PSI - Issue 13

A.M. Polyanskiy et al. / Procedia Structural Integrity 13 (2018) 1408–1413 Author name / Structural Integrity Procedia 00 (2018) 000–000

1411

4

where Gr is the Grassho ff number, Pr is the Prandtl number, λ is the coe ffi cient of thermal conductivity, d is the characteristic channel size. The characteristic size of the channel can be obtained the following way (3):

S P

(3)

d =

,

where S is the channel cross-sectional area, P is the perimeter of the channel cross-section. The Grassho ff number and the Prandtl number can be found by applying Eqns. (4, 5), respectively:

ν 2

T − T gs T gs

gd 3

Gr =

(4)

,

α C λ

Pr =

(5)

,

where g is the acceleration of gravity, ν is the coe ffi cient of kinematic medium viscosity, T − T gs is the temperature di ff erence between the heated or cooled object and the medium, T gs is the cooling gas temperature, α is the coe ffi cient of dynamic gas viscosity, C is the gas heat capacity. By applying all the coe ffi cients characterizing the flow and given by Eqns. (3) –(5), we can rewrite Eqn. (2) to calculate the heat transfer coe ffi cient in the following way:

1 T gs

λ d

0 . 25

gd 3 ν 2

T − T gs

= ˜ k gs T − T gs

α C λ

0 . 25

0 . 25

(6)

K = 0 . 5

.

To determine the temperature di ff erence between a helix, blown by a flow of pure argon, and a helix blown by a flow of a mixture of argon with hydrogen, we take into account that q IAr = q I Σ H 2 = q I , T Ar = T Σ H 2 = T gs . Then, the electric power dissipated by the gas in both sensitive platinum elements can be found by applying Eqn. (7) for ˜ k gs = ˜ k Ar , T Pt = T PtAr and ˜ k gs = ˜ k Σ H 2 , T Pt = T Pt Σ H 2 : q I = ˜ k gs S Pt T Pt − T gs 1 . 25 . (7) The equation for the temperature di ff erence between the helices of the thermal conductivity reads:

= ( T PtAr − T Ar )    1 −

2    .

1 . 25 ˜ k Ar ˜ k Σ H

1 . 25 q I

1 . 25

q I

∆ T = T PtAr − T Pt Σ H 2 =

(8)

˜ k Ar S Pt −

˜ k Σ H

2 S Pt

Let us use the following values of the parameters under normal conditions (according to specific measuring in struments): volumetric flow rate W Ar = 0 . 26 dm 3 min , analysis time t = 5 min. Then the maximum volume concentration of hydrogen in the carrier gas is Q VH 2 = 51 . 3 vppm for its concentration in the metal equal to 0.5 ppm and for the sample mass m sp = 5 . We can use a simple superposition for the coe ffi cients due to the smallness of the hydrogen concentration.

2 + 1 − Q VH 2

˜ k Σ H

˜ k Ar .

˜ k H

2 = Q VH 2

(9)

The operating temperature of the platinum element is a closed parameter. Obviously, the higher the temperature, the greater the sensitivity of the cell to the hydrogen concentration. Let us take the limiting values 20 ◦ C and 600 ◦ C for the temperature of the gas medium; 700 ◦ C and melting point 1770 ◦ C for the operating temperature of the platinum sensing element. In this case the maximum temperature di ff erence according to Eqn. (8) is ∆ T = 0 . 19 ◦ C.