In this study, the cracking phenomenon of methane taking place in a cylindrical cavity of 16 cm in diameter and 40 cm in length under the heat of concentrated solar radiation without any catalyst is analysed. Three cases have been chosen; in all cases the primary phase contains methane and hydrogen gases. In the first case, we consider two phases; the secondary phase is a homogeneous carbon black powder with 50 nm of diameter; in the second case we have three phases where the two secondary phases are a particles powder with two diameters 20 and 80 nm and finally, a third case of five phases with a powder of four different diameters 20, 40, 60 and 80 nm. The low Reynolds K-epsilon turbulence model was applied. A calculation code "ANSYS FLUENT" is used to simulate the cracking phenomena where an Eulerian - Eulerian model is applied. The choice of several diameters greatly increases the calculation time but it approaches more of the physical reality of the radiation by these particles during the cracking. Results have shown that increasing the number of diameters gives higher cracking rates; the case of the powder of 4 different diameters gives the highest cracking rate. A parametric study as a function of the inlet velocity, carbon particle diameters and the intensity of solar radiation is realized. For the cracking heat, provided by the choice of the two concentrators of 5 and 16 MW/m(2) used in this simulation, the CH4 inlet velocity is a decisive parameter for the cracking rate. Any increase in the inlet velocity requires more heat and this leads to a decrease in the cracking rate. For a velocity not exceeding 0.177 m/s (i.e. 0.3 L/min), both solar concentrations give the same amount of hydrogen produced. These quantities of hydrogen obtained reach maximum values for an inlet flow rate of CH4 between 0.58 L/min (i.e. 0.34 m/s) and 0.62 L/min (i.e. 0.3655 m/s) for both reactors. The results are interpreted and compared with experimental work. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.