One of the important objectives in thermal systems engineering is to analyze utilization of thermal energy in an efficient manner. Analysis based on second law of thermodynamics may give an insight about efficient usage of thermal energy in various industrial systems. In this regard, entropy generation analysis during conjugate natural convection within a differentially heated square cavity enclosed by vertical conducting walls of different thicknesses (t(1) and t(2)) has been carried out for various thermal systems. Finite element based numerical simulations are carried out for various location of vertical wall thicknesses (cases 1, 2, and 3) in the range of parameters, Ra (10(3) <= Ra <= 10(5)), Pr (Pr = 0.015-1000), wall thicknesses (t = 0.2 and 0.8), and conductivity ratios (K = 0.1,1 10 and infinity). Maximum entropy generation due to heat transfer (S-theta,S-max) occurs near the solid-fluid interface region due to high temperature gradient whereas maximum magnitude of the entropy generation due to fluid friction (S-psi,S-max) occurs near the cavity walls due to friction between the circulation cells and cavity walls. Larger heat transfer and high intensity fluid flow lead to larger S-theta,S-max and S-psi,S-max for K = 10 compared to that of K = 0.1 and K = 1 irrespective of Pr and location of solid wall thickness. Qualitative features of theta, psi, S-theta and S-psi for t(1) + t(2) = 0.8 are identical with t(1) + t(2) = 0.2. However, the magnitude of S-theta,S-max and S-psi,S-max is less for t(1) + t(2) = 0.8 compared to t(1) + t(2) = 0.2. Based on detailed discussion of average Nusselt number ((Nu) over bar (l)), average Bejan number (Be-avg) and total entropy generation (S-total) vs various governing parameters (Ra, Pr and t), it may be concluded that thermal processing is invariant of K in conduction dominant region (10(3) <= Ra <= 10(4)) irrespective of Pr and t. On the other hand, K <= 1 with t(1) + t(2) approximate to 0.8 may be optimal for thermal processing within the convection dominant region (10(4) <= Ra <= 10(5)) due to less entropy generation and reasonable heat transfer rate, irrespective of Pr.