Present study provides a theoretical investigation of the entropy generation analysis due to flow and heat transfer in nanofluids. For this purpose, the most common alumina-water nanofluids are considered as the model fluid. Since entropy is sensitive to diameter, three different diameters of tube in their different regimes have been taken. Those are microchannel (0.1 mm), minichannel (1 mm) and conventional channel (10 mm). To consider the effect of conductivity and viscosity, two different models have been used to represent theoretical and experimental values. It has been found that the reduced equation with the help of order of magnitude analysis predicts microchannel and conventional channel entropy generation behaviour of nanofluids very well. The alumina-water with high viscosity nanofluids are better coolant for use in minichannels and conventional channels with laminar flow and microchannels and minichannel with turbulent flow. It is not advisable to use alumina-water nanofluids with high viscosity in microchannels with laminar flow or minichannels and conventional channels with turbulent flow. Also there is need to develop low viscosity alumina-water nanofluids for use in microchannel with laminar flow. It is observed that at lower tube diameter, flow friction irreversibility is more significant and at higher tube diameter thermal irreversibility is more. Finally, for both laminar and turbulent flow, there is an optimum diameter at which the entropy generation rate is the minimum for a given nanofluid.