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Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory.Three types of 3-D circular disc heat sink models,i.e.without collection microchannels,with center collection microchannels,and with edge collection microchannels,are established respectively.Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels,that of circular disc heat sink with center collection microchannels is the minimum,so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages.Furthermore,the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes.With the mass flow rate increasing,both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease.With the heat flux increasing,the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged.With the same mass flow rate and heat flux,the larger the microchannel branch number,the smaller the maximum thermal resistance.While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.