APPENDIX 2a:  CONVECTIVE HEAT TRANSFER

The convective heat transfer coefficient, h_c, is given by (from Heat Transmission, W. H. McAdams, McGraw-Hill, NY (1942) pp 242-245):

or

             Watt/cm² K                                                                                                     (1)

where k = thermal conductivity, ρ = density, C_p = specific heat, μ = viscosity, g = gravitational acceleration.  Note that CGS units are used.

The subscript f means the quantities are to be evaluated at the “gas film” temperature, the arithmetic means of the temperature at the surface of the solid, and the temperature of the bulk of the gas.

The quantity L is the characteristic dimension of the system: e.g. diameter of a cylinder, spacing of parallel plates, or the edge length of a plane square.  Equation (1) is valid so long as

           > 10³
 

The actual heat flow Q is given by:

Q = h_c ∆T Watts/cm²

We evaluate expression (1) for several gases and conditions (using CGS units):

I.       Nitrogen at 293 K and 1 ATM

         k_f = 2.5x10^-4 w/cm K, ρf = 1.16x10^-3, C_p = 1.04 J/gm K, and μf = 17.4x10^-6 poise, so that

             = 4.04x10^-4 Watt/cm² K

II.      Nitrogen from 77 K to 293 K (T_f = 185 K, ∆T = 216 K)

          k_f = 1.8x10^-4 W/cm K, ρ_f  =  1.84x10^-3, μ_f = 121x10^-6  and

             = 4.89x10^-4  Watt/cm² K

III.     Helium from 15 K to 293 K (T_f = 154, ∆T = 278)

          k_f = 9.9x10^-4 W/cm K, ρ_f = 3.17x10^-4, C_p = 5.5 J/gm K, μ_f = 131x10^-6 poise, so that

              = 1.13 x10^-3  Watt/cm² K

IV.    Helium from 15 K to 77 K (T_f = 46 K, ∆T = 26 K)

         k_f = 4.52x10^-4 W/cm K, ρ_f = 1.06x10^-3,   μ_f = 60x10^-6 poise, thus

             = 1.89x10^-3  Watt/cm² K

V.      Helium from 77 K to 293 K (T_f = 185, ∆T = 216)

k_f = 1.11x10^-3 W/cm K, ρf = 2.64x10^-4, C_p = 5.5 J/gm K, μf = 148x10^-6 poise

             = 1.04x10^-3  Watt/cm² K