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 improvement 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. The referred investigation includes the phenomenon of natural convection process to analyse 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 107 and the results are summarized in a relative manner. The value of Prandlt number is kept constant i.e. 0.71 corresponding to that of the air. The effect of orientation of the two cylinder and the outcome of the variation of Rayleigh number are calculated with the help of corresponding streamlines, and temperature distribution. The value of average Nusselt number is calculated for different Rayleigh number. The divarication of natural convection from unsteady state to steady state is directly dependent on the value of Rayleigh number and the distance of hot cylinder from the centre of the enclosure. In case of Ra 103, 104, 105 the isotherms and flow-fields attains a steady state after certain period of time but in contradict to this the state of flow-field and isotherm becomes unsteady at Ra 106. The variation of Nusselt number with respect to flow time is also illustrated in the study.