Heat exchangers are widely used in various transportation, industrial, or domestic applications such as thermal power plants, means of heating, transporting and air conditioning systems, electronic equipment and space vehicles. In all these applications improvements in the efficiency of the heat exchangers can lead to substantial cost, space and material savings. Hence considerable research work has been done in the past to seek effective ways to improve the efficiency of heat exchangers. In this paper the effect of natural convection is justified between exterior solid wall surfaces and the surrounding air inside the enclosure. Designing of electronic devices, heavy industrial equipments such as boilers, turbines etc. and building aerodynamics are some of the real world application associated with this study. The referred investigation includes the phenomenon of natural convection process to analyses the pattern of heat transfer characteristics inside a square enclosure with two circular cylinders placed at different position inside it. Maximum heat exchange zones are identified so that goal of effective heat transfer can be achieved which helps the heat exchangers to work efficiently at every condition. However, in the present work only unsteady state natural convection technique has been considered. The study of unsteady state natural convection in a square enclosure with conjugate boundary condition is done numerically. The analysis is performed on a square enclosure within which are placed two circular cylinders eccentrically. The enclosure walls are maintained at low temperature to that of cylinders such that a temperature difference is maintained between both the bodies. The cylinders are tilted at different angles inside the enclosure. A transient state 2-D numerical investigation is conveyed for air as an enclosed fluid. The Rayleigh number is varied in the range of 103 to 106 and the results are summarized in a relative manner. The value of Prandtl number is kept constant i.e. 0.71 corresponding to that of the air. The effect of orientation of the two cylinders and the outcome of the variation of Rayleigh number is calculated with the help of corresponding streamlines, and temperature distribution.