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Building roofs are responsible for the huge heat gain in buildings. In the present work, an analysis of the influence of insulation location inside a flat roof exposed directly to the sun's radiation was performed to reduce heat gain in buildings. The unsteady thermal response parameters of the building roof such as admittance, transmittance, decrement factor, and time lags have been investigated by solving a one-dimensional diffusion equation under convective periodic boundary conditions. Theoretical results of four types of walls were compared with the experimental results available in literature. The results reveal that the roof with insulation placed at the outer side and at the center plane of the roof is the most energy efficient from the lower decrement factor point of view and the roof with insulation placed at the center plane and the inner side of the roof is the best from the highest time lag point of view among the seven studied configurations. The composite roof with expanded polystyrene insulation located at the outer side and at the center plane of the roof is found to be the best roof from the lowest decrement factor (0.130) point of view, and the composite roof with resin-bonded mineral wool insulation located at the center plane and at the inner side of the roof is found to be energy efficient from the highest time lag point (9.33 h) of view among the seven configurations with five different insulation materials studied. The optimum fabric energy storage thicknesses of reinforced cement concrete, expanded polystyrene, foam glass, rock wool, rice husk, resin-bonded mineral wool, and cement plaster were computed. From the results, it is concluded that rock wool has the least optimum fabric energy storage thickness (0.114 m) among the seven studied building roof materials. [ABSTRACT FROM AUTHOR]