Answer to Question #261305 in Mechanical Engineering for harry

Question

Air at a pressure of 101.3 k Pa and 288.8 K enters inside a tube having an inside diameter of 12.7 mm and a length of 1.52 m with a velocity of 24.4 m/s. Condensing steam on the outside of the tube maintains the inside wall temperature at 372.1 K . Calculate the convection coefficient of the air. ( Note: This solution is trial and error. First, assume an outlet temperature of the air. )

Answer 1

Solution;

Given;

Air pressure;$P_a=101.3kPa$

Air temperature,$T_a=288.8K$

Inside diameter,$D_i=12.7mm$

T ube length,$L=1.52m$

Air velocity,$v=24.4m/s$

Surface temperature,$T_s=372.1K$

Now;

$A_s=πDL=π×12.7×10^{-3}×1.52=60.65×10^{-3}m^2$

$A_c=\frac{π}{4}d^2=\frac{π}{4}×(12.7×10^{-3})^2=126.68×10^{-6}m^2$

Assume that temperature at outlet in great than at inlet.

Take $T_0=300K >T_a$

According to temperature distribution;

$\frac{T_s-T_o}{T_s-T_a}=e^{\frac{-hA_s}{\delta A_c vc_p}}$

In which;

$\delta_{air}=1.4kg/m^3$

$C_p=1006J/kgK$

By direct substitution;

$\frac{372.1-300}{372.1-288.8}=e^{\frac{-h×60.60×10^{-3}}{1.14×24.4×126.68×10^{-6}×1006}}$

Hence;

$h=8.88W/m^2K$