This paper reports a single-component two-dimensional pseudo-potential phase change model using lattice Boltzmann method (LBM) to investigate the enhancement of pool boiling heat transfer inside an array of solid pillars with square cross section. The entire saturated pool boiling curve for the flat surface comprising different nucleate boiling regimes from boiling incipience (BI) to critical heat flux (CHF), transition boiling regime between CHF to Leidenfrost point (LP) and the film boiling regime has been obtained numerically. The effect of the array of solid pillars with square cross section has been quantitatively evaluated and expressed in the form of its corresponding boiling curve. It is found that the boiling incipience in the presence of solid array occurs at a lower surface superheat compared with that of a plane surface. Further, the solid array effectively delays the onset of film boiling. Qualitative analysis of pool boiling phenomenon shows the bubble dynamics in such solid structure including bubble nucleation, coalescence, growth, entrapment, splitting, and escape to be very different compared with a flat surface. Based on the heat flux values and trends, the entire boiling curve could be classified into four distinct zones. To the best of our knowledge, this is the first instance where LBM could predict the entire pool boiling curve for a porous medium. Finally, two different pillar 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.