Question

A fluid of density $978{\text{kg/m}}^3$ is heated in pipe, enters a 20 mm diameter tube with a velocity of 2 m/s at $10{}^{\circ }C$. Convective heat transfer coefficient at outside surface of tube is equal to $10{\text{kW/m}}^2$. The length of tube is 5 meter and properties of water at mean temperature is approximated as following,
$k=0.332\text{WmK}$, $\mu =4\times {10}^{-4}\text{kg/m-s}$, $Pr=2.54$
the value of overall heat transfer coefficient is

• A. $4.73{\text{kW/m}}^2\text{K}$
• B. $8.73{\text{kW/m}}^2\text{K}$
• C. $3.53{\text{kW/m}}^2\text{K}$
• D. $1.73{\text{kW/m}}^2\text{K}$

Answer 1

The correct option is C $3.53{\text{kW/m}}^2\text{K}$

$D=20\text{mm}$,
$\rho =978{\text{kg/m}}^3$,
$\mu =4\times {10}^{-4}\text{kg/m}$,
$Pr=2.54$

$Re=\frac{\rho VD}{\mu }=\frac{978\times 2\times 0.02}{4\times {10}^{-4}}\Rightarrow Re=97800$

$Re>2300$ flow is turbulent

Using Dittus Boltier equation,

$Nu=0.023\left(Re{)}^{0.8}\right(Pr{)}^{0.4}$

$h_i=328.04\times \frac{0.332}{0.02}=5445.5{\text{W/m}}^2\text{K}$

$\frac{1}{U}=\frac{1}{h_i}+\frac{1}{h_0}=\frac{1}{5445.5}+\frac{1}{10000}$

$U=3525.6{\text{W/m}}^2\text{K}$