Simplified relations for natural convection in air are of the

Simplified relations for natural convection in air are of the form h = α(ΔT/L)β

where α, β are constants; L is a significant length, in ft; ΔT is Ts, – T, in oF; and h is the convective heat-transfer coefficient, Btulh ft2 °F. Determine the values for α and β for the plane vertical wall, using the equation from Problem 19.14.

Data From Problem 19.14

An engineered tissue system consists of a flat plate of cell mass immobilized on a scaffold measuring 5 cm in length, and is 0.5 cm thick. The bottom face of the scaffold is exposed to water and organic nutrients. The top face is exposed to flowing O2 gas to provide Ofor aerobic respiration. At present the specific oxygen consumption of the tissue mass is 0.5 mmol O2/cm3cells-hr, and from respiration energetics, the energy released by respiration is 468 J/rnmol O2 consumed. We are interested in using the flowing O2 gas at 1 atm to control the temperature at the surface of the tissue scaffold. The properties of O2 gas at 300 K are ρ = 1.3 kg/m3, Cp = 920 J/kg · K, µ = 2.06 × 10-5 kg/m sec, and k = 0.027 W/m K. We are interested in determining the O2 flow rate necessary to keep the surface temperature within 10°C of the flowing gas temper ature (i.e., surface temperature below 310 K or 37°C).


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