Question

Air flows through a 10 cm internal diameter tube at the rate of 75 kg/ hr. Measurements indicate that the temperature of air is 325 K while the tube wall temperature is 375 K. The heat transfer rate for one meter length in the range of this point is
Given data: Thermo physical properties of air at 325 K
k = 0.02792 W/mK
μ = 1.967 x 10${}^{-5}$ kg/ms
Pr = 0.713
Nu = 3.66 for laminar
Nu = 0.023 Re${}^{0.8}$ Pr${}^{0.4}$for turbulent

• A. 194.72 W
• B. 177.34 W
• C. 643.08 W
• D. 372.43 W

Answer 1

The correct option is B 177.34 W

Given; $\mu =1.967\times {10}^{-5}kg/ms,k=0.02792W/mK,Pr=0.713,m=75kg/hr$

Reynolds number, Re $=\frac{\rho Vd}{\mu }=\frac{md}{A\mu }$

$\Rightarrow Re=\frac{4m}{\pi d\mu }=\frac{4\left[\frac{75}{3600}\right]}{\pi \times 0.1\times 1.967\times {10}^{-5}}$

$\Rightarrow Re=13485$

$\therefore$ Flow is turbulent
$Nu=0.023\left[13485{]}^{0.8}\right(0.713{)}^{0.4}=40.44$

Now,
$h=Nu\times \frac{k}{d}$

$=40.44\times \frac{0.02792}{0.1}$

$\Rightarrow h=11.290W/m^{2}K$

$\Rightarrow Q=hA\Delta T=11.290\times (\pi \times 0.1\times 1)\times (375-325)$

$Q=177.343W$