The use of inserts to increase mixing and heat transfer in heat exchangers and solar collectors has gained significant recent attention, but not for photovoltaic thermal (PV/T) systems. We describe a 3D numerical study of a PV/T module with conical-leaf inserts using computational fluid dynamics. The numerical solution was validated against available experimental data. Inserts represent a trade-off as the increased mixing and heat transfer causes an additional pressure drop which requires increased pumping power. The trade-off shows that our base case of the conical-leaf insert increases the Nusselt number by a factor of nearly two compared to the plain tube without insert, which is attributed to the increased mixing and redeveloped thermal boundary. Consequently, it leads to improvement in thermal and electrical efficiencies compared to a PV/T module without insert by 12% and 2%, respectively. Moreover, the conical-leaf insert had a negligible effect on the pump power as compared to the electrical power output of the module and the cell temperatures were more uniform than when there was no insert. We then evaluate the performance of the PV/T module with different insert designs and arrangements, and operating conditions. Among the geometrical parameters, the best overall efficiency of 84.2% occurred when the leaf angle was 360 degrees, in other words, when it turns into a ring. Over the range of operating conditions that we studied, the reduction of the PV cell temperature with inserts is in the range of 2-7 K. This, in turn, increases the thermal efficiency and electrical efficiency by 10.2-14.1%, and 0.9-3.4% compared to the plain tube, respectively.