The objective of an experiment performed by ourstudents is

Chapter 7, Problem 7.73

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The objective of an experiment performed by ourstudents is to determine the effect of pin fins on thethermal resistance between a flat plate and an airstream.A 25.9-mm-square polished aluminum plate is sub-jected to an airstream in parallel flow at T??20?C andu??6 m/s. An electrical heating patch is attached tothe backside of the plate and dissipates 15.5 W underall conditions. Pin fins of diameter D?4.8 mm andlength L?25.4 mm are fabricated from brass and canbe firmly attached to the plate at various locations overits surface. Thermocouples are attached to the platesurface and the tip of one of the fins.Measured temperatures for five pin-fin configurationsare tabulated.Temperature (?C)Numberof Pin FinsFin Tip Plate Base070.2140.667.4239.564.7536.457.4834.252.1(a) Using the experimental observations and neglect-ing the effect of flow interactions between pins,determine the thermal resistance between the plateand the airstream for the five configurations.(b) Develop a model of the platepin fin system andusing appropriate convection correlations, predictthe thermal resistances for the five configurations.Compare your predictions with the observationsand explain any differences.(c) Use your model to predict the thermal resistanceswhen the airstream velocity is doubled.