Question

Two large parallel horizontal metal plates are separated by a 2.5 cm air gap, with the air at an average temperature of 100°C. How much hotter may the lower plate be (than the upper plate) without causing the onset of free convection in the gap? How much may this temperature difference be increased if a very thin metal sheet is placed midway between the two plates?

Answer 1

Air properties at 100°C (373K) & 1 atm

Viscosity = 2.173 x 10^-4 g/cm-s

Thermal expansion = 1/T = 1/373 = 0.002680 K-1

Specific heat capacity Cp = 1.015 J/g-K

Thermal conductivity k = 31.40 x 10^-5 W/cm-K

Now calculate the Prandtl number

density of air = PM/RT

= (1 atm x 29 g/mol)/(0.0821 L-atm/mol-K x 373K)

= 0.9461 g/L = 0.0009461 g/cm3

For the stability of air at given state,

Rayleigh number < 1708

GrPr < 1708

the temperature difference

if a very thin metal sheet is placed midway between the two plates

Put h = 0.5 h

Calculate the temperature difference