A study of finding empirical correlation for the Nusselt number and the factors influencing it for perforated fin array of different shapes

An experimental investigation of three-dimensional steady state forced convection heat transfer through perforated rectangular fins with three different materials were carried out. The experimental procedure has been done in turbulent region with Reynolds number range of (6200 ≤ Re ≤ 18,700) and (Pr = 0.71) and constant inlet air temperature of (Tin≈17°C) with a constant power input of (20 W ≤ Q ≤ 70 W) step 10 W. The current study used a rectangular fin array with three materials (stainless steel 430, aluminum 2014-T6, yellow brass), with various perforation shapes and patterns which includes [Rectangular, Circular, and V-shape, all (Inline, staggered)]. It is found that the mean deviation of average Nusselt number taken for previously published results to the experimental result of all specimens have been found to be ∓ 8 %. A general correlation has been derived based on average Nusselt number with an error of ± 5 % which is described with the formula (Nu¯=βRe¯αδRAFPrRAF). It is concluded that the general correlation equation derived has reasonably acceptable degree of accuracy and it’s more general and considers many materials with a wide range of RAF compared with the other equations. The average error found between the general correlation and previously published result is ± 9.8 %.