F: Pump capacity [m³/h], Value of 4m³/h is used for this analysis.

d: Diameter of the feed water inlet pipe [m]

v: Coeficient of kinematic viscosity

C_f: Friction coefficient of pipe

τ_w: Shear stress

μ_m: Average flow velocity [m/s]

μ_c: Flow velocity at axis of pipe [m/s]

t_m: Mixed mean temperature [｡? or [K]

t_c: Temperature at axis of pipe [｡? or [K]

ρ: Density [kg/m³]

f: Coefficient f = 0.9808

N_u: Nusselt number N_u = αd/λ

P_*: Prandtl number P_r = a/v

R_e: Reynolds number R_e = wl/v

S_t: Stanton number S_t = N_u/R_eP_r

λ: Thermal conductivity of feed water [W/mK]

a: Thermal diffusivity [m²/s]

ε_M: Eddy diffusivity for momentum

ε_H: Eddy diffusivity for heat

c_p: Specific heat of constant pressure

　

(2) Temperature distribution

Temperature distribution is calculated on the basis of steady heat conduction. The thermal stress distribution on large thickness pipe is calculated using this temperature distribution. In a case of steady heat conduction, temperature distribution in large thickness pipe can be given by

T_i: Temperature at the Inner edge of pipe [｡?

T₀: Temperature at outer edge of pipe (corresponding to saturated temperature of the boiler water) [｡?

r₁: Inner radius of pipe [m]

r₂: Outer radius of pipe [m]

r: A certain radius [m] [3]

It is assumed that there are no temperature differences by contact heat resistance on the connected boundary area between feed water inlet pipe and boiler drum. So temperature at the inner edge of the feed water Inlet pipe is calculated by the heat transfer formula (heat transfer between feed water and the inner edge of the feed water inlet pipe) [2];

Q = απd₁l/(θ_i - T_i) (4)

and the heat conduction formula(heat conduction between the inner edge of the pipe and the outer edge which is corresponding to the location in boiler drum whose temperature is near by the saturated boiler water temperature);

d₁: Inner diameter of pipe [m]

d₂: Outer diameter of pipe [ml

θ₁: Temperature of feed water [℃]

λ: Thermal conductivity of feed water pipe [W/mK]

And besides T₀ is saturated temperature of design pressure

　

(3) Evaluate of thermal stress

Circumferential stress and radial stress which are occurred by temperature distribution in the pipe, when feed water comes into boiler drum through feed water inlet pipe, are calculated by following formulas.

　

(4) Length between the Inner edge and a point of saturated boiler water temperature

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