Question

Liquid ammonia flows in a duct of a section of an equilateral triangle of 1 cm side. The average bulk temperature is 20°C and the duct wall is at a uniform temperature of 50°C. The heat transfer per unit length (in W/m) is __________.
$[Take,Nusseltnumber{N}_u=2.47,k=0.521W/mK]$

• A. 250
• B. 215
• C. 200
• D. 150

Answer 1

The correct option is C 200

$a=1cm\left(side\right),T_{avg}=20{}^{\circ }C,$

$T_s=50{}^{\circ }C,L=1m$

Cross-sectional area,

$A_C=\frac{\sqrt{3}}{4}\times a^2=\frac{\sqrt{3}}{4}\times {\left(0.01\right)}^2$

$A_C=4.33\times {10}^{-5}$

Perimeter, P = 3a = 0.03

$D_h=\frac{4\times A_C}{P}$

$D_h=5.7733\times {10}^{-3}$

$Nu=\frac{h{D}_h}{k}$

$2.47=\frac{h\times 5.7733\times {10}^{-3}}{0.521}$

$\Rightarrow h=222.898$

$Q=hPL(T_s-T_{avg})$

$\frac{Q}{L}=222.898\times 0.03\times (50-20)$

$\frac{Q}{L}=200.609W/m$