Abstrae~This paper reports the results of an experimental and numerical study of the optimal geometric arrangement of staggered parallel plates in a fixed volume with forced convection heat transfer. The objective of the geometric optimization effort is to maximize the total heat transfer rate between the given volume and the given external flow, when the maximum temperature at a point inside the volume cannot exceed a certain level. The geometric arrangement was varied systematically, by changing the spacing between plates, the number of plates installed in one row, the plate swept length, and the degree to which the plates are staggered. In the first part of the study, it is demonstrated experimentally that there exists an optimal spacing between two adjacent row of plates. Experimental results are reported for air in the range 1000 ~< ReL <<. 6000, where L is the swept length of the fixed volume. In the second part of the study, extensive numerical results support and extend these findings to 100 ~< ReL <<, 10000. In addition, it is shown that there is an optimal way to stagger the plates. In the concluding part of the paper, the optimal spacing and maximum heat transfer rate results are correlated based on the theoretical method of intersecting the two asymptotes (small spacing, large spacing) of the geometric arrangement.