The metallic foam of Problem 7.113 is brazed to the surface of a silicon chip of width W = 25 mm on a side. The foam heat sink is L = 10 mm tall. Air at T_i  27°C, V = 5 m/s impinges on the foam heat sink while the chip surface is maintained at 70°C. Determine the heat transfer rate from the chip. To calculate a conservative estimate of the heat transfer rate, neglect convection and radiation from the top and sides of the heat sink.

Data From Problem 7.113

Packed beds of spherical particles can be sintered at high  temperature to form permeable, rigid foams. A foam sheet of thickness t = 10mm is comprised of sintered  bronze spheres, each of diameter D = 0.6 mm. The metal  foam has a porosity of ε = 0.25, and the foam sheet fills  the cross section of an L = 40mm W = 40mm wind  tunnel. The upper and lower surfaces of the foam are at  temperatures T_s = 80°C, and the two other foam edges  (the front edge shown in the schematic and the corresponding  back edge) are insulated. Air flows in the wind  tunnel at an upstream temperature and velocity of  T_i = 20°C and V = 10 m/s, respectively. 

(a) Assuming the foam is at a uniform temperature T_s, estimate the convection heat transfer rate to the air. Do you expect the actual heat transfer rate to be equal to, less than, or greater than your estimated value?
(b) Assuming one-dimensional conduction in the x-direction, use an extended surface analysis to estimate the heat transfer rate to the air. To do so, show that the effective perimeter associated with Equation 3.70 is P_eff = A_p,t /L. Determine the effective thermal conductivity of the foam k_eff by using Equation 3.25. Do you expect the actual heat transfer rate to be equal to, less than, or greater than your estimated value?

Transcribed Image Text:

V, T₁ Ts T₂ Unsintered spheres Sintered spheres