1. A proposal of ion and aerosol vertical gradient measurement (as an example of application of the heat transfer equations) H. Tammet Pühajärve 2008

4. Measuring of vertical profiles by means of several simultaneously working instruments is expensive and requires extra fine calibration of instruments.

5. Long tube 2 Short tube 4 Long tube 1 Long tube 3 Instrument Inlet switch Tower

6. How to estimate the inlet losses?

7. Incropera, F.P. and Dewitt, D.P.: Fundamentals of Heat and Mass Transfer, Fifth Edition, Wiley, New York, 2002), see pages 355 ‑ 357, 470, and 491 ‑ 492. The mass transfer equations are derived from the heat transfer equations replacing the Nusselt number with the Sherwood number and the Prandtl number with the Schmidt number.

8. p – air pressure, Pa T – absolute temperature, K Φ – air flow rate through the tube, m 3 s –1 d – internal diameter of the tube, m L – length of the tube, m Z – electric mobility of ions or particles, m 2 V –1 s –1 Diffusion coefficient of ions or particles

9. Air density Air kinematic viscosity Average linear speed of the air in the tube Dynamic pressure Reynolds number. Average time of the passage

10. Moody friction coefficient, Petukhov approximation valid if 3000 < Re < 5000000 Pressure drop along the long tube Schmidt number Sc = ν / D Sherwood number, Gnielinski approximation valid if 3000 < Re < 5000000 and 0.5 < Sc < 2000

11. Linear deposition velocity on the internal wall of the tube n – concentration of particles N – flux of particles through a section of the long tube N = nΦ N o – flux through the inlet of the long tube Loss of particles in a short section of the tube (length dL) dN = –(πd×dL)×h×n = –πd×dL×h×N / Φ Relative loss in a short section Relative pass.

12. The inlet parameters were p, T, Φ, d, L, Z The outlet parameters are Re, Sc, t, p d, Δp, N/N o : Relative loss in a long tube:. Sorry, the explicit equations derived according to the algorithm above are awkward. An explicit equation can be derived using simplified approximation by Colburn However, the Gnielinski approximation is strongly preferred for quantitative calculations.

13. p = 1000 mb, T = 17 C l/s m mm Z Re Sc t pd dp pass% 10 8 50 3.162 17110 1.9 1.6 15.6 75.1 20.0 10 8 50 1.000 17110 6.0 1.6 15.6 75.1 44.3 10 8 50 0.316 17110 18.8 1.6 15.6 75.1 67.4 10 8 50 0.100 17110 59.6 1.6 15.6 75.1 82.9 10 8 150 3.162 5703 1.9 14.1 0.2 0.4 54.3 10 8 150 1.000 5703 6.0 14.1 0.2 0.4 74.6 10 8 150 0.316 5703 18.8 14.1 0.2 0.4 87.1 10 8 150 0.100 5703 59.6 14.1 0.2 0.4 93.7 20 8 50 3.162 34221 1.9 0.8 62.4 252.1 24.0 20 8 50 1.000 34221 6.0 0.8 62.4 252.1 47.5 20 8 50 0.316 34221 18.8 0.8 62.4 252.1 69.3 20 8 50 0.100 34221 59.6 0.8 62.4 252.1 83.9 20 8 150 3.162 11407 1.9 7.1 0.8 1.4 56.6 20 8 150 1.000 11407 6.0 7.1 0.8 1.4 75.3 20 8 150 0.316 11407 18.8 7.1 0.8 1.4 87.3 20 8 150 0.100 11407 59.6 7.1 0.8 1.4 93.8

14. Conclusion 1: The turbulent adsorption of ions and nanometer particles in long inlet tubes can be easily and exactly estimated when using the heat transfer equations

15. Conclusion 2: The turbulent adsorption is low enough to make possible the gradient measurements using single instrument and commutative inlet tubes

16. Thank you !