutions for high-performance electronics, and has therefore received increasing attention during the recent years. Despite the extensive literature, there is no general agreement yet about the effect of the channel cross-sectional shape on the boiling heat transfer performance, which results on a limited availability of thermal design guidelines and tools. This article presents the results of a systematic analysis of the impact of the channel shape on the bubble dynamics and heat transfer, under flow boiling conditions. Simulations are carried out using a customised version of OpenFOAM, and the Volume-Of-Fluid method is chosen to capture the liquid-vapour interface dynamics. A benchmark flow model is utilised, where a single isolated bubble is seeded at the channel upstream and transported by a liquid flow across the diabatic section, which is heated by a constant and uniform heat flux. Flow conditions that apply well to the flow boiling of water or refrigerant fluids in sub-millimetre channels at low heat flux ( ~ 10 kW/m2) are investigated, with cross-section width-to-height aspect-ratios ranging from 1 to 8, while the hydraulic diameter of the channel is fixed. This study emphasises that the heat transfer performances for different channel shapes are closely related to the perimetral distribution of the liquid film surrounding the very long bubbles. Square channels exhibit the highest heat transfer coefficients at low flow rates, due to a very thin liquid film that forms at the centre of the wall, but are more at risk of film dryout. High aspect-ratio rectangular channels may be beneficial at larger flow rates, as they promote the formation of an extended liquid film that covers up to 80 % of the cross-section perimeter. At larger aspect-ratios, the average heat transfer coefficient along the shorter wall becomes orders of magnitude smaller than the value detected along the longer wall, owing to a strong asymmetry in the liquid film perimetral distribution.