Question

In order to reduce heat loss, a steam line with a tube diameter of 1.0 cm is insulated with a material having thermal conductivity of 0.108 W/mK. Heat is dissipated from the outer surface of the insulating material by natural convection with a heat transfer coefficient of 12 $W/m^{2}K$ into the ambient at a constant temperature. The heat loss becomes maximum when the critical diameter is

• A. 18 mm
• B. 4 mm
• C. 2 mm
• D. 9 mm

Answer 1

The correct option is A 18 mm


$d_1=1cm$

$r_1=0.5cm=5mm$

$h_o$ = 12 $W/m^{2}K$

($k{)}_{insu}$ = 0.108 W/mK

For maximum heat transfer,

$\text{Critical radius =}{r}_c=r_2=\frac{k_{insu}}{h_0}=\frac{0.108}{12}=9\times {10}^{-3}m$

$r_2=9mm$

Critical diameter = 2 × 9 = 18 mm