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In this paper, thermal conductivity measurement of liquids and nanofluids is numerically investigated by the steady state method. In which, it is required to omit the natural convection effects on the inaccuracy of measurement for heat lost quantification. One of the well-known steady-state apparatus is circular parallel-plate where the distance between circular plates is filled with liquids or nanofluids. So, it has to be designed accurately to neglect the effects of free convection. The numerical simulation is a convenient method which can omit the mentioned effects. Water, Ethylene and Ethylene Glycol are considered as base liquids and Al2O3 as a Nano-fluid in this work. Thermal boundary conditions, the distance between two parallel discs, physical and thermal quantities of fluids, size and volume fraction of nano-particles have extensive effects on the measurement process. The main result of the simulation indicates that for all of the cases, the distance between two parallel discs has to get less than 2 mm for accurate measurement of thermal conductivity in the parallel circular plate, wherein, uncertainty in the presence of the natural convection can be easily omitted., Comment: 12 figures, 16 pages