The finite-difference and sector methods are applied to determine the efficiency of the continuous plate fin pierced by a regularly spaced array of circular tubes in staggered or in-line tube arrays. The comparison of the fin efficiency between the present numerical results, approximate solutions obtained from the sector method, and previous results is made. It is found that the sector method underpredicts the efficiency of the hexagonal and rectangular fins. However, the previous method can overpredict the fin efficiency for lower ro/ a values. Results also show that the plate fin with the staggered tube array is more efficient than that with the in-line tube array. A simple expression relating the fin efficiency to the tube radius, tube spacing, fin thickness, and material properties is obtained by using the least-squares fitting of numerical data. The main purpose of the present study is to determine the optimum dimensions of the continuous plate fin with various tube arrays that can give the greatest amount of heat dissipation under the conditions of the given physical quantities.
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