Question

A wire 1.5 mm in diameter and 150 mm long is submerged in water at

atmospheric pressure. An electric current is passed through the wire and is increased until the

water boils at 100°C. Under the condition if convective heat transfer coefficient is 4500 W/m2°C

find how much electric power must be supplied to the wire to maintain the wire surface at 120°C ?

Answer 1

Given,

Diameter of wire $(d)=1.5mm$

Length of wire $(l)= 150mm$

Boiling temperature of water $(T_1)=100^o C$

Heat transfer coefficient $(h)=4500 W/m^2°C$

Highest temperature $(T_2)=120^oC$

Surface area of wire $(A)=\pi ld$

Supplied electric power = Total conviction loss (Q)

$\Rightarrow Q=hA(T_2-T_1)$

$\Rightarrow Q=4500\times \pi \times 1.5\times 10^{-3}\times 150\times 10^{-3}(120-100)$

$\Rightarrow Q=63.6W$