Physics Division

Introduction

Reference Material

Policy and Requirements

Methods of Compliance

Operational Requirements

Appendices

 1. Properties of Liquids 2. Relief Valve Sizing 2a. 2b. Relief Vent Pressure Drops 3. Oxygen Deficiency Hazards

## APPENDIX 2a:  CONVECTIVE HEAT TRANSFER

The convective heat transfer coefficient, hc, 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, Cp = 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 = hc ∆T Watts/cm2

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

I.       Nitrogen at 293 K and 1 ATM

kf = 2.5x10-4 w/cm K, ρf = 1.16x10-3, Cp = 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 (Tf = 185 K, ∆T = 216 K)

kf = 1.8x10-4 W/cm K, ρf  =  1.84x10-3, μf = 121x10-6  and

= 4.89x10-4  Watt/cm2 K

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

kf = 9.9x10-4 W/cm K, ρf = 3.17x10-4, Cp = 5.5 J/gm K, μf = 131x10-6 poise, so that

= 1.13 x10-3  Watt/cm2 K

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

kf = 4.52x10-4 W/cm K, ρf = 1.06x10-3,   μf = 60x10-6 poise, thus

= 1.89x10-3  Watt/cm2 K

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

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

= 1.04x10-3  Watt/cm2 K