This paper reports our numerical investigations on enhancement of pool boiling heat transfer inside an array of solid cylinders of square cross section using lattice Boltzmann Method. The entire saturated pool boiling curve for the flat surface comprising of different nucleate boiling regimes has been obtained numerically. The effect of solid cylinder array has been quantitatively evaluated and expressed in the form of its corresponding boiling curve. It is found that the boiling incipience in presence of the cylinder array occurs at a lower surface superheat compared to that of a plane surface. Further, the solid array effectively delays the onset of film boiling. The bubble dynamics in such solid structure array including bubble nucleation, coalescence, growth, entrapment, splitting and escape is found to be very different compared to a flat surface. Based on the heat flux values and trends, the entire boiling curve could be classified into 4 distinct zones. To the best of our knowledge, this is the first instance where LBM could predict the entire pool boiling curve for any porous medium. Finally, two different cylinder arrays of porosity 90% and 98% are studied to examine the effect of porosity. It is found that the sensitivity of the heat transfer rates to porosity is significant especially at higher values of surface superheat.