Question

An electrical heater 150 mm long and 5mm in diameter is inserted into a hole drilled normal to the surface of a large block of material having a thermal conductivity of 10W/mK. The temperature of the electrical heater is 70 oC and the temperature of block surface is 40 oC. Estimate the power dissipation of the electrical heater. (in W)

Answer 1

Explanation:

From the table of conduction shape factor and dimensionless conduction rates for selected systems, for vertical cylinder in a semi-infinite medium

$S=& \frac{2 \pi L}{\ln \left(\frac{4 L}{D}\right)}$

$S=& \frac{2 \pi L}{\ln \left(\frac{4 L}{D}\right)}$

$\frac{2 \pi \times 0.1}{\ln \left(\frac{4 \times 0.1}{0.005}\right)}$

$=0.1433 \mathrm{m}$